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3 years ago

What is the volume of the composite figure? _?_ Cubic inches

Mathematics

2 answers:

qaws [65]3 years ago

4 0

1. To solve this exercise you must apply the formula for calculate the volume of a rectangular prism and the formula for calculate the volume of a rectangular pyramid:

2. Volume the rectangular prism:

V1=LxWxH

V1=(7 in)(3 in)(4 in)
V1=84 in³

3. Volume of the rectangular pyramid:

V2=BxH/3

B=(7 in)(3 in)=21 in

H=12 in-4 in=8 in

V2=(21 in)(8 in)/3
V2=56 in³

4. The volume of the composite figure is

V=V1+V2
V=140 in³

katrin2010 [14]3 years ago

4 0

140 is the answer on edge

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3 years ago

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is

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Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.

Consider the attached diagram

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3 years ago

Find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)

timama [110]

<h3>Answer: c = 7/4</h3>

================================================

Work Shown:

Compute the function value at the endpoints

$f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\$

With a = -5 and b = 4, we have

$f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\$

So,

$f(x) = \sqrt{4-x}\\\\f'(x) = -\frac{1}{2\sqrt{4-x}}\\\\f'(c) = -\frac{1}{3}\\\\-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\$

Use algebra to solve for c

$-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\\frac{1}{2\sqrt{4-c}} = \frac{1}{3}\\\\3 = 2\sqrt{4-c}\\\\2\sqrt{4-c} = 3\\\\\sqrt{4-c} = \frac{3}{2}\\\\4-c = \frac{9}{4}\\\\c = 4-\frac{9}{4}\\\\c = \frac{16-9}{4}\\\\c = \frac{7}{4}\\\\$

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3 years ago