The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.
To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.
320 = -197cos(π/15(t)) + 246
First, let's isolate the cosine term:
-197cos(π/15(t)) = 320 - 246
-197cos(π/15(t)) = 74
Next, divide both sides by -197:
cos(π/15(t)) = 74 / -197
Now, we can take the inverse cosine (arccos) of both sides to solve for t:
π/15(t) = arccos(74 / -197)
To isolate t, multiply both sides by 15/π:
t = (15/π) * arccos(74 / -197)
Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:
t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...
These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.
In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.
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Taking attempt 2 of 2.
Question #1*
Find the measure of the indicated arc
67°
134°
The measure of the indicated arc angle is 134 degrees.
How to find the measure of arc angle?The angle subtended by the arc at the centre of the circle is the angle of the arc.
Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.
Hence, the central angle is also known as the arc's angular distance.
Therefore, the measure of an arc is the measure of its central angle.
Hence, the measure of the indicated arc is 134 degrees.
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Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below
Part 1- The lower class boundary for the first class is 100.
Part 2- Approximately 75% of students take exactly two courses.
Part 1:
To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.
Given the class intervals:
100 - 104
105 - 109
110 - 114
115 - 119
120 - 124
125 - 129
130 - 134
The lower class boundary for the first class interval (100 - 104) would be 100.
So, the lower class boundary for the first class is 100.
Part 2:
To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.
Given the data:
of Courses Frequency Relative Frequency Cumulative Frequency
1 23 0.4423 23
2 - 39
3 13 0.25 -
We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.
Relative Frequency = Frequency / Total Number of Students
Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)
To convert this to a percentage, we multiply the relative frequency by 100.
Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%
Therefore, approximately 75% of students take exactly two courses.
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Question
Part 1.
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.
Lengths (mm) Frequency
100 - 104 1
105 - 109 16
110 - 114 71
115 - 119 108
120 - 124 83
125 - 129 18
130 - 134 3
What is the lower class boundary for the first class?
class boundary =
Part 2
In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:
Please round your answer to 4 decimal places for the Relative Frequency if possible.
# of Courses Frequency Relative Frequency Cumulative Frequency
1 23 0.4423 23
2 39
3 13 0.25
What percent of students take exactly two courses? %
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(a) The average cost in 2010 is $2088.82.
(b) A graph of the function g for the period 2006 to 2015 is: D. graph D.
(c) Assuming that the graph remains accurate, its shape suggest that: B. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.4Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2010 - 2006) + 6
x = 4 + 6
x = 10 years.
Next, we would substitute 10 for x in the function:
g(10) = -1736.7 + 1661.4In(10)
g(10) = $2088.82
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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What else would need to be congruent to show that ABC=AXYZ by SAS?
A. ZB=LY
B. BC = YZ
C. C= LZ
D. AC = XZ
Given:
AB XY
BC=YZ
To show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.
To show that triangles ABC and AXYZ are congruent by the Side-Angle-Side (SAS) criterion, we need to establish that two corresponding sides and the included angle are congruent.
Given AB ≅ XY and BC ≅ YZ, we already have two corresponding sides congruent.
To complete the congruence by the SAS criterion, we need to establish that the included angles are congruent. In this case, the included angle is angle BAC (or angle XYZ).
Therefore, to show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.
None of the answer choices directly addresses the congruence of the angles. So, none of the given options (A, B, C, D) are sufficient to show the congruence of the triangles by SAS.
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Determine the limit in the following equation.
The limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.
How did we get the value?To find the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches a certain value, we can simplify the expression and evaluate the limit.
First, let's simplify the expression:
lim (x² - √x⁴ + 3x²)
= lim (4x² - x² - √x⁴)
= lim (3x² - √x⁴)
Now, let's consider the behavior of the expression as x approaches a value.
As x approaches any finite value, the term 3x² will approach a finite value.
For the term √x⁴, as x approaches a finite value, the square root of x⁴ will approach the absolute value of x².
Therefore, the limit becomes:
lim (3x² - √x⁴) = lim (3x² - |x²|)
Next, let's consider the different cases as x approaches positive infinity, negative infinity, and zero.
1. As x approaches positive infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:
lim (3x² - |x²|) = lim (∞ - ∞)
In this case, the limit is indeterminate (∞ - ∞).
2. As x approaches negative infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:
lim (3x² - |x²|) = lim (∞ - ∞)
Again, in this case, the limit is indeterminate (∞ - ∞).
3. As x approaches zero, the term 3x² will tend to zero, and |x²| will also tend to zero. Thus, the expression becomes:
lim (3x² - |x²|) = lim (0 - 0) = 0
Therefore, the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.
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The grocery store has bulk pecans on sale, which is great since you're planning on making 9 pecan pies for a wedding. How many pounds of pecans should you buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How many pecans are needed for each pie? Your recipe calls for
cups pecans per pie. But there is no cup measure available, only a scale.
How many pecans are in a pound? Perhaps the nutritional info from a bag of pecans would be helpful.
Approximately 4.6 pounds of pecans are needed for one pecan pie.You should buy approximately 41.4 pounds of pecans to make 9 pecan pies.
To determine the number of pounds of pecans needed to make 9 pecan pies, we need to consider the amount of pecans required per pie and the number of pies we are making.
The recipe calls for 1 cup of pecans per pie, but we don't have a measuring cup available. However, we do have nutritional information from a bag of pecans, which states that there are 684 calories in 1 cup (99g) of pecans.
To find out how many pecans are in a pound, we can use the information that 1 cup of pecans weighs 99 grams. Since there are 454 grams in a pound, we can set up the following proportion:
1 cup (99g) = x pounds (454g)
Cross-multiplying, we get:
99g * x pounds = 1 cup * 454g
Simplifying, we have:
99x = 454
Dividing both sides by 99, we find:
x ≈ 4.5959 pounds
So, approximately 4.6 pounds of pecans are needed for one pecan pie.
Since we are making 9 pecan pies, we multiply the amount needed for one pie by the number of pies:
4.6 pounds/pie * 9 pies = 41.4 pounds
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Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If not, what would be sufficient to
prove the triangles similar? Explain your reasoning.
I need help on number 1 and 2
The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;
1. ΔAJK ~ ΔSWY according to the SAS similarity postulate
2. ΔLMN ~ ΔLPQ according to the AA similarity postulate
3. ΔPQN ~ ΔLMN
LM = 12, QP = 8
4. ΔLMK~ΔLNJ
NL = 21, ML = 14
What are similar triangles?
Similar triangles are triangles that have the same shape but may have different sizes.
1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;
24/16 = 3/2
18/12 = 3/2
The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.
2. The ratio of the corresponding sides in each of the triangles are;
MN/LN = 8/10 = 4/5
PQ/LQ = 12/(10 + 5) = 12/15 = 4/5
The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule
3. The alternate interior angles theorem indicates;
Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;
ΔPQN ~ ΔLMN by the AA similarity postulate
LM/QP = (x + 3)/(x - 1) = 18/12
12·x + 36 = 18·x - 18
18·x - 12·x = 36 + 18 = 54
6·x = 54
x = 54/6 = 9
LM = 9 + 3 = 12
QP = x - 1
QP = 9 - 1 = 8
4. The similar triangles are; ΔLMK and ΔLNJ
ΔLMK ~ ΔLNJ by AA similarity postulate
ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)
ML/NL = LK/LJ = (24 - 8)/24
(24 - 8)/24 = (6·x + 2)/((7·x + 7)
16/24 = (6·x + 2)/(7·x + 7)
16 × (7·x + 7) = 24 × (6·x + 2)
112·x + 112 = 144·x + 48
144·x - 112·x = 32·x = 112 - 48 = 64
x = 64/32 = 2
ML = 6 × 2 + 2 = 14
NL = 7 × 2 + 7 = 21
MN = 2 + 5 = 7
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Determine the point(s) at which the given function f(x) is continuous.
Answer: [tex](-\infty, 6) \cup (6, \infty)[/tex]
Step-by-step explanation:
Polynomials are continuous for all reals, so we only need to consider the rational part. Since the denominator is undefined at [tex]x=6[/tex], there is a vertical asymptote at [tex]x=6[/tex].
If f(x)=x+3 and g(x)=x^2-2, find the following.
a. f(g(0))
b. g(f(0))
c. f(g(x))
d. g(f(x))
e. f(f(-2))
f. g(g(4))
g. f(f(x))
h. g(g(x))
Step-by-step explanation:
a. f(g(0)) = f(0^2 - 2) = f(-2) = -2 + 3 = 1
b. g(f(0)) = g(0+3) = g(3) = 3^2 - 2 = 7
c. f(g(x)) = g(x) + 3 = x^2 - 2 + 3 = x^2 + 1
d. g(f(x)) = f(x)^2 - 2 = (x+3)^2 - 2 = x^2 + 6x + 7
e. f(f(-2)) = f(-2+3) = f(1) = 1+3 = 4
f. g(g(4)) = g(4^2 - 2) = g(14) = 14^2 - 2 = 194
g. f(f(x)) = f(x+3) = (x+3)+3 = x+6
h. g(g(x)) = g(x^2 - 2) = (x^2 - 2)^2 -2 = x^4 - 4x^2 + 2
so in the same Equation i have to do use the values x=-4,0,5 to verify my solution to the equation 5+x-12=x-7 in my final answer.
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Answer:
Step-by-step explanation:
Let's revisit the equation and the solution using the values x = -4, 0, and 5.
The given equation is: 5 + x - 12 = x - 7
Let's go through the steps again to solve it:
5 + x - 12 = x - 7
Combine like terms:
x - 7 = x - 7
Now, subtract x from both sides:
x - x - 7 = x - x - 7
Simplify:
-7 = -7
The equation simplifies to -7 = -7, which is true.
Now, let's use the values x = -4, 0, and 5 to verify the solution.
For x = -4:
5 + (-4) - 12 = (-4) - 7
-11 = -11
The equation is satisfied for x = -4.
For x = 0:
5 + 0 - 12 = 0 - 7
-7 = -7
The equation is satisfied for x = 0.
For x = 5:
5 + 5 - 12 = 5 - 7
-2 = -2
The equation is satisfied for x = 5.
Therefore, the solution x = 0 is correct, and it satisfies the equation for the given values. My earlier statement that x = -4 and x = 5 do not satisfy the equation was incorrect. I apologize for the confusion caused.
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
a) 9-12/2
b) 27-13/²2
a) Option a) 9 - 1/2 is equal to 17/2.
b) Option b) 27 - 2/3 is equal to 79/3.
a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.
Multiplying 9 by 2/2, we get:
9 * (2/2) = 18/2
So, the expression 9 - 1/2 can be simplified to:
18/2 - 1/2 = 17/2
Therefore, option a) 9 - 1/2 is equal to 17/2.
b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.
Multiplying 27 by 3/3, we get:
27 * (3/3) = 81/3
So, the expression 27 - 2/3 can be simplified to:
81/3 - 2/3 = 79/3
Therefore, option b) 27 - 2/3 is equal to 79/3.
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Un objeto que se hace girar, se desplaza 25 radianes en 0.8 segundos. ¿cuál es la velocidad angular de dicho objeto?
The angular velocity of the object is 31.25 radians/second.
Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.
Angular velocity (ω) = Total angular displacement / Time taken
Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:
ω = 25 radians / 0.8 seconds
Simplifying the equation gives:
ω = 31.25 radians/second
So, the angular velocity of the object is 31.25 radians/second.
Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.
In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.
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Note the translated question is:
An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?
You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have typed 765 words. Find the rate of change in words per minute. Round your answer to the nearest whole number.
Answer:
35
Step-by-step explanation:
18-4 = 14 minutes
number of words typed in 14 minutes is 765-275= 490 words
490 words/14 mins= appox 35
Joseph wants to factorise the following algebraic expression 3x squared + 6x + 4x + 8 provide yourself with a three-step guide on how to factorise the expression
The expression 3x² + 6x + 4x + 8 is factorized as (x + 2)(3x + 4).
To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:
Step 1: Grouping
Group the terms in pairs based on their common factors:
(3x² + 6x) + (4x + 8)
Step 2: Factor out common factors
Factor out the greatest common factor from each group of terms:
3x(x + 2) + 4(x + 2)
Now, we have a common factor of (x + 2) in both terms.
Step 3: Combine the factored terms
Combine the factored terms using the common factor:
(x + 2)(3x + 4)
The expression 3x² + 6x + 4x + 8 is factorized as (x + 2)(3x + 4).
In this process, we grouped the terms with similar variables and then factored out the greatest common factor from each group. Finally, we combined the factored terms using the common factor to obtain the fully factorized expression.
It's important to note that factoring algebraic expressions requires practice and familiarity with common factoring techniques. In some cases, you may encounter expressions that require additional methods such as factoring by grouping, using special factoring formulas, or applying quadratic factoring techniques.
By following these three steps, you can factorize the given expression by identifying common factors and combining terms accordingly.
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NEED HELP
Y
B
^^
CX
A
Previous Activity
N
Which would prove that AABC~ AXYZ? Select two
options.
OBA-BC-A
=
YX
YZ XZ
OBA = BC₁
YX
YZ
O
AC
XZ
=
=
BA
XX.
YX
AC
BC
BA = AE = 8C
YX
YZ
XZ
OBC=BA ₁ <=
XY
ZX
Next Activity
The conditions that prove that the triangles ΔABC and ΔXYZ are similar, ΔABC ~ ΔXYZ, based on the order of the lettering are;
BA/YX = BC/YZ = AC/XZ
AC/XZ = BA/YX, ∠A ≅ ∠C
What are similar triangles?Similar triangles are triangles that have the same shape (the same two or all three interior angles in each triangle) but in which may have different sizes.
Triangles are similar if they equivalent ratio for their sides and and if the angles in each triangle are congruent to the angles in the other triangle
Therefore, the conditions that indicates that two triangles are that one triangle is a scaled image of the other triangle, therefore, the ratio of the corresponding sides of the triangles are equivalent, which indicates;
ΔABC is similar to ΔXYZ if we get;
BA/YX = BC/YZ = AC/XZA condition that indicates that two triangle are similar is the Side Angle Side, SAS, similarity postulate, which states that two triangles are congruent if the ratio of two corresponding sides are equivalent and the angle between the two sides in the two triangles are congruent, therefore;
ΔABC is similar to ΔXYZ if we get;
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Taking the period of daylight on a certain day to be from 5.30am to 7.00pm, calculate the periods of daylight and a darkness on that day. C.202°3°, 157°30' D. 195°, 165° A. 187°30M72°301 B. 135°, 225°
The periods of daylight and darkness on that day are approximately:
Daylight: 202.5°
Darkness: 157.5°
Hence, the correct option is:
C. 202°3°, 157°30'
To calculate the periods of daylight and darkness on a certain day, we need to find the difference between the times of sunrise and sunset.
Sunrise time: 5.30 am
Sunset time: 7.00 pm
To find the period of daylight, we subtract the sunrise time from the sunset time:
Daylight = Sunset time - Sunrise time
First, let's convert the times to a 24-hour format for easier calculation:
Sunrise time: 5.30 am = 05:30
Sunset time: 7.00 pm = 19:00
Now, let's calculate the period of daylight:
Daylight = 19:00 - 05:30
To subtract the times, we need to convert them to minutes:
Daylight = (19 * 60 + 00) - (05 * 60 + 30)
Daylight = (1140 + 00) - (330)
Daylight = 1140 - 330
Daylight = 810 minutes
To convert the period of daylight back to degrees, we can use the fact that in 24 hours (1440 minutes), the Earth completes a full rotation of 360 degrees.
Daylight (in degrees) = (Daylight / 1440) * 360
Daylight (in degrees) = (810 / 1440) * 360
Daylight (in degrees) ≈ 202.5 degrees
To find the period of darkness, we subtract the period of daylight from a full circle of 360 degrees:
Darkness = 360 - Daylight
Darkness = 360 - 202.5
Darkness ≈ 157.5 degrees
Therefore, the periods of daylight and darkness on that day are approximately:
Daylight: 202.5°
Darkness: 157.5°
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A rectangular pyramid is sliced. The slice passes through line segment AB and is parallel to the base.
Which two-dimensional figure represents the cross section?
A. A rectangle the same size as the base
B. A rectangle that is smaller than the base
C. A quadrilateral that is not a rectangle
D. A triangle with a height the same as the pyramid
Answer:
Step-by-step explanation:
The correct answer is A. A rectangle the same size as the base.
When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.
The lines shown below are parallel. if the green line has a slope of 3 what is the slope of the red line?
Answer:
3
Step-by-step explanation:
parallel lines have the same gradient
 Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answer:
arc LKF = 208°
Step-by-step explanation:
the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so
arc LKF = 2 × 104° = 208°
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The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).
The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:
-x + 20y = 129
-x + 10y = 59
y = 7
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(7) = 129
x = 140 - 129
x = 11
-x + 10(7) = 59
x = 70 - 59
x = 11
Therefore, the system of equations has only one solution (11, 7).
For the year when the population are all the same for three countries, we have:
x = 2010 + (11 - 10)
x = 2011
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Here is a unit circle with point P at (1, 0) Find the coordinates of P after the circle rotates the given amount counter clockwise around its center
1. 1/3 of a full rotation: ?
2 1/2 of a full rotation: ?
3. 2/3 of a full rotation: ?
1/3 of a full rotation: (-0.5, √3/2)
1/2 of a full rotation: (-1, 0)
2/3 of a full rotation: (0.5, -√3/2)
These are the coordinates of point P after the corresponding rotations around the unit circle's center.
To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.
1/3 of a full rotation:
A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.
When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.
In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.
Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).
1/2 of a full rotation:
Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.
When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.
At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.
Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).
2/3 of a full rotation:
Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.
When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.
At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.
Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).
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GEOMETRY 50POINTS
TYSM
Answer:
40, 50, 30 Yes
13, 5, 12 Yes
10, 10, 15 Yes
41, 9, 40 Yes
Step-by-step explanation:
16, 10, 6
10 + 6 = 16
No
40, 50, 30
30 + 40 > 50
Yes
13, 5, 12
5 + 12 > 13
Yes
70, 20, 25
20 + 25 < 70
No
10, 10, 15
10 + 10 >15
Yes
41, 9, 40
9 + 40 > 41
Yes
I am a 6 digit number my highest place value and my lowest place value has a number equals to the number of days in a week my hundreds place is equal to the half it dozen
my turns place easy number of sides of a triangle by 1000 space is equal to the number of pose of earth and 10000 place is equal to result of subtracting any number from itself
Answer:
The description provides the clues for each digit in a 6-digit number. Let's break it down:
1. Highest place value and lowest place value has a number equals to the number of days in a week: There are 7 days in a week, so the first and last digits are 7.
2. Hundreds place is equal to half a dozen: Half a dozen is 6, so the third digit from the right (hundreds place) is 6.
3. Tens place is the number of sides of a triangle: A triangle has 3 sides, so the second digit from the right (tens place) is 3.
4. Thousands place is equal to the number of poles of earth: Earth has two poles, so the second digit from the left (thousands place) is 2.
5. Ten thousands place is equal to result of subtracting any number from itself: Subtracting any number from itself yields 0, so the third digit from the left (ten thousands place) is 0.
Putting it all together, the 6-digit number would be: 702,637.
[tex] \frac{350}{120} [/tex]
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The simplified fraction of 350/120 is 35/12
How to simplify the fractionfrom the question, we have the following parameters that can be used in our computation:
350/120
Divide the zeros
So, we have
350/120 = 35/12
Divide the fractions by 3
This is impossible
Hence, the simplified fraction is 35/12
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Simplify the f(x) and g(x) to get it
Answer:
(fg)(x)= (x²+6)(x²-x+9)
multiply the terms:
(fg)(x)= x²(x²-x+9) +6(x²-x+9)
add the like terms:
(fg)(x)= (x⁴-x³+9x²)+(6x²-6x+54)
and you get your final answer:
(fg)(x)= x⁴-x³+15x²-6x+54
elsa hikes up a mountain. she hikes back down at a constant rate the table shows elsas elevation at each hour after she begins her descent
The linear equation from the given table is expressed as:
y = -1500x + 8350
How to find the equation from the table?The general form for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line through two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
We will take the two coordinates (1, 6850) and (2, 5350)
Thus:
(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)
(y - 6850)/(x - 1) = -1500
y - 6850 = -1500x + 1500
y = -1500x + 1500 + 6850
y = -1500x + 8350
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Assume a class has 26 members.
a. In how many ways can a president, a vice president, and a secretary be selected?
b. How many committees of 4 people can be chosen?
a. The number of ways to select a president, a vice president, and a secretary is
b. The number of ways to form a 4-person committee is
$0.
a. There are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.
b. There are 14,950 ways to form a 4-person committee from a class of 26 members.
a. To select a president, a vice president, and a secretary from a class of 26 members, we can use the concept of permutations.
For the president position, we have 26 choices. After selecting the president, we have 25 choices remaining for the vice president position. Finally, for the secretary position, we have 24 choices left.
The total number of ways to select a president, a vice president, and a secretary is obtained by multiplying the number of choices for each position:
Number of ways = 26 * 25 * 24 = 15,600
Therefore, there are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.
b. To form a 4-person committee from a class of 26 members, we can use the concept of combinations.
The number of ways to choose a committee of 4 people can be calculated using the formula for combinations:
Number of ways = C(n, r) = n! / (r!(n-r)!)
where n is the total number of members (26 in this case) and r is the number of people in the committee (4 in this case).
Plugging in the values, we have:
Number of ways = C(26, 4) = 26! / (4!(26-4)!)
Calculating this expression, we get:
Number of ways = 26! / (4! * 22!)
Using factorials, we simplify further:
Number of ways = (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1) = 14,950
Therefore, there are 14,950 ways to form a 4-person committee from a class of 26 members.
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on a scale drawing 9 inches represents 11 miles how many inches represent 55 miles
Answer:
45 inches represent 55 miles on the scale drawing.
Step-by-step explanation:
To solve this proportion, we can set up the following ratio:
9 inches / 11 miles = x inches / 55 miles
We can cross-multiply to solve for x:
9 inches * 55 miles = 11 miles * x inches
495 inches = 11 miles * x inches
Now, we can isolate x by dividing both sides by 11 miles:
495 inches / 11 miles = x inches
Simplifying the expression:
45 inches = x inches
GEOMETRY 50POINTS
determine what type of triangle they will form.
BRILLIANT for the best answer
Answer:
acute triangle
Step-by-step explanation:
for the given sides to form a triangle
the sum of any 2 sides must be greater than the third side
given 56 , 90 , 100
56 + 90 = 146 > 100
56 + 100 = 156 > 90
90 + 100 = 190 > 56
the condition is met so the 3 lengths will form a triangle.
let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then
• if a² + b² = c² , then triangle is right
• if a² + b² > c² , then triangle is acute
• if a² + b² < c² , then triangle is obtuse
a² + b² = 56² + 90² = 3136 + 8100 = 11,236
c² = 100² = 10, 000
since a² + b² > c² , then triangle is acute