The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]
A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.
A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.
[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]
[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]
[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]
=1+x^2+y^2
[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]
[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]
[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]
[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]
[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]
[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]
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jess has $22 and saves $5 each week rosie has $10 and saves $8 each week how many weeks till they have the same amount of money
A high school has a population of 2,035 students and is increasing by 3% each year.
Write an exponential function to model the student population in terms of the number of years from now.
Predict the number of students that will be in the school after five years. Show all of your work.
The student population in the school can be modeled using an exponential function of the form:
P(t) = 2,035 * 1.03^t
where P(t) is the student population t years from now, and 1.03 is the factor by which the population increases each year.
To predict the number of students in the school after five years, we can substitute t = 5 into the function:
P(5) = 2,035 * 1.03^5
= 2,035 * 1.1895
= 2,408.76
Thus, there will be approximately 2,408.76 students in the school after five years.
Find the equation of the line
Answer:
y = 10x +
the picture is cut short so I can't help with the next box.
Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum fo a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72
Work out the value of Dylan's initial investment
The amount invested by Dylan will be £1200.
What is simple interest?Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate.
Given that Dylan invested some money in his bank. He agreed on a simple interest rate of 3% per annum for a period of 2 years. At the end of the 2-year period, the value of his investment increased by £72.
The amount of money invested will be calculated as,
SI = ( P x R x T ) / 100
72 = ( P x 3 x 2 ) / 100
7200 = 6P
P = 7200 / 6
P = £1200
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The first five terms of a sequence are shown. 4, 12, 36, 108, 324, ... What would be the 8th term in the sequence?
Answer:8748
Step-by-step explanation:
The pattern is multiplying the number by 3, 3x12=36. 36x3=108.
4, 12, 36, 108, 324, 972, 2916, 8748
A statistics class with 30 students has 10 males and 20 females. Suppose you choose 3 of the students in the class at random. Find the probability that all three are female
The probability that all three are female is 0.281
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.2030⋅1929⋅18282030⋅1929⋅1828 = 0.281
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Type in the missing values to complete the simplified form of the expression 4x-4+3y+ 6-2x+3y.
__ x +__ y + __
Answer:
2x+6y+2
Step-by-step explanation:
Edward works at a grocery store. He kept track of the number of coupons redeemed by the last 20 shoppers. The center of the dot plot was 1. No one redeemed 4 coupons. Most people did not redeem any coupons. Which dot plot displays this information correctly?
Therefore , the solution to the given problem of scatter plot comes out to be the data correctly represented as 0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot
Why a scatter plot is used ?Several dots are arranged along a vertical and horizontal axis to form a scatter plot. Because they can demonstrate the strength of the relationship, if any, between the two observed quantities or occurrences, scatter plots are crucial in statistics (called variables).
Here,
Given : the number of coupons redeemed by the last 20 shoppers
and
center dot plot is 1
thus,
No one redeemed each 4 coupons
So, In order to find the which plot displays data correctly
We get,
0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot
which represents the data correctly
Therefore , the solution to the given problem of scatter plot comes out to be the data correctly represented as 0 has 8 dots, 1 has 3 dots, 2 has 3 dots, 3 has 5 dots, 4 has 0 dots, and 5 has 1 dot
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A bag contains 9 red marbles, 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the bag. a. What is the probability that all three marbles are red when you replace each marble before selecting the next marble? Round your answer to the nearest tenth. about % b. What is the probability that all three marbles are red when you do not replace each marble before selecting the next marble? Round your answer to the nearest tenth. about %
Answer:
A) 9.1%
B) 7.4%
Step-by-step explanation:
Part A
Because you are replacing each marble before selecting the next, the probability of choosing one red marble remains the same, so choosing 3 red marbles with replacement would mean the probability gets multiplied by itself 3 times:
[tex]\displaystyle P(\text{Red+Replace})=\biggr(\frac{9}{20}\biggr)^3=\frac{9}{20}*\frac{9}{20}*\frac{9}{20}=\frac{729}{8000}\approx9.1\%[/tex]
Part B
[tex]\displaystyle P(\text{Red+No Replace})=\frac{C(9,3)C(4,0)C(7,0)}{C(20,3)}=\frac{\frac{9!}{3!(9-3)!}}{\frac{20!}{3!(20-3)!}}=\frac{\frac{9*8*7}{3*2*1}}{\frac{20*19*18}{3*2*1}}=\frac{9*8*7}{20*19*18}=\frac{7}{95}\approx7.4\%[/tex]This can also be calculated with [tex]\frac{P(9,3)}{P(20,3)}[/tex] because the order does matter in which you pick the 3 red marbles with no replacement.
Answer:
9.1%
7.4%
Step-by-step explanation:
please help me with math!!!
Answer:
Step-by-step explanation:
To move all the constants to the right side: Subtract 0.4 from both sides
-9x = 3.6
To isolate the variable: Divide both sides of equation by -9
x = -3.6/9
Solution of the equation: -0.4
A coin with probability p of showing up heads is tossed n times. What is the probability that the number of heads is odd
The chance you get a odd number of heads from the first coin is 1/3,
What is the probability that the number of heads is odd? The tosses of the coin are independent (neither affects the other). Hence, the probability of a head on Flip 1 and a head on Flip 2 is the product of P(H) and P(H), which is 1/2 x 1/2 = 1/4. The same calculation applies to the probability of a head on Flip 1 and a tail on Flip 2For n≥3, if the last outcome is T, then the probability that the first (n−1)tosses do not contain two (or more consecutive heads is p n−1 and if the last outcome is H, then (n−1)th outcome must be T and the probability the first(n−2) tosses do not contain two (or more) consecutive heads is p n−2 . Hence, p n =p n−1 ×P (nth toss results in a tail)+p n−2 ×P (nth toss results in a head and (n−1)th toss results in a tail)=(1−p)p n−1+p(1−p)p n−2To learn more about probability refers to:
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The prime factorization of a number is 2³× 5² . What is the number?
A. 1,196
B. 60
C. 35
D.200
Answer:
D.
Step-by-step explanation:
Marco ran 7 miles in 50.4 minutes. If he ran at the same pace the whole time, how long did it take him to run 1 mile?
Answer:
7.2 min
Step-by-step explanation:
50.4 / 7 = 7.2 min
In the figure, what is the value of a?
a
35
48
21
Encuentra dos numeros tales que el doble del mayor menos la mitad del menor exceda en 15 unidades a la quinta parte de la suma de ambos
Respuesta:
12, 13
Explicación paso a paso:
Dejar,
Número más pequeño = x
Número mayor = x + 1
Expresarse matemáticamente;
2 (x + 1) - (x / 2) = ((x + 1 + x) / 5) + 15
2x + 2 - 0.5x = 0.2 (2x +1) + 15
1.5x + 2 = 0.4x + 0.2 + 15
1.5x - 0.4x = 0.2 + 15 - 2
1,1 veces = 13,2
x = 13,2 / 1,1
x = 12
x + 1 = 12 + 1 = 13
I need help, it’s for my final grade
yeeeeeeeeeeeeeeeeeeee help
Answer:
x = 52
Step-by-step explanation:
180 - 72 = 108
108 + 20 + x = 180
128 + x = 180
180 - 128 = x
x = 52
Have a nice day!
Multiply.
(3x + 2)(x - 7)
Answer:
3x^2 - 19x - 14
Step-by-step explanation:
PLEASE HELP ASAP!! find the zeros of the function, will mark!
Answer:
The zeros are (0,0) and (4,0)
Step-by-step explanation:
Those are the 2 points of the parabola that are on the "x" axis
(Hope this helped! Please ask and questions about this in the comments) :D
What is the perimeter of a regular pentagon inscribed in a circle with radius 1 meter
Answer:
Step-by-step explanation:
The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. The length of each side of a regular pentagon inscribed in a circle with radius 1 meter can be found using the formula: side length = 2 * radius * sin(180/number of sides).
For a regular pentagon, the number of sides is 5. Plugging this into the formula gives us:
side length = 2 * 1 * sin(180/5) = 2 * 1 * sin(36) = 2 * 0.587785 = 1.175570
So the perimeter of the regular pentagon is equal to 5 * 1.175570 = 5.877849 meters.
Type the correct answer in each box.
Table A: Inventory Stock
Product Store A Store B Store C
X 543 356 643
Y 364 476 419
Z 376 903 409
Table B: July Unit Sales
Product Store A Store B Store C
X 102 78 97
Y 98 87 59
Z 54 89 79
Table A shows the total inventory of three products for three Sports Equipment Corporation stores on July 1. Table B shows unit sales data for the month of July.
If you create a matrix, C, to show the inventory at the end of July, the value of the entry represented by c22 is
.
In a matrix with components aij, which represent unit sales for July, the maximum possible value that a31 can have is
The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.
Table C: Ending Inventory
Product Store A Store B Store C
X 441 278 546
Y 266 389 360
Z 322 814 330
The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.
The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A.
The value of the entry represented by c22 in the matrix C that shows the inventory at the end of July is 389, and the maximum possible value that a31 can have is 903.
The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B. The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A. This value indicates that the maximum number of units of Product Z that can be stored in Store C is 903. In summary, the value of c22 in the matrix C is 389, and the maximum value of a31 is 903.
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Suppose you want to save $5000 to put towards remodeling your house in 18 months. You found a bank whose interest rate for savings accounts is 4.5% compounded monthly, but you are unsure of how much to invest to have $5000 saved in 18 months.
Using the compound interest formula, how much should you invest in order to have $5000 saved in 18 months?
The required money to be invested in order to save $5000 is $4677.26.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The principal for each interval is the sum of interest And the principal for the previous interval.
Suppose the amount to be invested be P.
The rate of interest for monthly compounding is given as 4.5/12 = 0.375%.
Time is given as 18 months.
This implies number of time period is 18.
Plug n = 18, r = 0.375% and A = 5000 in A = P(1 + r/100)ⁿ as,
⇒ 5000 = P(1 + 0.375/100)¹⁸
⇒ P = 4677.26
Hence, the amount of money that should be invested is obtained as $4677.26.
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Someone please answer?????
Answer:
y ≈±6.8556546
Step-by-step explanation:
y^2 = 47
Take the square root of each side
sqrt(y^2) = ±sqrt(47)
y ≈±6.8556546
Answer: y≈6.85565
Step-by-step explanation:
[tex]\sqrt{y}[/tex] =[tex]\sqrt{47}[/tex]
y≈6.85565
Whats the perimeter of this small parallelogram?
Answer:
Perimeter = 18 units
Step-by-step explanation:
one side = 4
other side² = 3² + 4² + 25
other side = √25 = 5
Perimeter = (2 x 4) + (2 x 5) = 18 units
if (1,-7) is in the solution area of the inequality y ≤ 1x + b, what is the smallest value of b possible?
Check your solution by first checking the end point , in the related equation. Pick a value greater than , such as 2, to check in the inequality. Solve for x. Divide both sides by 3 to isolate the variable.
Hello can someone please help me with this please What is the best possible geometric model for a set of rail tracks?
Ray ----Point ---- Line --- Plane
Fine the measure of an angle that is supplement to ABC if m < ABC is 82?
100 ---- 8---------278------
Fine the measure of an angle that is complementary to ABC is 32?
328------148------58------32
The intersection of two lines is a ?
Quadrilateral--------Point--------Line--------Plane
A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.
How to obtain the supplement of an angle?Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.
This means that the supplement of ABC = 82º is given as follows:
180º - 82º = 98º.
How to obtain the complement of an angle?Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.
This means that the supplement of ABC = 90º is given as follows:
90º - 32º = 58º.
Where do two lines intersect?Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.
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50 points + brainliest PLS HELP ME ASAP. All I need is a right answer and a clear solution. Ty in advance! :)
(anyone who gives absurd answers will be reported right away)
Dimensions of the parallelogram are:
Base is b = 2 ft, Side is a = 5 ft, Height is h = 4 ft.Its perimeter is:
P = 2(2 + 5) = 2(7) = 14 ftIts area is:
A = bh = 2*4 = 8 ft²When the scale factor is 2Perimeter is 2 times greater:
P = 2*14 = 28 ftArea is 2*2 = 4 times greater:
A = 4*8 = 32 ft²When the scale factor is 3Perimeter is 3 times greater:
P = 3*14 = 42 ftArea is 3*3 = 9 times greater:
A = 9*8 = 72 ft²When the scale factor is 1/2Perimeter is 2 times smaller:
P = 14/2 = 7 ftArea is 2*2 = 4 times smaller:
A = 8/4 = 2 ft²12. Find T in the diagram, if R = 110° and S = 60°.
Answer:
∠T = 130°
Step-by-step explanation:
The figure we are given is a quadrilateral, a 4 sided shape.
There are many different types of quadrilaterals, such as a rhombus, rectangle, etc.
How will we know which quadrilateral the given figure is?
We will have to look at the given properties of the figure to find out.
We are given that there are two adjacent pairs of congruent sides.
RS = RU, and ST = UT.
Thus, the given quadrilateral is a kite.
Now that we know that the given figure is a kite, we can utilize a kite's angle properties to find out ∠T.
In a kite, the non-vertex angles (∠S and ∠U) are congruent.
If ∠S = 60°, then ∠U = 60°.
In a kite, the sum of the interior angles is 360°.
Hence:
∠R + ∠S + ∠T + ∠U = 360°
Therefore, we can substitute the angles we know into the equation and solve for ∠T.
∠R + ∠S + ∠T + ∠U = 360°
110 + 60 + ∠T + 60 = 360
110 + 120 + ∠T = 360
230 + ∠T = 360
∴ ∠T = 130°
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A salesperson at a jewelry store earns 9% commission each week. Last week, sold $750
worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
The amount made in commission is $67.5.
The amount made in sales by the store is $682.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount sold last week = $750.
Commission = 9%
The amount of commission.
= 9/100 x 750
= $67.5
The sales made last week by the store.
= 750 - 67.5
= $682.5
Thus,
$67.5 was made in commission.
$682.5 was made from sales.
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A television is on sale for $75 off.
The price of the television with the sale is $300.
If you use the equation −75=300 to solve this problem, what does n represent?
In this equation, n represents the original price of the television before the sale.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions by using numbers, symbols, and operations. It is used to describe the relationship between different variables in a problem. Equations are usually written as a statement of equality, such as 2 + 2 = 4, where the left side of the equation (2 + 2) is equal to the right side (4). Equations can be used to solve for a single unknown value, or to determine the relationship between multiple variables.
In this equation, n represents the original price of the television before the sale.
This means that the original price of the television was $375.
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