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gladu [14]
3 years ago
11

The surface area of a rectangular prism is 32 square inches. The volume of the prism is 12 cubic inches. The sum of all edge len

gths is 28 inches. If the length width and height are increased by 1 inch, what is the volume?
Mathematics
1 answer:
Goryan [66]3 years ago
3 0

Answer:

36 cubic inches.

Step-by-step explanation:

Let the length, width and height of the rectangular prism are a, b, c respectively.

So, surface area, 2(ab + bc + ca) = 32 {Given} ............ (1)

Volume, abc = 12 {Given} ............ (2)

And, the sum of all the edges, 4(a + b + c) = 28 {Given} .......... (3)

Now, if the length width and height are increased by 1 inch, then the volume of the prism will be = (a + 1)(b + 1)(c + 1)

= abc + (ab + bc + ca) + (a + b + c) + 1

= 12 + 16 + 7 + 1 {From equations (1), (2) and (3)}

= 36 cubic inches. (Answer)

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Answer:

The equation that represents the motion of the string is given by:

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Substitute the given values in [1] we get;

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or

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(a)

The trigonometric function that models the motion of the string is given by:

y =0.6e^{-1.8t}\cos(210\pi t)

(b)

Determine the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24

Using graphing calculator for the equation

y =0.6e^{-1.8x}\cos(210\pi x)

let x = t (time in sec)  

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24 is, 0.5 sec


4 0
3 years ago
Identify an equation in slope intercept form for the line parallel to y= -2/3x+8 that passes through (4, -5)
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Answer:

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Step-by-step explanation:

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Unknown:

Equation of the line passing through (4, -5);

Solution:

To solve this problem;

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To solve this problem,

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    y =  -\frac{2}{3}x - \frac{7}{3}

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     3y = -2x -7

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