What is the answer a b or can it be c or d

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

<u><em>Dimension of box:-</em></u>

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

3 years ago

bank card is charging 1.4 monthly interest on credit card changes. If you charge $175 pair of running shoes on the card and did

ahrayia [7]

176.03 is the answer because A=P(+rt) P is the amount of money r is rate which is the interest and t is time which is the month

4 0

3 years ago

1. If OQ and RT are parallel lines which statement is true?

Kaylis [27]

Answer:

Step-by-step explanation:

Question (1).

OQ and RT are the parallel lines and UN is a transversal intersecting these lines at two different points P and S.

A). ∠OPS ≅ ∠RSU [corresponding angles]

B). m∠OPS + m∠RSP = 180° [Consecutive interior angles]

C). m∠OPS + m∠OPN = 180° [Linear pair of angles]

D). Since, ∠OPS ≅ ∠TSP [Alternate interior angles]

And m∠TSP + m∠TSU = 180° [Linear pair of angles]

Therefore, Option (A) is the correct option.

Question (2).

A). m∠RSP + m∠RSU = 180° [Linear pair of angles]

B). m∠RSP + m∠PST = 180° [Linear pair of angles]

C). ∠RSP ≅ ∠TSU [Vertically opposite angles]

D). m∠RSP + m∠OPS = 180° [Consecutive interior angles]

Therefore, Option (C) will be the answer.

3 0

2 years ago

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Use your knowledge of isosceles and equilateral triangle‘s to find the requested information.

djverab [1.8K]

Answer:

48 degrees

Step-by-step explanation:

6y=8y-16

y=8

8(8)-16= ?

64-16=

8 0

2 years ago

Read 2 more answers

I need help with this please. :) thanks

IgorC [24]

Answer:

d. V = π(x^3 + 90x^2 + 2,400x + 20,000)

Step-by-step explanation:

volume of cylinder = πr^2h

We have r = x + 20; h = x + 50

V = π(x + 20)^2(x + 50)

V = π(x^2 + 40x + 400)(x + 50)

V = π(x^3 + 50x^2 + 40x^2 + 2000x + 400x + 20,000)

V = π(x^3 + 90x^2 + 2,400x + 20,000)

8 0

3 years ago