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3 years ago

Please help asap

Mathematics

1 answer:

USPshnik [31]3 years ago

6 0

C!!!!!!!!!!!!!!!!!!!!!!!!!

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A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

3 years ago

A plant is already 52 centimeters tall, and it will grow one centimeter every month. Let H be the plant's health (in centimeters

Tasya [4]

Plant's height after 31 months:82 centimeters

<h3>How to find the height of the plant</h3>

The equation that can be used to find the height of the plant is given as

h = 52 centimeters + 1m

We have that the plant grows at 1 centimeter every month hence we have 1m in the equation.

Then the number of periods is m, Now we are to find the height in this period of time

h = 52 + 1*31

= 51 + 31

= 82

Hence the height after 31 months is given as 82 centimeters.

Read more on height here:

brainly.com/question/73194

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2 years ago

The product of (-5xy2) and (-4x2y)

solong [7]

Combine like variables:

(20x^2)(2y^3)

Combine coefficients:

40(x^2)(y^3)

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3 years ago

Write 180 feet per 12 seconds as a unit rate

Ber [7]

15ft per sec would be the unit rate.

7 0

3 years ago

How do I find x in this triangle?

Scilla [17]

Since the total degree of a triangle is 180, subtract 44 from 180 = 136. Divide it by two, and you get 68. I believe this is correct but don't take my word for it. Good luck!

7 0

3 years ago