A rectangle has a perimeter of 100 inches, and

one side has length x. Express the area of the

rectangle as a function of x.


Use the function in part a to find the dimensions of the rectangle with permitter 100 inches and the largest possible area

Answers

Answer 1

Answer:

a. A = 50x - x² b. length = 25 inches and width = 25 inches and the maximum area is 625 in²

Step-by-step explanation:

a. The perimeter of a rectangle P = 2(L + W) where L = length and W = width. Now, given that P = 100 inches and W = x, substituting these into the equation, we have

P = 2(L + W)

100 = 2(L + x)

dividing both sides by 2, we have

100/2 = L + x

50 = L + x

making L subject of the formula, we have

L = 50 - x

Now, the are of a rectangle A = LW. Substituting the values of L and W, we have

A = LW

A = (50 - x)x

A = 50x - x²

b. To find the largest possible area of rectangle with perimeter 100 inches, we differentiate A and equate it to zero to find the value of x that maximizes A.

So, dA/dx = d(50x - x²)/dx

dA/dx = d50x/dx - dx²/dx

dA/dx = 50 - 2x

dA/dx = 0 ⇒ 50 - 2x = 0

50 = 2x

dividing both sides by 2, we have

x = 50/2

x = 25

To find it this gives maximum value for A, we differentiate A twice.

d²A/dx² = d(50 - 2x)/dx

d²A/dx² = d50/dx - d2x/dx

d²A/dx² = -2

Since d²A/dx² = -2 < 0, so x = 25 gives maximum value for the area, A.

Since W = x = 25 in and L = 50 - x. So, L = 50 - 25 = 25 in

So, the maximum area A = LW = Lx = 25 in × 25 in = 625 in²

The dimension with perimeter 100 inches that give maximum area are length = 25 inches and width = 25 inches and the maximum area is 625 in²


Related Questions

how would you solve p-11=-14

Answers

Answer:

Step-by-step explanation:

all you would need to do is add 11 to both sides, and then you would get your answer.

The product of a number and -5 is at least 35. Write as an inequality.

Answers

Product hints at multiplication so -5n is AT LEAST meaning that it is at or greater than 35....

-5n ≥ 35

Answer:

-5x≥35

Step-by-step explanation:

The word "product" means to multiply so I know that -5 times a number x is at least 35. The phrase "at least" means greater than or equal to so I know its a ≥ sign.

Hope this helps you

A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the station together?

Answers

Answer:

7:12 a.m

Step-by-step explanation:

Given that:

Train to New York city leaves station every 7 minutes

Train to Boston leaves station every 6 minutes

Current time = 6:30 a.m

Time both will leave station together is obtained by finding the least common multiple of 6 and 7

Multiples of ;

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...

The least common multiple of 6 and 7 is 42.

Hence, both trains will leave the station together after 42 minutes ;

Current time + 42 minutes

6:30 a.m+ 42 minutes = 7:12 a.m

In the equation y = 2π^x, 2 is the ______ and π is the ______.

Answers

Answer:

pi(π) is the constant and x is the variable since pi is a numerical value and x can change according to the equation given.

Step-by-step explanation:

What is -5 5/8 + 3 1/2

Answers

Answer:

-2.125

Step-by-step explanation:

the pyramid shown has a rectangular base and faces that are isosceles triangles find the total surface area to the nearest tenth

Answers

I think d is the correct answer

Answer:

I think is C.

Step-by-step explanation:

I'm so sorry if wrong!

PLEASE HELP ME WITH THESE QUESTIONS ASAP

Answers

Answer:

D.

Step-by-step explanation:

Answer:

the answer is d 64 because a rational number is a whole number not decimals.

Step-by-step explanation:

brainliest pls

ax+by=c What is the equivalent equation

Answers

Ax plus BY equals C.

Can someone please help me it’s due in a few minutes.

Answers

Answer:

150

Step-by-step explanation:

go submit it

Solve the system using the elimination method. - Which one should I do first
3x-4y+z=-5
6x-4y+z=1
x+y+z=6

Answers

Answer:

first equation and second equation

Step-by-step explanation:

it is more easier because both of them have the same y

Answer:

Use equation (1) and equation(2) and eliminate 4y+z

Step-by-step explanation:

3x-4y+z=-5     ...(1)

6x-4y+z=1        ...(2)

x+y+z=6          ...(3)

First, you find the equation that you can use the elimination method on;

there are multiples of them.

However, I would use equation (1) and equation(2) and eliminate 4y+z :

 3x-4y+z=-5

- 6x-4y+z=1  

         -3x=-6

            x=2

As you can see, both the terms with y and z are eliminated in one step, exposing the variable x.

From here is just my advice:

There are multiple ways for you to answer this question. In math, the process may sometimes not matter if the answer was correct. Nevertheless, you should try finding one way that fits you or makes it easier to solve. I personally think that how I have been trying this helped me later when math got more complicated. (Also, it was fun for me to find another way that I was not taught of)

GOOD LUCK!! and I HOPE THIS HELPS YOU!!!!

What is the solution to this system of linear equations?

y − 4x = 7

2y + 4x = 2

A. (3, 1)
B. (1, 3)
C. (3, −1)
D. (−1, 3)

I WILL MARK AS BRAINLIEST IF CORRECT!

Answers

Answer:

[tex]x = - 1[/tex]

[tex]y = 3[/tex]

Step-by-step explanation:

[tex]y - 4x = 7(eqn \: 1)[/tex]

[tex]2y + 4x = 2(eqn \: 2)[/tex]

[tex]solving \: by \: eliminating \: one \: variable[/tex]

[tex](y - 4x = 7)[/tex]

[tex] + (2y + 4x = 2)[/tex]

[tex]3y = 9[/tex]

[tex]y = 3[/tex]

[tex]y - 4x = 7[/tex]

[tex]3 - 4x = 7[/tex]

[tex] - 4x = 7 - 3[/tex]

[tex] \frac{ - 4x}{ - 4} = \frac{4}{ - 4} [/tex]

[tex]x = - 1[/tex]

The solution to this system of linear equations will be (–1, 3). Then the correct option is D.

What is the solution of the equation?

The solution of the equation means the value of the unknown or variable.

The equations are given below.

 y − 4x = 7   ...1

2y + 4x = 2  ...2

Add both equations, then we have

3y = 9

 y = 3

Put y = 3 in equation 1, then we have

3 − 4x = 7

     4x = –4

       x = –1

The solution to this system of linear equations will be (–1, 3).

Then the correct option is D.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

What is the formula for the area of this triangle?

Answers

Answer:

A = h b/2

Step-by-step explanation:

Answer:

J =6,L=5,K=3

Step-by-step explanation:

this is kinda hard to do bur I'll try to do it.

On a number line ,4.1 would be located. choose all answers that make a true statement.

A. To the right of 4.5

B. between 5 and 6

C. to the left of 4.19

D. To the left of 4.4
Help me plz

Answers

Answer:

D

Step-by-step explanation:

D. To the left of 4.4.

The lower the number, the more left it will be, the higher the number, the more right it will be.

HELP!!!!!!!!!!!!!! I ONLY HAVE 5 MIN TO TURN THIS IN!!!!

Answers

Answer:

I think A but I might be wrong

If the x- intercept is 2 and the y- intercept is -5 and the slope is 1/3. Write in equation in slope intercept form and standard form.

Answers

Answer:

The equation in slope-intercept form is

[tex]y=\frac{5}{2}x-5[/tex]

The equation in the standard form will be:

[tex]\frac{5}{2}x-y=5[/tex]

Step-by-step explanation:

The x-intercept is obtained when we set the value y=0

As the x-intercept is 2, therefore the point representing

the x-intercept will be: (2, 0)

The y-intercept is obtained when we set the value x=0

As the y-intercept is -5, therefore the point representing

the y-intercept will be: (0, -5)

So we get the two points

(2, 0)

(0, -5)

Finding the slope between (2, 0) and (0, -5)

[tex]\left(x_1,\:y_1\right)=\left(2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:-5\right)[/tex]

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-5-0}{0-2}[/tex]

[tex]m=\frac{5}{2}[/tex]

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

Here m is the slope

substituting the values m = 5/2 and the point (2, 0)

[tex]y-0=\frac{5}{2}\left(x-2\right)[/tex]

so writing the equation in slope-intercept form

As we know that the slope-intercept form is

[tex]y=mx+b[/tex]

here

m = gradient or slop b = y-intercept

so

[tex]y=\frac{5}{2}\left(x-2\right)[/tex]

[tex]y=\frac{5}{2}x-5[/tex]

Hence, the equation in slope-intercept form is

[tex]y=\frac{5}{2}x-5[/tex]

Writing the equation in the standard form form

As we know that the equation in the standard form is

[tex]Ax+By=C[/tex]

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

[tex]y=\frac{5}{2}x-5[/tex]

so the equation in the standard form will be:

[tex]\frac{5}{2}x-y=5[/tex]

Simplify 10cm:30cm
Simplify 2cm:1m

Answers

Step-by-step explanation:

Simplest form=10/30=1/3

=1cm:3cm

Simplest form=2cm:1m

1m=100cm

2:100

2/100=1/50

1cm:50cm

Answer:

Simplest form=10/30=1/3

=1cm:3cm

Step-by-step explanation:

The equation f equals 9/5 C + 32 relates temperature measured in degrees celsius C to degrees Fahrenheit f Determine whether there is a proportional relationship between C and F explain your reason

Answers

Given:

[tex]F=\dfrac{9}{5}C+32[/tex]

where, F is degree Fahrenheit and C is degree Celsius.

To find:

Whether there is a proportional relationship between C and F.

Solution:

We know that, proportional relations is defined as

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where, k is constant of proportionality.

So, the line of proportional relationship passes through (0,0) and the equation must be true for (0,0).

If there is a proportional relationship between C and F, then the equation must be true for (0,0).

Substituting F=0 and C=0 in the given equation, we get

[tex]0=\dfrac{9}{5}(0)+32[/tex]

[tex]0=0+32[/tex]

[tex]0=32[/tex]

This statement is false because [tex]0\neq 32[/tex].

It means the line of given equation does not passes through (0,0). So, it s not a proportional relationship.

Hence, there is not a proportional relationship between C and F.

Ryan wrote a total of 8 pages over 2 hours. How many hours will Ryan have to spend writing
this week in order to have written a total of 48 pages? Assume the relationship is directly
proportional

Answers

Answer:

12 Hours

Step-by-step explanation:

So it says he writes 8 pages in 2 hours. Which would mean he takes an hour to write 4 pages. You divide 48 pages by 4 hours and you get 12.

I WILL GIVE BRAINLIEST. I NEED ANSWER ASAP.​

Answers

I believe it is C :)

Simplify the expression:

–3(9 − x) =

Answers

Answer:

Expand  [tex]-3(9-x): -27 + 3x[/tex]

Step-by-step explanation:

[tex]-3(9-x)[/tex]

Apply the distributive law: [tex]a(b-c)=ab-ac[/tex]

[tex]a = -3, b=9, c=x[/tex]

[tex]=-3*9-(-3)x[/tex]

Apply minus - plus rules:

[tex]-(-a)=a[/tex]

[tex]= -3*9+3x[/tex]

Multiply the numbers: [tex]3 * 9 = 27[/tex]

[tex]=-27+3x[/tex]

Hope this helps! If so, may I get Brainliest and a Thanks?

Thank you, have a good one! =)

Solve.
2x + 3 = 2x - 3

Answers

Step-by-step explanation:

Respuesta:13

Answer:

It is incorrect :( :(

Step-by-step explanation:

2x + 3 = 2x - 3

or, 2x - 2x = -3-3

or, 0 = -6

Complete the statements about circle Z. A central angle, such as angle ____ of circle Z, is an

Answers

Answer:

A central angle, such as angle of circle Z, is an angle whose vertex is and whose sides are radii of the circle.

Answer:

do you have a pic of the circle

Step-by-step explanation:

Find the y-intercept of a line that passes through the point (-5,-6) and has a slope of 2.

Answers

Answer:

The y intercept is 4

Step-by-step explanation:

Given:

-Given point: (-5,-6)

-Slope of 2

1) Put the equation into point-slope form y - y1 = m(x - x1)

With the given, we can plug it all in using this formula!

-y1 = -6

-x1 = -5

m = 2

(you would change these negative numbers into positives because the equation shows them being subtracted! remember that two negatives make one positive!)

y+6= 2(x+5)

2) Simplify

y+6= 2(x+5)

y+6=2x+10

y=2x+4

With y=2x+4, set x to 0 because the y intercept is where x is equal to 0 and you get 4!

umm i dont get none of this to be honest

Answers

Are you talking about brainly? If so, Brainly is an app/website where you can ask questions about your homework/ school work. When you first start on brainly you get 20 points? And each question you ask costs points. To get more points, you have to answer other people’s questions. Hope this helped!

What is the slope of a line that is perpendicular to the graph of y = 4/5x+9?

Answers

Perpendicular = opposite sign and reciprocal slope
4/5x slope turns into -5/4x
The slope of perpendicular line: -5/4x

Answer:

m = -5/4

General Formulas and Concepts:

Algebra I

The slope of the perpendicular line is the negative reciprocal of the original slope.

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Slope-Intercept Form (Original):   y = 4/5x + 9

Step 2: Break Original Function

Slope m = 4/5

y-intercept b = 9

Step 3: Find slope of perpendicular line

Take the negative reciprocal.

Perpendicular Slope m = -5/4

What is the system of equations represented by the table of values for continuous
linear functions, f(x) and g(x), shown below?

Answers

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

77 is 56% of what number

Answers

Answer:

137.50

Step-by-step explanation:

please give branliest

Answer:

137.5 I think I might be wrong..

Help please :((((((((((((((

Answers

Step-by-step explanation:

connect the points p and s

and comnect the points q and t

take triangle PQS and triangle TSQ

SQ similar to SQ

PQ similar to QS

QS similar to ST

therefore triangle PQS similar to triangle TSQ

Therefore , PQ/ QS = ST/ QS

PQ=ST

In the figure tw =3x+5 wx =10 and tx =5x-9

Answers

Answer:

Value of x = 12 unit

Step-by-step explanation:

Given:

tw = 3x+5

wx = 10

tx = 5x-9

Find:

Value of x

Computation:

tw + wx = tx

3x + 5 + 10 = 5x - 9

3x + 15 = 5x - 9

2x = 24

x = 12

Value of x = 12 unit

help immediate i will mark you brainliest

Answers

Answer:

What's the question?

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