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3 years ago

(08.01 MC)

Mathematics

1 answer:

Brilliant_brown [7]3 years ago

3 0

Answer:

d. 72 in³

Step-by-step explanation:

To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:

From the question volume of the cone = 24 cubic inches

volume of a cone = $\frac{1}{3}$ πr²h

and volume of a cylinder = πr²h

This implies

volume of a cone = $\frac{1}{3}$ πr²h

= $\frac{1}{3}$ (volume of a cylinder)

volume of a cone = $\frac{1}{3}$ (volume of a cylinder)

24 = $\frac{1}{3}$ (volume of a cylinder)

multiply both-side of the equation by 3

24×3 = $\frac{1}{3}$ (volume of a cylinder)

72 =volume of a cylinder

Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches

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Mr. Williams is driving on a highway at an average speed of 50 miles per hour. His destination is 100 miles away. The

svetlana [45]

Answer:

t = -d/50 + 2

0.5 hour

Step-by-step explanation:

Given the equation:

d = 50 - 100t

The inverse function:

A.) solving for t

d = 100 - 50t

d - 100 = - 50t

Divide both sides by - 50

d/-50 - (100/-50) = - 50t/-50

-d/50 - (-2) = t

t = -d/50 + 2

B) using the inverse function:

t = -d/50 + 2

Miles driven (d) = 75, find time (t)

t = - 75/50 + 2

t = - 1.5 + 2

t = 0.5

t is in hours, therefore time left to travel is 0.5 hours or 30 minutes

4 0

3 years ago

louise bought 80 metres of fencing to make an enclosure for her pet dog .tommy if louise expects a rectangular enclosure what is

OleMash [197]

Answer:

400 m^2.

Step-by-step explanation:

The largest area is obtained where the enclosure is a square.

I think that's the right answer because a square is a special form of a rectangle.

So the square would be 20 * 20 = 400 m^2.

Proof:

Let the sides of the rectangle be x and y m long

The area A = xy.

Also the perimeter 2x + 2y = 80

x + y = 40

y = 40 - x.

So substituting for y in A = xy:-

A = x(40 - x)

A = 40x - x^2

For maximum value of A we find the derivative and equate it to 0:

derivative A' = 40 - 2x = 0

2x = 40

x = 20.

So y = 40 - x

= 40 - 20

=20

x and y are the same value so x = y.

Therefore for maximum area the rectangle is a square.

3 0

3 years ago

Find d a * a * a = 216 a * b * c = 96 b * c = 52 a + b + c = d

Slav-nsk [51]

$a\cdot a\cdot a=216\\\\a^3=216\to a=\sqrt[3]{216}\\\\\boxed{a=6}\\\\\text{Substitute}\ b\cdot c=52\ \text{to the second expression}\ a\cdot b\cdot c=96:\\\\abc96\ \wedge\ bc=52\to a(52)=96\qquad\text{divide both sides by 52}\\\\a=\dfrac{96}{52}\to a=\dfrac{24}{13}\neq6$