Find the absolute maximum and minimum values of the following function on the given interval. f(x)=3x−6cos(x), [−π,π]

Answers

Answer 1

Answer:

Absolute minimum: x = -π / 6

Absolute maximum: x = π

Explanation:

The candidates for the absolute maximum and minimum are the endpoints and the critical points of the function.

First, we evaluate the function at the endpoints.

At x = -π, we have

[tex]f(-\pi)=3(-\pi)-6\cos (-\pi)[/tex][tex]\Rightarrow\boxed{f(-\pi)\approx-3.425}[/tex]

At x = π, we have

[tex]f(\pi)=3(\pi)-6\cos (\pi)[/tex][tex]\Rightarrow\boxed{f(\pi)\approx15.425.}[/tex]

Next, we find the critical points and evaluate the function at them.

The critical points = are points where the first derivative of the function are zero.

Taking the first derivative of the function gives

[tex]\frac{df(x)}{dx}=\frac{d}{dx}\lbrack3x-6\cos (x)\rbrack[/tex]

[tex]\Rightarrow\frac{df(x)}{dx}=3+6\sin (x)[/tex]

Now the critical points are where df(x)/dx =0; therefore, we solve

[tex]3+6\sin (x)=0[/tex]

solving for x gives

[tex]\begin{gathered} \sin (x)=-\frac{1}{2} \\ x=\sin ^{-1}(-\frac{1}{2}) \end{gathered}[/tex]

[tex]x=-\frac{\pi}{6},\; x=-\frac{5\pi}{6}[/tex]

on the interval [−π,π].

Now, we evaluate the function at the critical points.

At x = -π/ 6, we have

[tex]f(-\frac{\pi}{6})=3(-\frac{\pi}{6})-6\cos (-\frac{\pi}{6})[/tex][tex]\boxed{f(-\frac{\pi}{6})\approx-6.77.}[/tex]

At x = -5π/6, we have

[tex]f(\frac{-5\pi}{6})=3(-\frac{5\pi}{6})-6\cos (-\frac{5\pi}{6})[/tex][tex]\Rightarrow\boxed{f(-\frac{5\pi}{6})\approx-2.66}[/tex]

Hence, our candidates for absolute extrema are

[tex]\begin{gathered} f(-\pi)\approx-3.425 \\ f(\pi)\approx15.425 \\ f(-\frac{\pi}{6})\approx-6.77 \\ f(-\frac{5\pi}{6})\approx-2.66 \end{gathered}[/tex]

Looking at the above we see that the absolute maximum occurs at x = π and the absolute minimum x = -π/6.

Hence,

Absolute maximum: x = π

Absolute minimum: x = -π / 6


Related Questions

Polynomial Functions:Find P(-1) and p(2) for each function.“P(x) = 4-3x”

Answers

[tex]P(x)=4-3x[/tex]

P(-1):

[tex]\begin{gathered} P(-1)=4-3(-1) \\ P(-1)=4+3 \\ P(x)=7 \end{gathered}[/tex]

P(2):

[tex]\begin{gathered} P(2)=4-3(2) \\ P(2)=4-6 \\ P(2)=-2 \end{gathered}[/tex]

work out sues total pay

Answers

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

What is the total pay?

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

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We have seen the isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use information to the right to help the measure of angles 1, 2, 3, 4, and 5.

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

triangle diagram

Step 02:

angles:

we must analyze the diagram to find the solution

angle 1:

angle 1 = 180° - 155° = 25°

angle 2:

angle 2 = angle 1 = 25°

angle 3:

angle 3 = 180° - 25° - 25° = 130°

angle 4:

angle 4 = 155°

angle 5:

angle 5 = 180° - 25° = 155°

That is the full solution.

Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)

Answers

Given:

[tex]\sqrt{100}-\sqrt{64}[/tex]

To find:

We need to solve this sum and find the final answer

Step-by-step solution:

To solve this problem, we need to know the square root of 100 and 64.

√100 = 10

√64 = 8

[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]

Final answer:

Thus 2 (Option A) is the correct answer.

write an equation of each parabola in vertex form. Vertex (3,-2) Point (2,3)

Answers

The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .

The equation of parabola with vertex (h,k) is denoted by the equation

y = a(x-h)² + k

In the question ,

it is given that

the vertex of the Parabola is (3,-2) and the point is (2,3)

So, the equation of the parabola with vertex (3,-2) will be

y = a(x-3)² - 2

Since the point (2,3) lies on the parabola ,

So, 3 = a(2-3)² - 2

3 + 2 = a*(-1)²

5 = a

Substituting a in the equation  y = a(x-3)² - 2 ,

we get

y = 5(x-3)² - 2

Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .

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what is the y intercept of y = 250 + 15x

Answers

The y-intercept of y = 250 + 15x is (0,250)

What is y-intercept?

A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

Here to determine the y-intercept put x=0,

Given, y = 250 + 15x

Replacing x by 0 in the above equation we get,

y = 250 + 15×0

y=250 +0

y=250

Therefore, the y-intercept of y = 250 + 15x is (0,250)

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On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(t/2)a) Define a new function, a′(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).

Answers

a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:

[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]

b) the derivative of a(t) is the following:

[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]

c) the critical values of a(t) over the interval [0, 24) are:

[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]

A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet
per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=1612 +32t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?

Answers

You have to find the vertex.

Find X of the vertex by using -b/2a

Then take X and plug back into equation for y.

X= time
Y= height

Equation makes a parabola that opens down.

Fill in the missing statements and reasons in each proof shown below. You must mark the diagram forcredit.15.Given: g | h and 21 22Prove: p | r3рStatementReason2.ghgh21 2 2321 2222 223pllr

Answers

To prove that p || r, we will complete the data in the given table

[tex]\begin{gathered} \text{Statement: g}\mleft\Vert h\mright? \\ R\text{eason : Given} \end{gathered}[/tex]

[tex]\begin{gathered} \text{Statement: <1}\cong<3 \\ \operatorname{Re}\text{ason: Corresponding angles} \end{gathered}[/tex]

[tex]\begin{gathered} \text{Statement: <1}\cong<2 \\ \operatorname{Re}\text{ason:Given} \end{gathered}[/tex]

[tex]\begin{gathered} Statement\colon\text{ <2}\cong<3 \\ Re\text{ason: Alternate exterior angle} \end{gathered}[/tex]

[tex]\begin{gathered} \text{Statement: P}\mleft\Vert r\mright? \\ \operatorname{Re}\text{ason:<2}\cong<3 \end{gathered}[/tex]

Please help! I have 3 questions that I'm not sure what to do about :( if you could answer them that would be great

Answers

The resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

What is a Matrix?

Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].

Given are the three different matrices as -

A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]

C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]

We can solve the given expressions as follows.

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Therefore, the resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

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8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?

Answers

Explanation:

If she spent $28 of the $50 she withdrew, she now has:

[tex]50-28=22[/tex]

$22

The fraction is:

[tex]\frac{22}{50}=\frac{11}{25}[/tex]

Answer:

Anna has 11/25 of her money left.

Hello, I really need help on this assignment I don't understand what to do.

Answers

Answer:

-2 and -10

Explanation:

There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.

So, the number that is 4 units to the right is equal to

-6 + 4 = -2

And the number that is 4 units to the left is equal to

-6 - 4 = -10

Therefore, the numbers are -2 and -10 and they are represented as

The fraction models below represent two fractions of the same whole: How much of the8음을16

Answers

[tex]\begin{gathered} \frac{5}{8}x=\frac{1}{2} \\ x=\frac{1}{2}\times\frac{8}{5}=\frac{4}{5} \end{gathered}[/tex]

So 4/5 times 5/8 is 1/2.

(a) Teresa owns 9 shares of a certain stock. Yesterday the total value of her shares went down by90 dollars. What was the change in value for each share?dollarsHelp ASAP PLEASE

Answers

we have that

Divide $90 by the number of shares

so

90/9=$10

the answer is $10

I need help with this question... it's about special triangles and I need to find y and z.. it should also not be a decimal.

Answers

To find z, consider the right-angled triangle at the botton in the diagram showm

[tex]\begin{gathered} \sin 45\text{ = }\frac{z}{20} \\ z\text{ = 20 }\sin 45 \\ z\text{ = }20\text{ }\times\frac{1}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ z\text{ = }\frac{20\sqrt[]{2}}{2} \\ z\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]

Let the common base of both triangles be m

[tex]\begin{gathered} \cos 45\text{ = }\frac{m}{20} \\ m\text{ = 20 }\cos 45 \\ m\text{ = }\frac{20}{\sqrt[]{2}} \\ m\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ m\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]

To find y:

[tex]\begin{gathered} \tan 30\text{ = }\frac{y}{m} \\ \tan 30\text{ = }\frac{y}{10\sqrt[]{2}} \\ \frac{1}{\sqrt[]{3}}=\text{ }\frac{y}{10\sqrt[]{2}} \\ y\text{ = }\frac{10\sqrt[]{2}}{\sqrt[]{3}} \\ y\text{ = }\frac{10\sqrt[]{6}}{3} \end{gathered}[/tex]

To find x:

[tex]\begin{gathered} \sin 30=\frac{y}{x} \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\div x \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\times\frac{1}{x} \\ x\text{ = }\frac{20\sqrt[]{6}}{3} \end{gathered}[/tex]

22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale

Answers

SOL

Step 1 :

In this question, we are meant to find the value of

the hypotenuse in the right angle below:

Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Step 2 :

From the above theorem, we can see that that the two adjacent sides are :

14 inches and 48 inches.

From the principle of Pythagoras' Theorem,

[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]

CONCLUSION :

The value of the hypotenuse in the Right angle, c = 50 inches.

Send me Answers for Questions A, B, and C

Answers

Answer: A) 4 B) 30 C) 6

Step-by-step explanation:

For question A, you subtract the highest number and the lowest number (10-6)

For question B, you add all the frequency numbers together

For question C, you use your answer on B and divide it by 5

An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. The envelope is __ centimeters tall.

Answers

An envelope is rectangular in shape.

Given the width = 15cm, and diagonal = 17cm

Let h represent the tall length of the envelope

Applying Pythagoras theorem, we have

[tex]\begin{gathered} 17^2=15^2+h^2 \\ 289=225+h^2 \\ h^2=289-225 \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8\operatorname{cm} \end{gathered}[/tex]

The envelope is 8cm tall

what property is used to solve this?

4x-3

x=2

4(2)-3

Answers

commutative property

Which values are solutions to the inequality below?Check all that apply.√x ≤ 5A. 1B. 18C. -5D. 25E. 24F. 625

Answers

Given the inequality:

[tex]\sqrt[]{x}<5[/tex]

We need to solve the inequality to get a range of values for x.

This we can do by finding the square of both sides:

[tex]\begin{gathered} (\sqrt[]{x})^2<5^2 \\ x<25 \end{gathered}[/tex]

On checking the options given, we will pick the numbers that are strictly less than 25.

Therefore, the correct options are:

OPTION A

OPTION B

OPTION C

OPTION F

J(-6-2)3-*NWMark this and return2--9-8-7-6-5-4-3-2-3₁ 1 2 3 4 5 61-5737-2-cd-6--7--8-2 do-9--10--11--12--13-8 9 10 11 xK(8,-9)What is the x-coordinate of the point that divides thedirected line segment from J to K into a ratio of 2:5?X == (m²²7 m )(x₂ − ×₁) + X₁m+n0 000-22Save and ExitNextSubmit

Answers

Use the given formula:

[tex]x=(\frac{m}{m+n})(x_2-x_1)+x_1[/tex]

Being m: 2 and n: 5

x1: -6

x2: 8

[tex]\begin{gathered} x=(\frac{2}{2+5})(8-(-6))+(-6) \\ \\ x=\frac{2}{7}*(14)-6 \\ \\ x=4-6 \\ \\ x=-2 \end{gathered}[/tex]Then, the x-coordinate of th point that divides the directed line segment from J to K into a ratio 2:5 is -2Answer: -2

Four points are labeled on the number line. M K L zo 0.5 1 Which point best represents 3? F. Point K G. H. Point 2 Point M Point N J.

Answers

The point that best represents 1/3 is point M .

The number line ranges from 0 to 0.5 with 10 divi

In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence

Answers

Given:

[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]

To find:

The value of n.

Explanation:

The nth term formula for the arithmetic sequence is,

[tex]a_n=a_1+(n-1)d[/tex]

Substituting the given values we get,

[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]

Thus, -24 is the 4th term of the sequence.

Final answer:

The term -24 is the 4th term of the sequence.

I am struggling with this question. could you help me please??

Answers

Problem

Solution

Let x = age, W= weight the two variables of interest

We have the following probabilities given:

P(x<37) =0.142

P(W< 2500) = 0.051

P(x <37 AND W<2500)= 0.031

And we want the following probability and we can use the total probability rule:

P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)

If we replace we got:

P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162

Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A?

Answers

1) Let's sketch this out to better grasp it

2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines:

[tex]undefined[/tex]

Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?

Answers

We have the correct statement about the vectors in the graph.

We can already see that it is a sum of vectors like:

[tex]v+w=u[/tex]

As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:

[tex]v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}[/tex]

As w starts at (3, 3) and ends on (5, 2), we can describe it as:w

[tex]w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}[/tex]

Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:

[tex]u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}[/tex]

Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].

compare and contrast the graphs y=2x+1 with the domain {1,2,3,4} and y=2x+1 with the domain of all real numbers

Answers

Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

As given in the question,

Given function for the graphs are:

y =2x+1

Different domains

Domain ={1,2,3,4}

Domain =All real numbers

Compare with y=mx +c

Slope m =2

For y-intercept put x=0

y=2(0) +1

 =1

For x-intercept put y=0

0 =2x+1

⇒x=-1/2

Contrast:

For domain ={1,2,3,4}

Range is :

y = 2(1)+1

  =3

y=2(2)+1

 =5

y=2(3) +1

 =7

y=2(4)+1

 =9

Range ={ 3, 5, 7,9}

For domain= all real numbers

Range = set of all real numbers

Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Solve the inequality and describe the solution set.y-6 > 1232, Math symbolsRelations► Geometry► Groups► Trgonometry3 of 3 AnsweredType here to searcho66F Mosty clou

Answers

The problem gives the inequality:

[tex]y-6\ge12[/tex]

solving for y we get:

[tex]\begin{gathered} y\ge12+6 \\ y\ge18 \end{gathered}[/tex]

The solution set is all real numbers equal or greater than 18, i.e.,

[tex]\lbrack18,+\infty)[/tex]

I will show you a pic

Answers

GIven the table above :

We have that

x y

2 8

4 4

6 0

8 4

The table represents a Non - Linear Function

Reason: It is because there is no constant ratio or proportion between x and y.

SOMEONE PLEASE HELP ME QUICKLY WITH THIS,ITS AN EMERGENCY!!!!! pls explain how you get the solution as well, sorry!

Thank you <3

Answers

The statement that reflects the running rates is Pepe ran 9/8  mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.

What is the speed?

Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.

Speed = distance / time

Speed if Paul ran 1/5 mile in 4/15 hour

Speed = 1/5 ÷ 4/15

1/5 x 15/4 = 3/4 miles per hour

Speed if Pepe ran 8/10 mile in 1/4 of an hour

Speed = 8/10 ÷ 1/4

8/10 x 4 = 16/5 = 3 1/5 mile per hour

Difference in speeds =

[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]

Speed if Paul ran 4/15 mile in 1/5 hour

Speed = 4/15 ÷ 1/5

4/15 x 5 = 4/3 = 1 1/3 miles per hour

Speed if Pepe ran 1/4 mile in of 8/10 an hour

Speed = 1/4 ÷ 8/10

1/4 x 10/8 = 5 / 16

Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]

Speed if Paul ran 1/3 mile in 19/24 hour

Speed = 1/3 ÷ 19 / 24

1/3 x 24/19 = 8/19 miles per hour

Speed if Pepe ran 1/2 mile in of 9/8 an hour

Speed = 1/2  ÷ 9/8

1/2 x 8/9 = 4/9 mile per hour

Difference = 4/9 - 8/19 = 4/171

Speed if Pepe ran 9/8  mile in 1/2 hour

Speed = 9/8 ÷ 1/2

9/8 x 2 = 2 1/4  miles per hour

Speed if Paul ran 19 / 24 mile in of 1/3 an hour

Speed =  19 / 24  ÷ 1/3

19 / 24 x 3 = 2 3/8 miles per hour

Difference =

[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]

[tex]\frac{3 - 2}{8}[/tex] =  [tex]\frac{1}{8}[/tex] miles per hour

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If a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2.+224t Find the maximum height of the projectile. Louis borrowed $500 from his bank. His bank will charge Louis 8% simple interest per year to loan him the money. If he paid back the total amount he owed the bank, including interest, in 6 months, how much should he have paid? this painter worked for aristocrats, royalty, and many churches in europe. his images were sensual and he employed a loose brushwork that influenced many painters of the time. who was he? Hi, the area of a circle is 100 sq. mm. The radius is 5.64 mm. What is the circumference? Pistil of the flower how do you solve for -2x + 6y = 18 mary alice just won the lottery and is trying to decide between the options of receiving the annual cash flow payment option of $250,000 per year for 25 years beginning today, or receiving one lump-sum amount today. mary alice can earn 6% investing this money. at what lump-sum payment amount would she be indifferent between the two alternatives? If f(2)= Vwhat is the rule of the inverse? Find all the factors of 99. when one mole of caffeine(c8h10n4o2)is burned in air 4960 kj of heat is released. 5.00g of caffeine is burned in a bomb calorimeter. the temperature is observed to increase by 11.37oc. what is the heat capacity of the calorimeter in kj/oc? f(x) varies inversely with x and f(x)=10 when x = 20. What is the inverse variation equation? Responses f(x)=2x f ( x ) = 2 x f(x)=5x f ( x ) = 5 x f(x)=200x f ( x ) = 200 x f(x)=0.5x f ( x ) = 0.5 x a team asked to manage an entire line of products including making decisions about products to produce, managing the production of the product lines, marketing them, and staffing their division, is given which kind of task? an appliance manufacturer has partnered with a non-governmental organization dedicated to rebuilding used consumer products for communities in developing economies that need safe and reliable household goods. as a result of this collaboration, the manufacturer has redesigned its appliances to include post-consumer recycled plastics from developing nations, to reduce their landfill waste while providing for their basic needs. which element of sustainability does this best describe? You are playing a game that uses two fair number cubes. If the total on the number cubes is either 6 or 10 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your answer asa percent. If necessary, round your answer to the nearest tenth.O 1.2%O 13.9%O 77.8%O 22.2% y=-5x+6y=-3x-2x=y= and the grap What was the initial population at time t=0?Find the size of the bacterial population after 4 hours. Cleo can paint a room in 8 hours, while Phil can paint the same room in 6 hours. If they paint theroom together, how long will it take them to paint the room?How many hours and how many minutes? Suppose the supply chain for a clothing industry is as follows: raw materials > parts manufacturing > final assembly > retailer > customer if a final assembly company wants to expand into the manufacturing industry, it is pursuing which integration? Determine whether the lines are parallel, intersect, or coincideY = 4x - 53x + 4y = 7 The Swiss are a polyglot people; it is not unusual for a Swiss to speakGerman, French, English, and Italian.a. a commonplace b. a memorable c. a multilingual d. an absurd.