Answers
The vector equations of L₂ when expressed as Cartesian equations are
y = 0
x = (z ± √(z² - 4(z-2))) / 2
z = [(4 - ((x-1)/(-z))²) ± √((4 - ((x-1)/(-z))²)² + 64)] / 8
What is the vector equation of the line L₂To find the vector equation of the line L₂, we need to find a vector that is perpendicular to L₁ and passes through the point (1,0,2). Let's start by finding the vector equation of L₁.
Let P(x,y,z) be a point on L₁. Then the vector equation of L₁ is given by:
r₁ = P + t * d₁
where d₁ is the direction vector of L₁ and t is a scalar parameter.
Since L₂ is perpendicular to L₁, its direction vector must be perpendicular to d₁. Thus, we can find a vector that is perpendicular to d₁ by taking the cross product of d₁ with any non-zero vector that is not parallel to d₁. Let's choose the vector (0,1,0):
v = d₁ x (0,1,0) = (-z,0,x)
Note that we can choose any non-zero vector that is not parallel to d₁, and we will still get a vector that is perpendicular to d₁.
Now we have a point on L₂ (1,0,2) and a direction vector (v), so we can write the vector equation of L₂:
r₂ = (1,0,2) + s * v
where s is a scalar parameter.
To express the Cartesian equations of L₂, we can write the vector equation as a set of three parametric equations:
x = 1 - sz
y = 0
z = 2 + sx
We can eliminate the parameter s by solving for it in two of the equations and substituting into the third equation:
s = (x - 1) / (-z)
s = (z - 2) / x
Setting these two expressions equal to each other and solving for x, we get:
[tex]x^2 - zx + z - 2 = 0[/tex]
This is a quadratic equation in x, so we can solve for x using the quadratic formula:
[tex]x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2[/tex]
Substituting this expression for x into one of the parametric equations, we get:
y = 0
And substituting the expressions for x and s into the other parametric equation, we get:
[tex]z = 2 + [(z \± \sqrt{(z^2 - 4(z-2)})) / 2] * [(1 - sz) / (-z)][/tex]
Simplifying this equation, we get:
[tex]4z^2 - (4 - s^2)z - 4 = 0[/tex]
Again, this is a quadratic equation in z, so we can solve for z using the quadratic formula:
[tex]z = [(4 - s^2) \± \sqrt((4 - s^2)^2 + 64)] / 8[/tex]
z = [(4 - s²) ± √((4 - s²)² + 64)] / 8
Finally, we can substitute these expressions for x and z into one of the parametric equations to get:
[tex]y = 0\\x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2\\z = [(4 - ((x-1)/(-z))^2) \± \sqrt{((4 - ((x-1)/(-z))^2)^2} + 64)] / 8[/tex]
These are the Cartesian equations of L₂.
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Related Questions
Mastery: 40% Correct answers: 29/72
5351 5799
A store sees 120 customers in 8 hours. What is the unit rate (in customers per hour)?
12 customers per 20 customers per 16 customers per
hour
hour
hour
15 customers per
hour
BAR Mar 10 303 US
Answers
Therefore , the solution of the given problem of percentage comes out to be 15 customers per hour make up the unit cost. 15 clients per hour, to be exact.
What precisely is a percentage?A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.
Here,
We must divide the overall number of customers by the number of hours in order to determine the unit rate (in customers per hour).
There are 120 total clients.
There are 8 hours in all.
Unit rate is equal to the sum of all clients times the number of hours.
=> Unit rate: 120 / 8
=> Rate per unit: 15
Consequently, 15 customers per hour make up the unit cost. 15 clients per hour, to be exact.
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What is the equation of the linear relationship that has a slope of 200 and a y-intercept of 100?
A. y = 100x + 200
B. y = 200x + 100
C. y = −200x + 100
D. y = −100x + 200
Answers
The solution is B. [tex]y = 200x + 100[/tex] is a linear equation with a slope-intercept form.
How do linear and nonlinear differ?When a function is displayed in a graph, a linear function makes a straight line, but a nonlinear function, which is bent in some way, does not. Whereas the slopes of a non - linear function is changing constantly, the slopes of a linear model remains constant.
Why is a function linear?The graph of a linear function is a direct line. One regression coefficient and one predictor variables make up a linear function. The variables that are both independent and dependent are X and Y, respectively. The y interception, often known as the constant term a.
The slope-intercept form of a linear equation is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept. Using the given values, we have:
slope [tex]= 200[/tex]
[tex]y-[/tex]intercept [tex]= 100[/tex]
So, the equation of the linear relationship is:
[tex]y = 200x + 100[/tex]
Therefore, the answer is B. [tex]y = 200x + 100[/tex].
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The radius of a cylindrical water tank is 4 ft, and its height is 6 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
0
4 ft
6 ft
Answers
In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.
what is cylinder?A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:
[tex]V = \pir^2h[/tex]
Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.
[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]
Therefore, the volume of the tank is approximately 301 cubic feet.
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2. Zara stores in the United States stocks a particular type of designer denim jeans in the United States. It stores 500 pairs of jeans each month from its two suppliers. The Hong Kong supplier charges Zara $11 per pair of jeans, and the Colombian supplier charges $16 per pair (and then Zara marks them up almost 1,000%). Although the jeans from Hong Kong are less expensive, they also have more defects than those from Colombia. Based on past data, Zara estimates that 7% of the Hong Kong jeans will be defective compared to only 2% from Colombia and Zara does not want to import any more than 5% defective items. However, Zara does not want to rely on a single supplier, so it wants to order at least 20% from each supplier every month. a. Formulate a linear programming model for this problem. b. Solve the linear programming model graphically. Use either iso-line or corner point method. How many of each should Zara buy? c. How much will Zara pay for them? d. If the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to %5, what would be the effect on the solution. Solve c in a separate sheet. First copy the sheet you solved a, b and c. Then change the necessary line and re-solve.
Answers
Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia for a total cost of $6,000.
See below for other solutions
Formulation of the linear programming model:Let x be the number of pairs of jeans ordered from Hong Kong and y be the number of pairs ordered from Colombia.
Objective function:
Maximize profit, C(x, y) = 11x + 16y
Subject to the following constraints:
The total number of jeans ordered cannot exceed 500: x + y ≤ 500Zara wants to order at least 20% from each supplier: x ≥ 0.2(x+y) and y ≥ 0.2(x+y)Zara does not want to import more than 5% defective items: 0.07x + 0.02y ≤ 0.05(x+y)Non-negativity constraint: x, y > 0Graphical solution using the corner point method:See attachment for the graph, where we have the following corner points
(x, y) = (100, 400), (300, 200), (400, 100)
By substitution, we have
C(100, 400) = 11(100) + 16(400) = 7500
C(300, 200) = 11(300) + 16(200) = 6500
C(400, 100) = 11(400) + 16(100) = 6000
The minimum cost above is $6000
So, Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia.
The amount paid for themThe amount paid for them is $6,000
Reducing the percentage of defective pairsIf the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, we would need to update the constraint accordingly:
0.05x + 0.02y ≤ 0.05(x+y)
The new optimal solution would be to order 425 pairs of jeans from the Hong Kong supplier and 75 pairs of jeans from the Colombian supplier, for a total cost of $5875
i.e. C(425, 75) = 11(425) + 16(75) = 5875
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Find the differance quotient of y=4x³-5x
Answers
Answer:
12x² + 12xh + 4h² - 5
Step-by-step explanation:
f(x + h) - f(x) / h
= [4(x + h)³ - 5(x + h)] - [4x³ - 5x] / h
= [4x³ + 12x²h + 12xh² + 4h³ - 5x - 5h] - [4x³ - 5x] / h
= 4x³ + 12x²h + 12xh² + 4h³ - 5x - 5h - 4x³ + 5x / h
= 12x²h + 12xh² + 4h³ - 5h / h
= 12x² + 12xh + 4h² - 5
Hope this helps :)
A coach spent $975.84 on new uniforms for his team. If he bought uniforms for 16 players, how much did each uniform cost? Use r to represent the price of each uniform.
Answers
Answer: for each of the players' uniform it would be $60.99
Step-by-step explanation:
so here would be the equation written out.
975.84=16x
so, to get x by itself you would need to divide by 16.
x=60.99
Gideon took out an R150 000 loan this morning, to buy a house. The interest rate on a mortgage is 7,35%. The loan is to be repaid in equal monthly payments over 20 years. The first payment is due one month from today. How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)
Answers
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for calculating the fixed monthly payment on a mortgage:
P = (r * PV) / (1 - (1 + r)^(-n))
where:
P = fixed monthly payment
r = monthly interest rate (annual interest rate divided by 12)
PV = present value of the loan (loan amount)
n = total number of payments (number of years multiplied by 12)
Using the given values:
r = 0.0735 / 12 = 0.006125
PV = R150,000
n = 20 x 12 = 240
Then we can calculate the monthly payment:
P = (0.006125 * 150000) / (1 - (1 + 0.006125)^(-240)) = R1,181.91
This means that Gideon will have to pay R1,181.91 every month for 20 years to repay his loan.
To determine how much of the second payment applies to the principal balance, we need to calculate the interest and principal amounts of the first payment.
For the first payment, the interest can be calculated as:
interest1 = r * PV = 0.006125 * 150000 = R918.75
This means that the first payment consists of R918.75 in interest and the rest, R1,181.91 - R918.75 = R263.16 is principal.
To find out how much of the second payment applies to the principal balance, we need to subtract the interest and add the calculated principal amount from the first payment to the amount of the second payment:
principal2 = (P - interest1) + principal1 = (1181.91 - 918.75) + 263.16 = R525.32
Therefore, R525.32 of the second payment applies to the principal balance.
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
Answers
The Correct answer is D) Most students read more often than they draw.as the median of the "read" plot is lower than the median of the "draw" plot.
Based on the box plots, we can see that:
The median for the "read" data is around 8 days per month, and the interquartile range (IQR) is between 4 and 12 days.
The median for the "draw" data is around 12 days per month, and the IQR is between 8 and 16 days.
So, we can conclude that:
A) Most students read less than 12 days a month. This is true, since the median for the "read" data is below 12 days per month, and the box plot shows that most of the data is concentrated in the lower half of the range.
B) Most students draw at least 12 days a month. This is not true, since the median for the "draw" data is around 12 days per month, and the box plot shows that there is a considerable amount of data below that median.
C) Most students draw more often than they read. This is not true, since the median for the "read" data is lower than the median for the "draw" data.
D) Most students read more often than they draw. This is true, since the median for the "read" data is lower than the median for the "draw" data, and the box plot shows that most of the "read" data is concentrated in the lower half of the range, while most of the "draw" data is concentrated in the upper half of the range.
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
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Which two statements best describe Michael’s height while on the two roller coasters?
Answers
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
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Find the Perimeter of the given figure. Remember that this is a composite figure. Be sure to show your work or explain how you found your answer in question
Answers
Answer:
Start off with the 20ft sides
20x2 =40ft
40ft + 8ft = 48ft
Now we need to find the perimeter of the half circle.
Since we know the diameter of the half circle is 8ft, we can use the following formula: Diameter x Pi = Circumference
Plug in:
8ft x 3.14159 = 25.132ft
25.132 /2 gives us the perimeter of the half circle
25.132 / 2 = 12.566
Rounded = 12.57 ft
48 ft + 12.57 ft = 60.57 feet perimeter.
The perimeter of the given solution is 76.56 feet.
We need to find the perimeter of the figure by splitting the figure into a rectangle and a semi-circle. The radius for the semi-circle is found by dividing the diameter by 2, Radius = 8 ÷ 2 = 4.
Therefore, the formula for finding the Perimeter of the given rectangle is
P = 2( l+b )
P = 2( 20 + 8)
P = 56 feet.
now, the formula for the circumference of a semi-circle is
C = [tex]\pi[/tex]r + 2r
C = 3.14( 4) + 2 (4)
C = 20.56 feet.
Therefore, the perimeter of the given figure is
The perimeter of the rectangle + circumference of the Semi-circle
= 56 + 20.56
= 76.56 feet
Therefore, the perimeter of the given solution is 76.56 feet.
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A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nall
Number
of Nails
67
18
10
Abundance
(%)
[7]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
Med Nail % Abund.
Enter
Answers
According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.
Explain medium?Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.
To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:
Total number of nails = 67 + 18 + 10 = 95
Next, we can calculate the percent abundance of the medium nails using the formula:
Percent abundance = (number of medium nails / total number of nails) x 100%
Using the values from of the table as inputs, we obtain:
Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%
As a result, the sample's average percentage of medium nails is roughly 18.95%.
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6. This is an example of a O reflection O rotation O translation transformation.
Answers
Answer:
translation
Step-by-step explanation:
becuz it can't be rotation as it isn't rotated in any way.
it also cant be reflection as it isnt facing the other way.
so its translation
The list below represents the number of novels written
by each of Amir's 10 favorite authors.
1 3 3 4 5 7 8 10 12 23
What is the interquartile range of the number of novels
written by each of Amir's 10 favorite authors?
Answers
The interquartile range of the number of novels written by each of Amir's 10 favorite authors is 6.
What is the interquartile range ?
In statistics, the interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide the data set into four equal parts, with the interquartile range being the difference between the upper (third) and lower (first) quartiles. The IQR represents the middle 50% of the data, and is used as a measure of spread or dispersion in a data set, particularly when the data set contains outliers.
To find the interquartile range (IQR), we need to first find the first quartile (Q1) and the third quartile (Q3).
To find Q1:
Arrange the data in order from smallest to largest: 1 3 3 4 5 7 8 10 12 23
Find the median of the lower half of the data (the first five numbers): (3+3)/2 = 3
This is the first quartile (Q1)
To find Q3:
Arrange the data in order from smallest to largest: 1 3 3 4 5 7 8 10 12 23
Find the median of the upper half of the data (the last five numbers): (8+10)/2 = 9
This is the third quartile (Q3)
Now we can calculate the IQR:
IQR = Q3 - Q1 = 9 - 3 = 6
Therefore, the interquartile range of the number of novels written by each of Amir's 10 favorite authors is 6.
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A charity organization has to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets they were still at a net loss of $800 (due to the production costs). They sold each tickets for $70.
Answers
the organization needs to sell at least 22 tickets to break even.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let C be the total production cost and n be the number of tickets sold.
From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:
10(70) - C = -800
Simplifying, we get:
C = 1500
This means that the total production cost was $1500.
The revenue from selling n tickets at $70 per ticket is given by:
R = 70n
Substituting the values of R and C, we get:
70n = 1500
Solving for n, we get:
n = 1500/70 = 21.43
Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.
Therefore, the organization needs to sell at least 22 tickets to break even.
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The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
Answers
SA = 2r^2 + 2rh
1632 = 2(12^2) + 2(12)(h)
1632 = 288 + 24h
24h = 1344
h = 56 cm
the height of the cylinder is 56 cm.
A dilation centered at the origin maps the point (4,6) to the point (5/2,15/4). What is the scale factor of the dilation
Answers
We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).
The dilation is given as (4,6) to (5/2,15/4). That is to say:
[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]
We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
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Help with this problem guys
no trolling please i really need it
Answers
Answer:
[tex]\textsf{1.}\quad \sf \overline{AZ} = 28 \; meters[/tex]
[tex]\textsf{2.}\quad \sf \overline{AM} = 28 \; meters[/tex]
[tex]\textsf{3.}\quad b = \sf 4[/tex]
[tex]\textsf{4.}\quad \sf Perimeter = 112\; meters[/tex]
[tex]\textsf{5.}\quad \sf \overline{MX} = 22\; meters[/tex]
[tex]\textsf{6.}\quad \sf \overline{AX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{7.}\quad \sf \overline{EX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{8.}\quad \sf \overline{AE} = 20\sqrt{3}\; meters[/tex]
Step-by-step explanation:
Side lengths and value of bAll sides of a rhombus are the same length. Therefore, for rhombus MAZE:
[tex]\sf \overline{AZ} = \overline{AM} = \overline{ZE} = \overline{EM}[/tex]
Given:
[tex]\overline{\sf AZ} =8b-4[/tex][tex]\overline{\sf AM} =5b+8[/tex]As the sides of a rhombus are the same length, we can equate the expressions for sides AZ and AM, and solve for b:
[tex]\begin{aligned}\overline{\sf AZ}&=\overline{\sf AM}\\8b-4&=5b+8\\8b-4-5b&=5b+8-5b\\3b-4&=8\\3b-4+4&=8+4\\3b&=12\\3b \div 3&=12 \div 3\\b&=4\end{aligned}[/tex]
Therefore, the value of b is 4.
To find the length of AZ and AM, substitute the found value of b into one of the expressions:
[tex]\begin{aligned}\overline{\sf AZ}&=8b-4\\&=8(4)-4\\&=32-4\\&=28\end{aligned}[/tex]
Therefore, as AZ = AM, then AZ = 28 and AM = 28.
[tex]\hrulefill[/tex]
PerimeterAs the sides of a rhombus are equal in length, each side length is 28 meters (as found previously).
The perimeter of rhombus MAZE is the sum of its side lengths. Therefore:
[tex]\begin{aligned}\sf Perimeter\;MAZE&=\sf \overline{AZ} +\overline{AM} +\overline{ZE}+ \overline{EM}\\&=28+28+28+28\\&=112\; \sf meters\end{aligned}[/tex]
Therefore, the perimeter of rhombus MAZE is 112 meters.
[tex]\hrulefill[/tex]
DiagonalsThe point of intersection of the diagonals of rhombus MAZE is point X.
As the diagonals of a rhombus are perpendicular bisectors of each other, then:
[tex]\sf \overline{AX}=\overline{EX}\quad and \quad \overline{AX}+\overline{EX}=\overline{AE}[/tex]
[tex]\sf\overline{MX}=\overline{ZX}\quad and \quad\overline{MX}+\overline{ZX}=\overline{MZ}[/tex]
Given MZ = 44 meters, and MX is half of MZ, then:
[tex]\sf \overline{MX}=\overline{ZX}=22\;meters[/tex]
As the diagonals bisect each other at 90°, m∠MXA= 90°. Therefore, ΔMXA is a right triangle with hypotenuse AM = 28 and leg MX = 22.
As we know the lengths hypotenuse AM and leg MX, we can use Pythagoras Theorem to calculate the length of the other leg, AX:
[tex]\begin{aligned}\sf \overline{AX}^2+\overline{MX}^2&=\sf \overline{AM}^2\\\sf \overline{AX}^2+22^2&=\sf 28^2\\\sf \overline{AX}^2&=\sf 28^2-22^2\\\sf \overline{AX}&=\sqrt{\sf 28^2-22^2}\\\sf \overline{AX}&=\sf 10\sqrt{3}\; meters\end{aligned}[/tex]
As the diagonals bisect each other, AX = EX. Therefore:
[tex]\sf \overline{EX}=\sf 10\sqrt{3}\; meters[/tex]
The length of diagonal AE is the sum of segments AX and EX. Therefore:
[tex]\begin{aligned}\sf \overline{AE}&=\sf \overline{AX}+\overline{EX}\\&=\sf 10\sqrt{3}+10\sqrt{3}\\&=\sf 20\sqrt{3}\; meters\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Note: The attached diagram is drawn to scale.
can you solve this quesiton?
y'=?
Answers
The derivative οf [tex]y = e^{(-5tan(\sqrt{x}))[/tex] is [tex]-5/2x^{(1/2)[/tex] [tex]* sec^2(\sqrt{x}) * e^{(-5tan(\sqrt{x}))}).[/tex]
What is derivative?A functiοn's varied rate οf change with respect tο an independent variable is referred tο as a derivative. When there is a variable quantity and the rate οf change is irregular, the derivative is mοst frequently utilised.
The derivative is used tο assess hοw sensitive a dependent variable is tο an independent variable (independent variable). In mathematics, a quantity's instantaneοus rate οf change with respect tο anοther is referred tο as its derivative. Investigating the fluctuating nature οf an amοunt is beneficial.
[tex]dy/dx = d/dx (e^{(-5tan(\sqrt{x}))}) = e^{(-5tan(\sqrt{x}))} * d/dx (-5tan(\sqrt{x}))[/tex]
Next, we need tο find the derivative οf -5tan(√x) using the chain rule and the prοduct rule:
d/dx (-5tan(√x)) = -5 * d/dx (tan(√x)) = -5 * sec^2(√x) * d/dx (√x)
Tο find the derivative οf √x, we use the pοwer rule:
[tex]d/dx (√x) = 1/2x^{(1/2)[/tex]
Substituting this back intο the derivative οf -5tan(√x), we have:
[tex]d/dx (-5tan(\sqrt{x})) = -5 * sec^2(\sqrt{x}) * (1/2x^{(1/2)})[/tex]
Nοw we can substitute this back intο the derivative οf y:
[tex]dy/dx = e^{(-5tan(\sqrt{x}))} * (-5 * sec^2(\sqrt{x}) * (1/2x^{(1/2)}))[/tex]
Simplifying this, we get:
dy/dx = -5/2x^(1/2) * sec^2(√x) * e^(-5tan(√x))
Therefοre, the derivative of y = [tex]e^{(-5tan(\sqrt{x}))[/tex] is [tex]* sec^2(\sqrt{x}) * e^{(-5tan(\sqrt{x}))}).[/tex]
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Math
Unitary method
#Question
a) If a motor needs 25l pertol to travel 125 km, find the quantity of pertol to travel only 75 km by the same number.
b)If the cost of 32m clothing is Rs. 401.60,find the cost of 45m of the cloth.
c) If the cost of 5 shirt is Rs. 1125,find the cost of 75 such shirts
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Answers
In the unitary method,
a) For 75km we need = 15 l
b) cost of 45m cloth is Rs 564.75
c) cost of 75 shirts is Rs 16875.
What is the unitary method?
The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
a) Here using unitary method , we need to find petrol for 1 km.
To travel 125 km we need 25 l pertrol. Then,
for to travel 1 km = [tex]\frac{25}{125} =\frac{1}{5} = 0.2 l[/tex]
Then to travel 75km we need = 0.2×75 = 15 l.
b) Cost of 32m cloth = Rs. 401.60
Then cost of 1m cloth is = [tex]\frac{401.60}{32}=Rs 12.55[/tex]
Now cost of 45m cloth is = 12.55×45 = Rs 564.75
c) Cost of 5 shirts = Rs 1125
Then cost of 1 shirt = [tex]\frac{1125}{5}=Rs 225[/tex]
Now cost of 75 shirts = [tex]225\times75[/tex] = Rs 16875.
Hence using unitary method the answers are,
a) For 75km we need = 15 l
b) cost of 45m cloth is Rs 564.75
c) cost of 75 shirts is Rs 16875.
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The average salary for a Queens College full professor is $85,900. If the average salaries is normally distributed with
standard deviation of $11,000, find the percentage of professors that make more than $75,000.
Answers
According to the question approximately 83.89% of professors make more than $75,000 calculated by forming the equation.
Explain equation?When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.
This issue can be resolved using the conventional normal distribution. First, we need to standardize the value of $75,000 using the formula:
z = (x - μ) / σ
where x is indeed the value we wish to standardise, is indeed the mean, and is the deviation.
z = (75,000 - 85,900) / 11,000
z = -0.99
Next, we look up the area to the right of z = -0.99 in the standard normal distribution table or by using a calculator. The area to the left of z = -0.99 is 0.1611, so the area to the right of z = -0.99 is:
1 - 0.1611 = 0.8389
Therefore, approximately 83.89% of professors make more than $75,000.
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6. Atwo-story building measures 21 feet from the ground. A scale model shows the building to be 3 inches tall. How many inches would an 84-foot building be in the model?
Answers
Answer:
84 feet is equal to 1008 inches. So, the 84-foot building would be 1008 inches divided by 21 feet, which is 48 inches tall in the model.
Construct the confidence interval for the population variance for the given values. Round your answers to one decimal place.
n=9
, s2=17.3
, and c=0.98
Answers
With 98% confidence, we can say that the population variance is between 7.36 and 71.09.
What is probability?
Probability is a branch of mathematics that deals with the study of chance or randomness in events. It is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To construct the confidence interval for the population variance, we will use the chi-squared distribution.
First, we need to calculate the chi-squared values for the lower and upper bounds of the confidence interval using the following formulas:
χ²_L = (n - 1) * s² / χ²(α/2, n-1)
χ²_U = (n - 1) * s² / χ²(1-α/2, n-1)
where n is the sample size, s² is the sample variance, α is the level of significance, and χ²(α/2, n-1) and χ²(1-α/2, n-1) are the chi-squared values with α/2 and 1-α/2 degrees of freedom, respectively.
Substituting the given values, we get:
χ²_L = (9 - 1) * 17.3 / χ²(0.01, 8) ≈ 3.355
χ²_U = (9 - 1) * 17.3 / χ²(0.99, 8) ≈ 29.587
Next, we can use these chi-squared values to construct the confidence interval for the population variance:
(V_L, V_U) = [(n - 1) * s² / χ²_U, (n - 1) * s² / χ²_L]
Substituting the given values, we get:
(V_L, V_U) = [(9 - 1) * 17.3 / 29.587, (9 - 1) * 17.3 / 3.355]
Simplifying, we get:
(V_L, V_U) ≈ [7.36, 71.09]
Therefore, with 98% confidence, we can say that the population variance is between 7.36 and 71.09.
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highlight formation of linear programming model
Answers
Answer:
The formation of a linear programming model involves the following steps:
1. Define the objective: Determine what you want to optimize or minimize, such as maximizing profit or minimizing costs.
2. Identify the decision variables: Identify the variables that affect the objective, such as the number of units produced.
3. Formulate the constraints: Establish the limitations that the model needs to operate within, such as production capacity, labor availability, or budget constraints.
4. Write the mathematical equations: Use the identified decision variables, constraints and objective function to write a set of linear equations.
5. Test and solve the model: Test the model by solving the linear equations using mathematical techniques such as simplex method or graphical method.
6. Interpret the results: Analyze the results of the model to gain insights into the optimization of your objective and how changes in variables or constraints can affect the outcome.
Express using algebra
Z increased by 16%
Answers
Answer:
Z(1.16)
Step-by-step explanation:
Let's start by expressing "Z increased by 16%" using algebra.
Let Z be the original value of some quantity.
To increase Z by 16%, we need to add 16% of Z to Z:
Z + 0.16Z
Simplifying this expression by factoring out Z, we get:
Z(1 + 0.16)
Combining like terms, we have:
Z(1.16)
Therefore, "Z increased by 16%" can be expressed algebraically as:
Z increased by 16% = Z(1.16)
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.
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f(x)= |x-51+
f(x) = -2|2|-
-
f(x)= |x-1| +4
f(x)=x+11-4
Vertex
(-1,-4)
(5, 1)
(0, -1)
(2, 4)
f(x) = |z|-
f(2)=|z-|+{
Absolute Value Function
Answers
Answer:
[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]
[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]
[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]
[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]
Step-by-step explanation:
The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b
Plugging this into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex
[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]
You can do the others in a similar manner.
Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices
Find the speed a car will travel with a gear ratio of 3.2 with 27 inch diameter tires , 2690 RPM engine.
Answers
To find the speed of the car, we need to use the formula:
speed = (RPM * tire diameter * pi * gear ratio) / (336 * 12)
where:
RPM is the engine speed in revolutions per minute
tire diameter is the diameter of the tires in inches
pi is the mathematical constant pi (approximately 3.14)
gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear
336 is a constant representing the number of inches per minute that a car will travel at 1 mile per hour
12 is a constant representing the number of inches in a foot
Plugging in the given values, we get:
speed = (2690 * 27 * 3.14 * 3.2) / (336 * 12)
simplifying the equation, we get:
speed = 63.8 mph (rounded to one decimal place)
Therefore, the car will travel at a speed of approximately 63.8 miles per hour
In a restaurant, there are 5 managers, 15 servers, 10 cooks and 15 other personnel. If a person is selected at random, what is the probability that the person is either a manager or a cook?
Answers
Answer:
0.33
Step-by-step explanation:
There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.
The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).
The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.
The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.
Therefore, the probability of selecting either a manager or a cook is:
P(manager or cook) = P(manager) + P(cook)
P(manager or cook) = 5/45 + 10/45
P(manager or cook) = 15/45
P(manager or cook) = 1/3
So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333
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Use the simple interest formula to determine the missing value.
P= $1275, R= ?, T= four years, I= $112.20.
R= —-%
Do not round into the final answer, then round to one decimal place as needed
Answers
Step-by-step explanation:
2.2 percentage answer you silly
A primary credit card holder has a current APR of 14.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent? 12.29% 14.75% 0.01% 1.23%
Answers
Answer:
12.29 I thin
Step-by-step explanation:
The monthly periodic interest rate is 0.01%.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
APR=14.75%
Now,
The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:
r = (1 + i/m)^(m/n) - 1
Where:
r = periodic interest rate
i = nominal annual rate
m = number of compounding periods per year
n = number of payments per year
In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:
r = (1 + 0.1475/12)^(12/12) - 1
r = (1 + 0.012292) - 1
r = 0.012292 or 1.23%
Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.
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A carpenter attaches a brace to a rectangular picture frame. If the dimensions of the picture frame are 30 inches by 40 inches, what is the length of the
brace?
Answers
The brace measures 50 inches in length.
What is Pythagoras's Theorem?The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equals the sum of the squares on the legs of the triangle, a2 + b2 = c2.
The other two sides of the picture frame are its length and width. We thus have:
Length of the hypotenuse (brace)² = Length² of the picture frame + Width² of the picture frame
Let's enter the picture frame's specified dimensions:
Length of the brace² = 30² + 40²
Length of the brace² = 900 + 1600
Length of the brace² = 2500
Taking the square root of both sides, we get:
Length of the brace = √(2500)
Length of the brace = 50
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