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ra1l [238]
3 years ago
5

The volume V of a cube with sides of length x inches is changing with respect to time t (in seconds). When the sides of the cube

are 10 in. long and increasing at the rate of 0.5 in/sec, how fast is the volume of the cube increasing?
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
5 0

Answer:

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

Step-by-step explanation:

Volume V = length l^3

V = x^3

Differentiating both sides;

dV/dt = 3x^2 dv/dt

Given;

x = 10 in

dx/dt = 0.5 in/sec

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

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A chest shaped as a rectangular prism can hold 576 wooden cube blocks with edge lengths of 1/4 ft.
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Please help if you can thanks ^^
Neko [114]

Given:

AD is an angle bisector in triangle ABC. m\angle CAB=44^\circ, m\angle ACB=72^\circ, m\angle ABC=64^\circ.

To find:

The value of m\angle ADC.

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AD is an angle bisector in triangle ABC.

m\angle CAD=m\angle BAD=\dfrac{m\angle CAB}{2}

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Using angle sum property in triangle CAD, we get

m\angle CAD+m\angle ADC+m\angle ACB=180^\circ

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3 0
3 years ago
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
enyata [817]
You forgot to include the given line.

We need the given line to find the slope. The slope of parallel lines are equal. So, the slope of the line of the equation you are looking for is the same slope of the given line.

I can explain you the procedure to help you to find the desired equation:

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Remember that the slope-intercept equation form is y = mx + b where m is the slope and b is thye y-intercept.

If you clear y in every equation you get:

a) y = (3/4)x + 17/4 => slope = 3/4

b) y = (3/4)x + 20/4 = (3/4)x + 5 => slope = 3/4

c) y = -(4/3)x - 2/3 => slope = -4/3

d) y = (-4/3)x - 6/3 = (-4/3)x - 2 => slope = -4/3

So, you just have to compare the slope of the given line with the above slopes to see which equations are candidates.

2) Point (-3,2)

You  must verify which equations pass through the point (-3,2).

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b) 3x - 4y = - 20

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c) 4x + 3y = - 2

4(-3) + 3(2) = - 2
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d) 4x + 3y = - 6

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