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The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3

Zepler [3.9K]

Answer:

We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.

Its volume is equal to the area of its base times its height.

Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.

Let's test each of these answers to see which gives us the correct volume.

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a base area of 4y square units and height of 4y² + 4y + 12 units

We find the volume by multiplying the base area by the height...

4y(4y² + 4y + 12)

Distribute the 4y to each term inside the parentheses.

16y³ + 16y² + 48y

This is not the right volume, so these can not be dimensions of our prism.

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a base area of 8y² square units and height of y² + 2y + 4 units

We find the volume by multiplying the base area by the height...

8y²(y² + 2y + 4)

Distribute the 8y² to each term inside the parentheses.

8y⁴ + 16y³ + 32y²

This is not the right volume, so these can not be dimensions of our prism.

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a base area of 12y square units and height of 4y² + 4y + 36 units

We find the volume by multiplying the base area by the height...

12y(4y² + 4y + 36)

Distribute the 12y to each term inside the parentheses.

48y³ + 48y² + 432y

This is not the right volume, so these can not be dimensions of our prism.

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a base area of 16y² square units and height of y² + y + 3 units

We find the volume by multiplying the base area by the height...

16y²(y² + y + 3)

Distribute the 16y² to each term inside the parentheses.

16y⁴ + 16y³ + 48y²

The volume fits, so these could be the base area and height of our prism.

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D. a base area of 16y² square units and height of y² + y + 3 units

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Step-by-step explanation:

7 0

2 years ago

If the distance covered by an object in time t is given by s(t)=t^2+5t , where s(t) is in meters and t is in seconds, what is th

alisha [4.7K]

Answer:

E. 44 meters

Step-by-step explanation:

The function that models the distance covered by the object is

$s(t)=t^2+5t$

where s(t) is in meters and t is in seconds.

The distance covered by the object after 1 second is

$s(1)=1^2+5(1)=6m$

The distance covered by the object after 1 second is

$s(1)=5^2+5(5)=50m$

The distance covered between 1 second and 5 seconds is

50-6=44m

6 0

2 years ago

The figure below shows the circle inside of a square if the radius of the circle Is 8cm find the following by showing the formul

Goryan [66]

A. The circumference of the circle:
C = 2 π r = 2 * 3.14 * 8 = 50.24 cm

B. The area of the circle:
A = π r² = 3.14 * 8² = 200.96 cm²

C. The area of the square:
Let's calculate first the side of the square. It is equal to 2r = 2*8=16 cm

The area of the square is:
16*16 = 256 cm²

Hope that helps.

7 0

2 years ago

Read 2 more answers

5.1million x 2.9 thousand

d1i1m1o1n [39]

Answer:

fourteen billion seven hundred ninety millio

4 0

2 years ago

On a 15 hour trip, Rob drove 35% of the time and Mark drove the remainder of the time. How many hours did Mark drive? Explain 9.

Zigmanuir [339]

Answer:

9.75 hours

Step-by-step explanation:

If Rob drove 35% of the time and Mark drove the remainder of the time, the total is 100 %

100-35 = 65

so Mark drove 65% of the time

The total time driven was 15 hours, so we multiply the total time driven by the percentage of time that Mark drove to find the number of hours that Mark drove.

15 * 65%

15*.65

9.75 hours

7 0

2 years ago

Here is a better pic​

Here is a better pic