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3 years ago

Write the decimal as a fraction or mixed number in simplest form. 9.75

Mathematics

1 answer:

brilliants [131]3 years ago

4 0

✨Answer:✨

9 3/4 (simplest form)

✨Step-by-step explanation:✨

1. Convert decimal into fraction:

9.75 = 975/100

2. Simplify:

975/100 = 39/4 = 9 3/4

A. Reduce fraction to lowest terms (25 is the greatest common divisor of 975 and 100. Reduce by dividing both numerator and denominator by 25):

975/100 = 975 ÷ 25 = 39/4

100 ÷ 25

B. Convert improper fraction to mixed number:

39/4 = 9 3/4

(39 ÷ 4 = 9 remainder 3)

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3 years ago

A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the len

aniked [119]

Answer:

a. V = (20-x) $x^{2}$ $in^{3}$

b . 1185.185 $in^{3}$

Step-by-step explanation:

Given that:

The height: 20 - x (in )
Let x be the length of a side of the base of the box (x>0)

a. Write a polynomial function in factored form modeling the volume V of the box.

As we know that, this is a rectangular box has a square base so the Volume of it is:

V = h * $x^{2}$ $in^{3}$

<=> V = (20-x) $x^{2}$ $in^{3}$

b. What is the maximum possible volume of the box?

To maximum the volume of it, we need to use first derivative of the volume.

<=> dV / Dx = -3 $x^{2}$ + 40x

Let dV / Dx = 0, we have:

-3 $x^{2}$ + 40x = 0

<=> x = 40/3

=>the height h = 20/3

So the maximum possible volume of the box is:

V = 20/3 * 40/3 *40/3

= 1185.185 $in^{3}$

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3 years ago