The height, above the ground, of a block on a vertical spring is a sinusoidal (trigonometric) function of time. In the interval from time 2.1 seconds to time 2.7 seconds, the block's height decreases from its maximum of 48 inches to its minimum of 30 inches. Which function h(t) could model the block's height in inches above the ground at time t seconds?
Answers
The cosine function that could model the block's height in inches above the ground at time t seconds is:
h(t) = 9cos(1.67π(x - 2.1)) + 39.
What is the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2pi/B.c: phase shift.d: vertical shift.In this problem, we have that the maximum value is of 48 and the minimum value is of 30(difference of 18), hence the amplitude is given as follows:
2a = 18
a = 9.
A standard cosine function with amplitude 9 would vary the between -9 and 9, while this one varies between 30 and 48, hence the vertical shift is of d = 39.
The minimum and maximum values form half the period, hence:
π/B = 2.7 - 2.1
B = π/0.6
B = 1.67π.
The maximum value in the standard function is at x = 0, while at this function is at x = 2.1, hence the phase shift is of 2.1 units to the right, that is, c = -2.1.
Hence the cosine function is:
h(t) = 9cos(1.67π(x - 2.1)) + 39.
This function is graphed at the end of the answer, showing that the minimum and the maximum values are as desired.
More can be learned about cosine functions at brainly.com/question/21558626
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Related Questions
What is the slope of the line that passes through the points (–20, 18) and (30, 14)? Negative StartFraction 25 Over 2 EndFraction Negative five-halves Negative two-fifths Negative StartFraction 2 Over 25 EndFraction.
(100 Points)
Answers
Answer: Negative Start Fraction 9 over 4 EndFraction divided by (negative two-thirds)
or
-9/4 / -2/3
which is basically d if your confused
Step-by-step explanation:
Took the test and got it right
Answer:
The answer is D. 2 Over 25
Step-by-step explanation:
Congressional Terms Below is given the summary from
112th Congress of Senators whose
terms end in 2013, 20.
2017.
2015
20
15
CAPPARE
PRESENTADAL
SCHED
2013
Democrat
21
Republican 8
Choose one of these Senators at random and find
a. P(Democrat and term expires in 2015)
b. P(Republican or term expires in 2013)
c. P(Republican given term expires in 2017)
2017
Answers
The answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.A table is drawn according to the given information.
(Refer to the table below)
So,
let d be the event that the person is a Democrat.let r be the event that the person is republican.let 2013 be the event that the person retires 2013.let 2015 be the event that the person retires 2015.let 2017 be the event that the person retires in 2017.From the table:
p(d) = 42 / 78 because there are 42 democrats out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(r) = 36 / 78 because there are 36 republicans out of a total of 78 senators who retired in either 2013 or 2015 or 2017.p(2013) = 29 because there are 29 senators who retired in 2013 out of a total of 78 senators who retired in all 3 yearsp(2015) = 35 because there are 35 senators who retired in 2015 out of a total of 78 senators who retired in all 3 years.p(2017) = 14 because there are 14 senators who retired in 2017 out of a total of 78 senators who retired in all 3 years.Then,
Our universe is 78 senators who retired in all 3 years (2013, 2015, 2017).
42 are democrats and 36 are republicans.29 retired in 2013 and 35 retired in 2015 and 14 retired in 2017.(A) From the table, we can see that there are 20 democrats who retired in 2015.
p(d and 2015) = 20/78.(B) This one is asking for p(r or 2013)
The formula to use here is p(r or 2013) = p(r) + p(2013) - p(r and 2013).
From the table, we can see that:
p(r) = 36/78p(2013) = 29/78p(r and 2013) = 8So, p(r or 2013) is equal to p(r) + p(2013) - p(r and 2013) which is equal to 36/78 + 29/78 - 8/78 = 57/78.
(C) This is one is asking for p(r given 2017).
The formula to use here is p(r given 2017) = p(r and 2017) / p(2017).
From the table, you can see that:
p(2017) = 14/78p(r and 2017) = 13/78So, p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) = 13/14.
(D) if they were independent, then p(r and 2017) would be equal to p(r) * p(2017).
Therefore p(r given 2017) would be equal to p(r and 2017) / p(2017) which would be equal to p(r) * p(2017) / p(2017) which would be equal to p(r).From the table, you can see that p(r) = 36/78.From the table, you can see that p(r and 2017) = 13/78) and p(2017) = 14/78.Therefore p(r given 2017) = p(r and 2017) / p(2017) = (13/78) / (14/78) which is equal to 13/14 which is not equal to p(r) = 36/78Therefore the two events are not independent.Therefore, the answers to all the subparts are:
(A) P(Democrat and term expires in 2015) = 20/78(B) P(Republican or term expires in 2013) = 57/78(C) P(Republican given term expires in 2017) = 13/14(D) The two events are not independent.Know more about the random selection here:
https://brainly.com/question/24466382
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The complete question is given below:
Congressional Terms Below is given the summary from
112th Congress of Senators whose
terms end in 2013, 20.
2017.
2015
20
15
CAPPARE
PRESENTADAL
SCHED
2013
Democrat
21
Republican 8
Choose one of these Senators at random and find
a. P(Democrat and term expires in 2015)
b. P(Republican or term expires in 2013)
c. P(Republican given term expires in 2017)
d. Are the events “Republican” and “term expires in 2015” independent? Explain.
Explain how to find 27% of 16 using multiplication by
decimal. Then explain how to use estimation to chec
your answer.
Answers
Answer:
4.32
Step-by-step explanation:
You can multiply 16 by 0.27 to get the answer.
16*0.27=4.32
You can check your work with estimation because 27% is about 1/4 of the number, and just by looking at the number, 4 is 1/4 of the number.
Answer:
4.32
Step-by-step explanation:
Convert 27% to the equivalent decimal 0.27. Multiply 16 by 0.27 to get 4.32. Use estimation to check the answer by choosing the friendly percent 25%. 25% of 16 is equal to 16 ÷ 4 = 4. The answer is reasonable.
Convert 27% to the equivalent decimal 0.27.
Multiply 16 by 0.27 to get 4.32.
Use estimation to check the answer by choosing the friendly percent 25%.
25% of 16 is equal to 16 ÷ 4 = 4. So the answer is reasonable.
1. The vapour density of ethyl alcohol vapour is (C,H,OH)
D 22
Answers
A package of 8 notebooks cost $5. How much will 24 notebooks cost?
О.
Oь
Ос
12
15
10
Answers
Answer: B: 15
Step-by-step explanation:
(-1,1)becames? (0,0)becomes?(1,1)becomes?
Answers
Answer:
(-1,1) becames 0, (0,0) becomes 0, (1,1) becomes 2
Trust Onepunchman (and maybe brainlist if I get it right)
Three limes weigh 4.28 ounces,4.82 ounces and 2.85 ounces.What is the difference between the weight of the heaviest lime and the lightest lime,Show your work
Answers
Answer:
The difference is 1.43oz.
Step-by-step explanation:
4.28 - 2.85 is 1.43.
During a particular football game, the Chicago Bears made 17, 3, -6, 32, -11 yards. What was the total gain or loss made by the team? Please indidate whether it was a gain or loss along with the yards. (Note a positive number would be a gain and a negative number would be a loss
Answers
Answer:
Step-by-step explanation:
Line g is dilated by a scale factor of 3 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related? coordinate plane with point E at negative 4 comma 0 and point F at 0 comma 2, line g intersects points E and F The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' intersect at point F. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related. The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Answers
Dilation involves changing the size of a shape.
The true statement is that the locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
The given parameters are:
[tex]k =3[/tex] --- the scale factor
[tex]E = (-4,0)[/tex]
[tex]F =(0,2)[/tex]
Multiply the coordinates of point E and F by the scale factor (k), to determine the new coordinates of E and F.
[tex]E' = E \times k[/tex]
[tex]E' = (-4,0) \times 3[/tex]
[tex]E' = (-12,0)[/tex]
[tex]F' = F \times k[/tex]
[tex]F' = (0,2) \times 3[/tex]
[tex]F' = (0,6)[/tex]
Given that line g is represented by points E and F; line g' would be represented by points E' and F'
So, both lines would be parallel.
Hence, the true option is (d)
Read more about dilation at:
https://brainly.com/question/3457976
Answer:
The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Step-by-step explanation:
a plant measured x inches tall this week
Answers
Yeah not sure what is your question?
3 bananas cost $0.99. At this rate, how much do 5 bananas cost?
Answers
Answer:
$1.65
Step-by-step explanation:
first i divided 0.99 by 3, equalling 0.33. i then multiplied 5 times 0.99 to equal 1.65.
In analyzing this diagram, which statement represents a crucial step to proving the pythagorean theorem using this diagram?
A) The large square on the left contains two smaller squares
B) The large square on the right contains a smaller square with side length c
C) The perimeter of the blue square is equal to the perimeter of the yellow square.
D) Recognize that BOTH of the large squares contain 4 right triangles with base a and height b
Answers
Answer:
D: recognize that BOTH of the large squares contain 4 right triangles with base a and height b
Step-by-step explanation:
The following is a listing of the amount of sugar in six popular snacks found on a high school campus:
34g 34g 42g 50g 52g 58g
What is the median?
Answers
Answer:
The median is 46 g
Step-by-step explanation:
The median of a data set is the middle value. Since there are six snacks, which is an even number, you can't pick out a single middle value. Instead, to get the middle value you have to add the middle 2 numbers together and then divide them by 2 for the median.
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent. From 67 to 75
Answers
Answer:
Increase 11.94 %
Step-by-step explanation:
In my bingo game you have to match 3 balls to win.
20 balls are drawn from a 60 ball total.
I’m able to deduce that I have a 1 / 34,220 chance of winning.
However, I win more like 1 / 100 attempts.
Please identify where my maths is going wrong:
My maths:
For the first ball there are 60 options.
For the second ball there are 59 options.
For the third ball there are 58 options.
I need to multiply these 3 options:
60 x 59 x 58 = 205,320
1 / 205,320.
However, the order of the numbers doesn’t matter, so we’ll exclude permutations from the total combinations:
Permutations = 3! = 3x2 = 6
205,320 / 6 = 34220
So to win a this game I have a 1 / 34,220 chance.
Why then am I winning 1/100 attempts? Something is very wrong.
Answers
Using the hypergeometric distribution, it is found that you are going to win approximately 3.33% of the time. The reason for the difference is that you considered that only 3 balls would be drawn, and not 20.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the parameters are given as follows;
N = 60, k = 3, n = 20.
You win if you have the 3 correct balls, hence the probability is P(X = 3), found as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,60,20,3) = \frac{C_{3,3}C_{60,20}}{C_{60,20}} = 0.0333[/tex]
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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Mark has $5,272.56 in an investment account. On Monday, the account earned $26.74. On Tuesday, the account lost $38.63.
What is the value of Mark's investment account after Tuesday?
Answers
5,260,67 because I used the calculator
Given x=1/2 and y=-x, what is the value of x-y
Answers
Answer:1
Step-by-step explanation:x=1/2 , y =-1/2
X-y = 1/2-(-1/2)=1
Answer:
x-y = 1
Step-by-step explanation:
Question: Given x = 1/2 and y = -x, what is the value of x - y?
Step-by-step:
We know that x = 1/2 and y = -x but we need to find out what -x is equal to.
To find the value of -x, we need to multiple -1 on both sides of the equation: x = 1/2
(You can think of it like -1 acts like an invisible number)
x*-1 = 1/2*-1 which is -x = -1/2
Since y is equal to -x, y = -1/2
We need to find x - y which is 1/2 - (-1/2)
Because the negative and subtraction signs cancel out, we add instead. The equation becomes 1/2 + 1/2
One half + half = 1
Therefore, x-y = 1
Which of the following are partial products for 43 × 17? Choose all that apply.
Answers
Answer:
21
400
Step-by-step explanation:
Plz HELP BRAINLIEST IF CORRECT IM KINDA IN A RUSH PLZ HELP ;)
Answers
Answer:
0.5 quarts of orange juice per quart of punch
Step-by-step explanation:
1.5/3=0.5
Answer:
0.5
Step-by-step explanation:
Since 1.5 quarts are required for 3 quarts you need to divide 1.5 and 3.
1.5 ÷ 3 = 0.5
A truck driver is carrying eleven bills. Some of the bills are
$10 bills (x), and some are $5 bills (y). Together, the bills
total $85. How many $10 bills does she have?
Answers
Answer:
6 ten-dollars bills
Step-by-step explanation:
x + y = 11
10x + 5y = 85
5( x + y ) = 5(11)
5x + 5y = 55
10x + 5y = 85
-5x + 0 = -30
x = 6
Does 400000 equal 4*10 to 6 power
Answers
Answer:
yes!
Step-by-step explanation:
Answer:
No.. 4×10^6 is 4000000
..........
A new process for producing a type of novolac resin is supposed to have a mean cycle time of 3.5 hours per batch. Six batches are produced, and their cycle times, in hours, were 3.45 3.47 3.57 3.52 3.40 3.62. Can you conclude that the mean cycle time is greater than 3.5 hours
Answers
Answer:
Yes, the mean cycle time is greater than 3.5 hours
Step-by-step explanation:
Let us try to calculate the mean cycle time here. Consider the given cycle times. To obtain the mean cycle time, we have.
3.45 + 3.47 + 3.57 + 3.52 + 3.40 + 3.62/6 = 3.505 hours
Hence the difference 3.505 -3.5 = 0.005
Hence mean cycle time is greater than 3.5 by 0.005
What is the slope of the equation of a line that passes through the point
(10, 4) and has a y-intercept of -4?
Answers
Answer:
y = 0.8x – 4
or
y = 4 /5x- 4
Step-by-step explanation:
the slope is 4/5 or 0.8 either one work :)
Help meeeeeeeeereeeeeeeeeeeeeeeeeeeeeee
Answers
but i’m not sure cause i’m not learning what your learning.
A credit card company charges 22% interest fee on any charges not paid at the end of the month.. If the bill totals $450 for this month, how much interest would you have to be paid on the balance?
Answers
Answer:
B
Step-by-step explanation:
Because
I WILL GIVE BRAINLIST IF THE ANSWER IS RIGHT
state of these are like terms or a pair of terms
-6x, 10x
3y,6z
1/4k, 0.5k
Answers
Answer:
Pair of terms
Step-by-step explanation:
This is for Geometry.
If it is blurry Zoom in.
Please helps me, Thx!
Answers
Answer:
Altitude - a segment drawn from the vertex perpendicular to the other side (also called the height).
Given f(x) = -8 + 1, find f(5)
Answers
Answer:
im guessing its actually -8x +1, so
-8 (5) +1
-40 +1
-39
Determine weather the following graph represents a function
Answers
Answer:
it doesn't because there are places where there are two y values which just doesn't work out.
100 points if you can get this correct what is the 10nth of 800 then what is the 800th of the tenth score that=43565
Answers
Answer:
43565?
what kind of math is this?
Step-by-step explanation:
Answer:
76970
Step-by-step explanation: