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Marina86 [1]
3 years ago
14

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

Mathematics
1 answer:
vaieri [72.5K]3 years ago
7 0

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

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I NEED HELP NOOOOOWWWW!!!!!!!!
In-s [12.5K]

Answer: 1590cm^3

Step-by-step explanation:

V=\frac{3\sqrt{3} }{2}a^2h

a = base

h = height

V=\frac{3\sqrt{3} }{2}(6cm)^2(17cm)

Solve the parentheses squared first.

V=\frac{3\sqrt{3} }{2}(36cm^2)(17cm)

2 and 36 can be simplied

2/2=1

36/2=18

V=3\sqrt{3}(18cm^2)(17cm)

V=3\sqrt{3}(306cm^3)\\ V=1590.02cm^3

Rounded to the nearest whole number... 1590cm^3

3 0
3 years ago
Anybody knows the answer?
vladimir1956 [14]

The top and bottom faces are 3 inches by 3 inches.

Area = 3 in. * 3 in. * 2 = 18 in.^2

The front, back, right, and left faces are 3 in. by 6 in.

Area = 3 in. * 6 in. * 4 = 72 in.^2

Total surface area = 18 in.^2 + 72 in.^2 = 90 in.^2

Answer: B. 90 square inches

3 0
3 years ago
Plz tell the answers in the correct order​
Nimfa-mama [501]

Answer:

a) 120°

Step-by-step explanation:

i think this is the right answer

7 0
3 years ago
You invest $500.00 in a savings account that gives 4.9% annual interest, compounded quarterly. How much money will you have at t
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6 0
3 years ago
two weeks ago i bought 2 cupcakes last week i bought 7 today id like to follow this pattern how many cupcakes do i want
monitta

Answer:

12

Step-by-step explanation:

2+5=7

7+5=12

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3 years ago
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