Mathematics College

I need help with this problem

Answers

Answer 1

We have the following function:

[tex]H(t)=10\sin (2\pi(t-\frac{1}{4}))+15[/tex]

a) The initial height occurs at t=0. By substituting this value into the function, we get

[tex]H(0)=10\sin (2\pi(0-\frac{1}{4}))+15[/tex]

which gives

[tex]\begin{gathered} H(0)=10\sin (-2\pi\frac{1}{4})+15 \\ H(0)=10\sin (-\frac{2\pi}{4})+15 \\ H(0)=10\sin (-\frac{\pi}{2})+15 \end{gathered}[/tex]

since sin(-Pi/2) is equal to -1, we have

[tex]H(0)=-10+15[/tex]

Then, H(0)= 5, so the height is 5 feets.

b) The car will make a full rotation when the argument is shifted 2Pi:

[tex]H(t)=10\sin (2\pi(t-\frac{1}{4})+2\pi)+15[/tex]

at this point H(t) must be equal to 5 feets. Then, we have

[tex]5=10\sin (2\pi(t-\frac{1}{4})-2\pi)+15[/tex]

and we must find t. If we move +15 to the left hand side, we obtain

[tex]\begin{gathered} 5-15=10\sin (2\pi(t-\frac{1}{4})-2\pi) \\ \text{then} \\ 10\sin (2\pi(t-\frac{1}{4})-2\pi)=-10 \end{gathered}[/tex]

By moving the coefficient 10 the the right hand side, we get

[tex]\begin{gathered} \sin (2\pi(t-\frac{1}{4})-2\pi)=-\frac{10}{10} \\ \sin (2\pi(t-\frac{1}{4})-2\pi)=-1 \end{gathered}[/tex]

we can note that when

[tex]\sin \theta=-1\Rightarrow\theta=-90=-\frac{\pi}{2}[/tex]

this implies that the argument of our last result is

[tex]2\pi(t-\frac{1}{4})-2\pi=-\frac{\pi}{2}[/tex]

By moving 2Pi to the right hand side, we have

[tex]\begin{gathered} 2\pi(t-\frac{1}{4})=-\frac{\pi}{2}+2\pi \\ 2\pi(t-\frac{1}{4})=\frac{3\pi}{2} \end{gathered}[/tex]

Now, by moving 2Pi to the right hand side, we have

[tex]t-\frac{1}{4}=-\frac{\frac{3\pi}{2}}{2\pi}[/tex]

which gives

[tex]t-\frac{1}{4}=\frac{3}{4}[/tex]

so, t is given by

[tex]\begin{gathered} t=\frac{3}{4}+\frac{1}{4} \\ t=1 \end{gathered}[/tex]

That is, n 1 minute, the car will take one full rotation.

c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get

[tex]H(\frac{1}{2})=10\sin (2\pi(\frac{1}{2}-\frac{1}{4}))+15[/tex]

which gives

[tex]\begin{gathered} H(\frac{1}{2})=10\sin (2\pi(\frac{1}{4}))+15 \\ H(\frac{1}{2})=10\sin (\frac{\pi}{2})+15 \\ H(\frac{1}{2})=10(1)+15 \\ H(\frac{1}{2})=25 \end{gathered}[/tex]

that is, the maximum height is 25 feets

Related Questions

PLS HELP I WILL GIVE LOTS OF POINTS PLS HELP

Answers

Answer:

21 kilograms

Step-by-step explanation:

Every hour she produces 3 kilograms of dough. 9/3 = 3. So, in 7 hours, she can produce 21 kilograms of dough

Answer:

I want points

Step-by-step explanation:

let y=ln(x^2+y^2) determine y prime at the point -(e^4-16)^1/2

Answers

dy/dx = -2√e⁴ - 16/e⁴ - 8 is differential equation .

The meaning of a differential equation?

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics.

y = In( x² + y² )

now doing implicit differentiation

dy/dx = d/dx In( x² + y² )

dy/dx = 1/(x² + y² ) × d/dx ( x² + y² )

dy/dx = 1/x² + y² × ( 2x + 2y dy/dx)

(x² + y² )dy/dx = 2x + 2y dy/dx

dy/dx (x² + y² - 2y) = 2x

dy/dx = 2x/(x² + y² - 2y)

we need to calculate dy/dx at ( - √e⁴ - 16 , 4 )

dy/dx = [tex]\frac{2 * ( - \sqrt{e^{4} - 16} }{-\sqrt{(e^{4 - 16)^{2} }+ ( 4)^{2} - 2 * 4 } }[/tex]

dy/dx = - 2√e⁴ - 16/e⁴ - 16 + 16 - 8

dy/dx = -2√e⁴ - 16/e⁴ - 8

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the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?

Answers

Answer:

The new price of the article is $270

Step-by-step explanation:

270-240/240

x 100% = 12.5%

12.5x240/100

= 30

help meeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

find the answer to this problem (15/16) - ( -3/16)

A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8

Answers

Answer;D.
First you would do change change and it would be (15/16)+3/16,then do 15+3=18,then put it over 16,18/16,then you simplify and it would be 9/8,but you can’t have a bigger numerator over a denominator,so you would divide 9/8 and it would be 1 1/8.

Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x

Answers

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual
mean of 53.2 degrees.
Low Temperature (o F)
Frequency
40-44 45-49 50-54 55-59
1
6
9
6
The mean of the frequency distribution is
(Round to the nearest tenth as needed.)
degrees.
...
60-64
3

Answers

Answer:

7777777777777777777777770

Step-by-step explanation:

7777777777777777777777770

1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points

Answers

First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

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find all real and complex zeros for f(x)=x^3-x^2+3x-3

Answers

The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

How to determine the zeros of the function?

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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HELP ME QUICK!! I’LL MARK YOU BRAINLIEST!!
3-8. Find the distance between each pair of points if they were graphed on a number line. Represent your work
using absolute value symbols.
a. -10 and 10
b. -15 and -7

Answers

The answers were
a-21
n-23

HELP! 100 POINTS!!!
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.

Recipe A Recipe B
Sample #1 26 67
Sample #2 48 89
Sample #3 22 56

A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.

B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?

Answers

Answer:

Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.

Question B: 31% of people would prefer cookie A over cookie B

Step-by-step explanation:

What is a different common Denominator you could use in problem 2

Answers

Answer:

what is the problem ???

Step-by-step explanation:

Well we need problem 2 to know the answer

The numbers of trading cards owned by 9 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
352, 409, 424, 471, 497, 503, 515, 525, 561
Send data to calculator
Suppose that the number 561 from this list changes to 768. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
OOO
It decreases by
It increases by
It stays the same.
It decreases by .
0.
It increases by 0.
It stays the same.
X
S

Answers

The mean increases by 23 and the median stays the same.

What are the mean and median?

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.

Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561

(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]

Mean = [tex]\frac{4257}{9}[/tex]

= 473

The number 561 from this list changes to 768.

New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]

= [tex]\frac{4464}{9}[/tex]

= 496

Thus, the mean increases by 496 - 473 = 23.

(b) Median = mid value

= 497

When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.

Therefore, the mean increases by 23 and the median stays the same.

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Leroi is using coordinate geometry to prove this theorem.
Theorem: The diagonals of a parallelogram bisect one another.
Given: AD//BC; AB//CD; AC and BD intersect at M.
Prove: M bisects AC and BD.
Which of these is the BEST strategy for this proof?
A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
B) Use the equations of line AC and line BD to find the coordinates of M, then use the Distance Formula to verify that AC= BD
C) Use the equations of line AC and line BD to find the coordinates of M, then use the midpoint Formula to verify that M is the midpoint of both AC and BD
D) Use the Distance Formula to find the coordinates of M, then use the Midpoint Formula to verify that M is the midpoint of both AC and BD

Answers

The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD

How to determine the best strategy for the proof?

The theorem is given as

Theorem: The diagonals of a parallelogram bisect one another.

Also, we have the following given parameters

AD//BC; AB//CD;

AC and BD intersect at M.

The above means that:

Lines AD and BC are parallel lines, and AB and CD are parallel lines

The statement AC and BD intersect at M implies that

AM = MC and BM = MD.

The above means that we need to calculate the lengths of the above segments, and then make comparison

The lengths of the segments can be calculated using the distance formula

Other than that, the coordinate of the point M needs to be calculated

The option that satisfies the above conditions is (a)

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What is an equation in slope-intercept form for the line
perpendicular to y = 3x + 9 that
contains (-6, 3)?

Answers

An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.

What is slope-intercept form?

The most "popular" type of a straight line is one with a slope-intercept. Due to its simplicity, this is helpful to a lot of students. The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.

The equation for a line written in slope-intercept form

y = mx + b

Where,

m is the slope, and b is the y-intercept.

We know that the slope of a line perpendicular to given equation becomes reciprocal with opposite sign.

So, here slope is 3 and in perpendicular line it will become -1/3.

Now we will go with slope-intercept form and put the values (-6, 3) as x and y in y = mx + b

⇒ 3 = -1/3(-6) + b

Lets solve for b

⇒ b = 3 - ( -1/3(-6))

= 3 - (2)

= 1

Now we have the desired equation

3 = -1/3(-6) + 1

Thus, An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.

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Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.

Answers

The first unit is kilograms because the bus is really heavy.

The second is kilometers because meters are too small.

The third one is milliliters because liters are too much for ice cream.

m=85kg, a=4.29m/s^write an expression for the magnitude of the force, F

Answers

The magnitude of force is 364.65 Kg / ( m/s²)

What is force?

An influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate.

given:

m = 85 Kg

a= 4.29 m/s²

We know

Force = mass x acceleration

F= 85 x 4.29

Force = 364. 65

Hence, the magnitude of force is 364.65 Kg / ( m/s²)

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on a highway there are billboards located every 1 1/2 km there are 14 billboards in that highway how long is the highway

Answers

Answer:

1 1/2 = 3/2

3/2 x 14

= 42/2

=21

Step-by-step explanation:

Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10

Answers

As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

Then, the minute hand rotates π radians

Find the value of (-3/8) x (+8/15)

A. -1/5
B. -1/3
C. 11/15
D. 11/23

Answers

Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]

Step-by-step explanation:

Given expression

[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]

Combine the fractions

[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]

Cancel out the 8 on both the numerator and denominator

[tex]=\dfrac{-3}{ 15}[/tex]

Divide 3 on both the numerator and denominator

[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]

[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer is A. -1/5

Step by step

Multiply across and simplify

-3/8 x 8/15

-3 x 8 = -24 over 120

Simplified to -1/5

Rectangle ABCD is shown with the dimensions given in units. The length of AB is greater than the length of AD which inequality represents this situation?

A: 9x-16<1.5+42
B: 9x-16>1.5x+42
C: 10.5x<26
D: 10.5x>26

Answers

Answer:

Step-by-step explanation:

it is simple.

because AB > AD, their size representations must have the same relationship.

therefore,

9x - 16 > 1.5x + 42

that could be simplified to

7.5x > 58

The inequality that represents AB > AD is B: 9x - 16 > 1.5x + 42.

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, In Rectangle ABCD the length of AB is greater than the length of AD.

∴ The inequality that represents this is AB > AD which is,

9x - 16 > 1.5x + 42.

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What is the sum of the first 7 terms for the geometric sequence with first term 3, seventh
term 46,875, and common ratio 5?

A. 58,593
B. 19,531
C. 35,154

Answers

The sum of the first 7 terms for the geometric sequence with first term 3, seventh term 46,875, and common ratio 5 is 58,583.

A geometric progression is a sequence where each and every succeeding term is formed by multiplying the preceding term by a constant number. That constant number is called common ratio.

The common ratio is provided to be 5. While the first term is 3.

The seventh term is 46875.

The formula for sum of n terms of a GP is,

Sn = a(rⁿ-1)/(r-1)

We have to find sum of seven terms,

Sn = a(r⁶.r - 1)/(r-1)

Putting,

a = 3

r = 5

n =6

Sn = 3(5⁶.5 - 1)/(5-1)

Sn = (3.5⁶.5 - 3)/4

Sn = (46875×5 - 3)/4

Sn = (234375-3)/4

Sn = 234372/4

Sn = 58593.

The sum is 58593.

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2320 is what percent of 2000

Answers

2320 is 116% of 2000. We can do this by dividing 2320 by 2000 and then multiplying it by 100.

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)

Answers

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Maximum height

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?

Answers

In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.

To determine what is the least common multiple number you proceed as follow:

You list different multiples of each number 14 and 10.

For 14: 14 28 42 56 70 84 98 112

For 10: 10 20 30 40 50 60 70 80

The least common multiple is 70, becasue is the first common number in each list.

Hence the 70th person in the line will win both prizes.

[tex]3-\sqrt{x} 5[/tex]

Answers

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1