1. The graph shows the distance y, in centimeters, a pendulum moves to the left (negative displacement) and right (positive displacement), for a given number of seconds x. (a) From its resting position, how long does it take the pendulum to swing one direction, then the other, and then return to its resting position? (b) What is the pendulum’s maximum displacement? (c) What percent of a full cycle is completed within 1 s? (d) How is the pendulum moving during the time period from x = 5 to x = 5.625? (e) What is the equation of the graph?
Answers
A) In order to calculate how long it takes the pendulum to swing one direction, then the other, and then return to its resting position, you need to look at the graph and see where the function returns to zero after going once up and once down. This time is called period (T), which is defined as the time taken to perform one complete oscillation.
In our case, T = 5 s (see the second picture attached for reference).
B) In order to find the pendulum's maximum displacement, you need to look at the graph and see how high and low on the y-axis the function goes. This displacement is called amplitude (A), which is defined as the maximum displacement from the resting position in either direction.
In our case, A = 20 cm (see the second picture attached for reference).
C) Since the period of the pendulum is 5 seconds and it swings constantly, the fraction of a cycle completed in 1 second is calculated by simply dividing
p = 1 / 5 = 0.20
Therefore, in 1 second the pendulum completes 20% of its cycle.
D) During the time period from x = 5 to x = 5.625, we can see from the graph that the pendulum has just started its second oscillation, therefore it starts from the resting position and it moves towards the right (positive values of y)decreasing its velocity.
E) The equation of the graph is a sinusoidal function, therefore it will have an equation like
[tex]f(t) = A \cdot sin( \frac{2 \pi}{T} \cdot t - b) + c [/tex]
where:
A = amplitude
T = period
b and c = shifting constants
In order to find b and c, we recall that the graph starts at (0,0) and therefore it is not shifted either horizontally or vertically, and therefore we can infer that b = c = 0.
Substituting the values, we find:
[tex]f(t) = 20 \cdot sin( \frac{2 \pi}{5} \cdot t) [/tex]
Related Questions
In a game, you have a 1/36 probability of winning $85 and a 35/36 probability of losing $4. what is your expected value? (don't include dollar sign in your answer; just a positive or negative number rounded to the nearest hundredth)
Answers
The lateral area of a cone is 112π cm^2. The radius is 8 cm. Find the slant height of the cone.
Answers
[lateral area of a cone]=pi*r*l
where
l is the slant height
r is the radius
lateral area=pi*r*l---------> l=lateral area/(pi*r)-----> l=112*pi/(pi*8)---> l=14 cm
the answer is
14 cm
What are the coordinates of the point that corresponds to -7x/4 on the unit circle
Answers
(1)[tex]y = \frac{-7x}{4}[/tex]
(2)[tex]x^{2}+y^{2}=1[/tex]
We introduce (1) into (2):
[tex]x^{2}+(\frac{-7x}{4})^{2}=1[/tex]
[tex]x^{2}+\frac{49x}{16}^{2}=1[/tex]
[tex]65x^{2}=16[/tex]
There are two values, namely:
[tex]\left \{ {{x_{1} = +0.4961 } \atop {x_{2} = -0.4961 }} \right.[/tex]
Then, substituing these values in the first (1) equation, we find:
[tex]\left \{ {{y_{1} = -0.8681 } \atop {y_{2} = +0.8681 }} \right.[/tex]
Finally, the points are two:
[tex]P_{1}=(0.4961,-0.8681)[/tex]
[tex]P_{2}=(-0.4961,0.8681)[/tex]
Which expression is another way to show 9/2?
2x 1/9
2x 9/2
2 divide by 9
9 divided by 1/2
9 divided by 2
Answers
How do you do it????
Answers
The lengths of two sides of a triangle are 5 inches and 16 inches find the range of possible lengths for the third side
Answers
Answer: A2+B2=C2
(๑╹ᆺ╹ ) i hope this is right
9 students ask to visit the counselor and each visit includes one student. how many ways can they be scheduled?
Please explain, not just answer!
Answers
Multiply out 9, 8, 7, ..., 3, 2, 1 to get
9*8*7*6*5*4*3*2*1 = 362,880
(note: this concept shows up a lot in probability and counting problems, so much so that it's given a special name of "factorial")
Answer: 362880
A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?
Answers
1000 times .001 gives you 1
It's correct on apex
Answer:
The area under the curve is one.
Step-by-step explanation:
A density curve for all of the possible weights between 0 pounds and 1000 pounds is in the shape of a rectangle. What is the value of the density curve in this interval?
The area under the curve is one.
Reason
Lets draw an histogram. On the vertical axis is the frequency distribution. horizontal axis is the weights. the interval between the bars will be 1.
the height of the bars will be the frequency distribution.
we get the area of the bars by multiplying the bars width and height. add up all with the other weight.
we get 1
Pre-image ABCD is dilated to image A'B'C'D'. Squares What scale factor is used to create the dilation?
3
1/3
9
1/9
Answers
(length of image)/(length of pre-image)
Length of image=3
Length of pre-image=1
thus the scale factor will be:
scale factor=3/1=3
Answer: 3
If two people are selected at random, the probability that they do not have the same birthday (day and month) is startfraction 365 over 365 endfraction times startfraction 364 over 365 endfraction . explain why this is so. (ignore leap years and assume 365 days in a year.)
Answers
The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).
Explanation:The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.
Let's break down the process:
The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.
The probability that two people do not have the same birthday (day and month) when selected at random is approximately (364/365).
Explanation:The probability that two people do not have the same birthday (day and month) when selected at random can be calculated using the principle of complementary probability. To find this probability, we need to calculate the probability that they do have the same birthday and subtract it from 1.
Let's break down the process:
The probability that the second person does not have the same birthday as the first person is (364/365).Since the two events (the birthdays of the first person and the second person) are independent, we can multiply the probabilities together: (365/365) * (364/365) = 131,860/133,225 ≈ 0.9878.Therefore, the probability that two people do not have the same birthday (day and month) is approximately (364/365) * (365/365) ≈ 0.9878.
A dog is standing 12 feet from a tree looking at a bird in the tree. the angle of elevation from the dog to the bird is 50°. how far above the ground is the bird? round to the nearest tenth of a foot.
Answers
tan θ=opposite/adjacent
θ=50°
opposite=h
adjacent=12 ft
plugging in the values in the formula we get:
tan 50=h/12
thus
h=12tan50
h=14.301 ft
=14.3 ft
Which expressions are equivalent to the one below? Check all that apply.
8^x
A. 32^x/4
B. (32/4)^x
C. 8 * 8^x + 1
D. x^4
E. 32^x/4^x
F. 8 * 8^x-1
Answers
32/4 = 8
Let's analyze each expression:
A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻².
This expression is not equivalent to 8ˣ, so it's incorrect.
B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.
D. x⁴ is not equivalent to 8ˣ, so it's correct.
E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
So, the expressions equivalent to 8x are: B, E, and F.
Let's assess each expression:
A. (32ˣ/4) can be rewritten as ((2⁵)ˣ/(2²)) = (2⁵ˣ/2²) = 2⁵ˣ⁻². This expression is not equivalent to 8ˣ, so it's incorrect.
B. (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
C. 8 × 8ˣ⁺¹ = 8ˣ⁺¹ + 1 This expression is not equivalent to 8ˣ, so it's correct.
D. x⁴ is not equivalent to 8ˣ, so it's correct.
E. (32ˣ/4ˣ) = (32/49)ˣ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
F. 8 × 8ˣ⁻¹ = 8ˣ⁻¹⁺¹ = 8ˣ This expression is equivalent to 8ˣ, so it's correct.
So, the expressions equivalent to 8ˣ are: B, E, and F.
Complete Question:
Which expressions are equivalent to the one below? 8x
A. 32ˣ/4
B. (32/49)ˣ
C. 8 × 8ˣ⁺¹
D. x⁴
E. (32ˣ/4ˣ)
F. 8 × 8ˣ⁻¹
Your favourite Tv station has ten minutes of commercials per hour. What is the expected number of times you could randomly select this channel without hitting a commercial?
Answers
To calculate the expected number of times without hitting a commercial on your favorite TV station, divide 1 by the probability of not hitting a commercial.
Explanation:To calculate the expected number of times you could randomly select this TV station without hitting a commercial, we need to find the probability of not hitting a commercial in one selection. Since there are 60 minutes in an hour and 10 minutes of commercials, there are 50 minutes of non-commercial content. Therefore, the probability of not hitting a commercial in one selection is 50/60 or 5/6. To find the expected number of times without hitting a commercial, we can use the formula:
Expected number = 1 / Probability of not hitting a commercial
Expected number = 1 / (5/6) = 6/5 = 1.2 times
Learn more about probability here:https://brainly.com/question/22962752
#SPJ11
Answer:
5
Step-by-step explanation:
Reword the question: "Select this channel without hitting a commercial" = "How many selects until hitting a commercial"
Success (p) = hit
Failure (q) = no hit
p (probability of hitting a commercial): 10/60
q (probability of not hitting a commercial): 50/60
E(x) = q/p
E(x) = 50/60 / 10/60
E(x) = 5
Therefore, five selects without hitting a commercial
Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .
Answers
In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle.
Midpoint = [tex]( \frac{x_{1}+ x_{2} }{2}, \frac{ y_{1} + y_{2} }{2} ) [/tex]
So plug in the ordered pairs given to get:
Midpoint = [tex]( \frac{6-4}{2}, \frac{-2-4}{2}) [/tex]
Midpoint = [tex]( \frac{2}{2}, \frac{-6}{2}) [/tex]
Midpoint = (1, - 3)
This is your center.
Now for the distance between the endpoints.
Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26
So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long.
Now we plug in to the equation of a circle:
(x - h)² + (y - k)² = r²
The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r.
So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²
Which simplifies to your final answer:
(x - 1)² + (y + 3)² = 26
Anyone know this geometry question?
Answers
You rotate the 'p' 180° to the left or right to get the 'd'.
Hope this helped.
A jar of dimes and quarters is worth $4.55. If there are the same number of dimes as quarters, what is the value of only the dimes?
Answers
To find the value of the dimes in a jar with an equal number of dimes and quarters totalling $4.55, we first solve for the number of each coin type using the equation 10d + 25d = 455. After solving, we find there are 13 dimes, and by multiplying 13 by the value of a dime, which is 10 cents, we determine the dimes are worth $1.30.
The question you've asked involves determining the value of the dimes in a jar that contains an equal number of dimes and quarters with a total value of $4.55. Let's solve this step by step.
First, we need to establish the value of each coin type. A dime is worth 10 cents and a quarter is worth 25 cents. Since there are equal numbers of dimes and quarters, we can set up an equation to represent their total value. Let the number of dimes and quarters be represented by d. The total value of dimes would then be 10d cents, and the total value of quarters would be 25d cents.
The combined value of the dimes and quarters is 455 cents (since $4.55 is equivalent to 455 pennies). So, our equation would be: 10d + 25d = 455. Simplifying the equation, we get 35d = 455. Dividing both sides by 35 gives us d = 13. This means there are 13 dimes and 13 quarters in the jar.
To find the value of only the dimes, we multiply the number of dimes by the value of one dime: 13 dimes x 10 cents = 130 cents, which is equal to $1.30. Therefore, the value of only the dimes is $1.30.
Find the surface area of the cylinder in terms of .
A) 108 cm2
B) 144 cm2
C) 180 cm2
D) 216 cm2
Answers
The surface area of this cylinder in terms of [tex]\pi[/tex] is [tex]216\pi\;cm^2[/tex]
Given the following data:
Height of cylinder = 12 cm.Radius of cylinder = 6 cm.To calculate the surface area of this cylinder in terms of [tex]\pi[/tex]:
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]S.A = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]S.A = 2\pi (6)(12) + 2\pi (6)^2\\\\S.A = 144\pi+72\pi\\\\S.A = 216\pi\;cm^2[/tex]
Read more on surface area here: brainly.com/question/21367171
You get how to do this. Plzz helo me
Answers
In ΔVWX, the measure of ∠X=90°, the measure of ∠W=25°, and WX = 61 feet. Find the length of XV to the nearest foot.
Answers
The length of XV in triangle VWX is approximately 26 feet.
Explanation:To find the length of XV, we can use the trigonometric relationship in a right triangle. In triangle VWX, the measure of angle W is 25° and angle X is 90°. We can use the sine function to find the length of XV. The sine of angle W is equal to the length of the side opposite angle W divided by the length of the hypotenuse. So, we have sin(25°) = XV/61. Rearranging the equation, we get XV = 61 * sin(25°). Plugging in the values, we find that XV is approximately 26 feet.
Add. Express your answer in simplest mixed-number form.
2 3/4 + 4 3/4
Answers
= 6 6/4
= 7 2/4
= 7 1/2
(a) An angle measures 43 . What is the measure of its complement? (b) An angle measures 81 . What is the measure of its supplement?
Answers
1. By definition, Completary angles are those angles whose sum is 90 degrees and Suplementary angles are those angles whose sum is 180 degrees.
2. Keeping the information above on mind, you have:
(a) An angle measures 43 . What is the measure of its complement?
=90°-43°
=47°
(b) An angle measures 81 . What is the measure of its supplement?
=180°-81°
=99°
The answers are:
a) 47°
b) 99°
The complement of a 43-degree angle is 47 degrees, and the supplement of an 81-degree angle is 99 degrees.
To find the complement and supplement of an angle, you need to subtract the given angle from specific values. For a complement, this value is 90 degrees, and for a supplement, it is 180 degrees.
(a) To find the measure of the complement of a 43-degree angle, you subtract the angle from 90 degrees:
90 degrees - 43 degrees = 47 degreesSo, the complement is 47 degrees.
(b) To find the measure of the supplement of an 81-degree angle, you subtract the angle from 180 degrees:
180 degrees - 81 degrees = 99 degreesTherefore, the supplement is 99 degrees.
Can someone help me!!!
Answers
Answer: 7.6 units
given that f(x)=x^2+2x+3 and g(x)=x+4 over 3 solve for f(g(x)) when x=2
Answers
Hope this helps :)
How do you know if it is a adding or subtraction problem when you combine like terms?
Answers
2x + 8 - 4x
You are going to subtract 2x - 4x because there is a negative sign behind the 4x.
8y + 1 + y
You are going to add 8y + y because there is a positive sign behind the y.
4 + 2x - 5 + 7x
You are going to subtract 4 - 5 because there is a negative sign behind the 5.
You are going to add 2x + 7x because there is a positive sign behind the 7x.
What is the simplified form of \sqrt((72x^(16))/(50x^(36))) ? Assume x ≠ 0.?
Answers
sqrt(72/50) x sqrt(x^16/x^36)= sqrt(36/25) x sqrt(x^-20)= 6/5 x x^-10= 6/(5x^10)
What is 15% of 60? Create a model to prove your answer.What is 15% of 60 ?
Answers
Multiply:
0.15 × 60 = 9
Answer = 9
Hope this helped☺☺
====================================================================
SOLVING...
To find 15% of 60 just multiply 0.15 (note: 0.15 = 15%) by 60
0.15 x 60 = 9
or
15% x 60 = 9
(either way works)
====================================================================
Your Answer - 9 is 15% of 60
Find the volume of each composite figure. Round to the nearest tenth
Answers
To calculate the volume of a composite figure, individual volumes of simple geometric shapes that make up the figure are calculated using dimensionally consistent formulas and then summed up to find the total volume.
Explanation:To find the volume of a composite figure, we must analyze each part of the figure separately and then combine their volumes. Volume is a measure of how much space an object occupies and for common shapes like cylinders, prisms, and cones, there are specific volume formulas. According to the information given, dimensionally consistent volume formulas would be those where volume is calculated by combining length measurements in such a way that the result has dimensions in cubic units. For example, for a cylinder, the volume is found by multiplying the area of the base by the height (V = πr²h), which is dimensionally consistent because it's the product of an area (with units squared) with a length (with a unit), resulting in units cubed, i.e., cubic units which represent volume.
For example, if we are to find the volume of a cylinder with a radius 'r' and height 'h', we would use the formula V = πr²h, where π is approximately 3.14159. If the radius is 2 cm, and the height is 5 cm, then the volume would be V = 3.14159 * (2²) * 5 cm³, which simplifies to V = 3.14159 * 4 * 5 cm³ = 62.8 cm³, after rounding to the nearest tenth.
As per the subject of composite figures, when the figure is made of multiple simple geometric shapes, we first find the volume of each part separately and then sum them all up to get the total volume of the composite figure. Understanding the dimensional analysis principles helps identify and correct potential errors in geometric formulas by ensuring that the dimensions on either side of an equation are consistent.
To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
The formula to find the volume of a cube is V = s^3, where s is the length of the side. It is shown in the figure that the length is 8 feet. Substitute this into the formula to find the volume of the cube.
V = s^3
= (8 ft)^3
= 512 ft^3
The formula to find the volume of a cylinder is V = πr^2h, where "r" is the radius and "h" is the height of the cylinder. It is shown in the figure that the diameter of the cylinder is 8 feet and its height is 8 feet. However, we need the value of the radius, not the diameter. To find the radius, we will divide the length of the diameter by 2 since the radius is half the length of the diameter.
r = d/2
= 8/2
= 4 ft
We already solve the length of the radius. Substitute the length of the height and radius to the formula to find the volume of the cylinder.
Volume (V) = πr^2h = π(4 ft)^2(8 ft) = π(16 ft^2)(8 ft) = 128π ft^3
We have solved the volume of the cube, which is 512 ft^3, while the volume of the cylinder is 128π ft^3. To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
V = V_cube - V_cylinder
V = 512 ft^3 - 128π ft^3
V = 109.9 ft^3
If someone runs 4 miles in 30 minutes how many will they run in 48 minutes
Answers
30 minutes / 4 miles = 7.5 minutes per mile
now we know how fast they run divide the new overall time (48 minutes) by the speed (7.5 minutes) to find the number of miles they will run
48 / 7.5 = 6.4 miles
M and n are integers such that 6 < m < n. what is the value of n ?
Answers
An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.
Answers
let the dimensions be x in by x in by x in
thus
V=x×x×x
32=x³ in³
hence:
x=∛32
x=2∛2 inches
Hence the length=width=height=2∛2