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2 years ago

A prism has three times the volume of a pyramid with the same base and altitude.

Mathematics

2 answers:

ad-work [718]2 years ago

8 0

Answer:

A) True.

Step-by-step explanation:

Volume of any prism = base area x Height.

Volume of any Pyramid = Base area x height ÷3.

The volume of Pyramid is volume of prism divided by 3.

In other words we can say the volume of prism is 3 times the volume of a pyramid which will have the same base and height.

So the statement A prism has three times the volume of a pyramid with the same base and altitude is True.

AVprozaik [17]2 years ago

4 0

The correct answer is true.

To go from a prism to a pyramid with the same base and altitude, you simply need to divide it by 3. There is a factor of 3 between them.

This is also true of cylinders and cones.

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Sam and Annika ride their bikes to school. Sam rides his bike (k) kilometers . Annika rides her bike 2 less than 4 times as many

BaLLatris [955]

4(k-2) when it says 2 less than it means you are subtracting from the constant and 4 times means you are multiplying the whole equation with 4.

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2 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec

masha68 [24]

Using the washer method, the volume is given by the integral

$\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx$

where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

$\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}$

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2 years ago

Explain how u would use the integer tiles to find the quotient of -15 and 3

vova2212 [387]

Answer:

(-15)/3 = -5

Step-by-step explanation:

(-15)/3

Assume that your positive tiles are yellow, and your negative tiles are red.

The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"

How can you model the first value of -15? With 15 red tiles.

Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.

Step 1.

Start with 15 red tiles, as in the first picture.

Step 2.

Start by moving tiles one at a time to begin creating three new groups.

The middle picture shows the situation after you have moved the first three tiles.

Step 3.

Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.

The third picture shows the situation when you have finished.

How many red tiles are in each group? There are five.

Is the answer positive or negative? The answer is negative, because there are five red negative tiles in each group.

Conclusion? (-15)/3 = -5

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2 years ago

Read 2 more answers

The annual interest rate of Marta's savings account is 7.2% in a simple interest is calculated quarterly. What is the periodic i

kkurt [141]

1. You have the following information:

-The annual interest rate is 7.2%.
- The simple interest is calculated quarterly.

2. Then, to solve this exercise and calculate the periodic interest rate of Marta's Account, you only have to divide the annual interest rate (7.2%) by 1/4 year. So, you have:

=(7.2%)(1/4)
=(7.2%)/4
=1.8%

What is the periodic interest rate of Marta's Account?

The answer is: 1.8%

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2 years ago

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Daniel [21]

Answer:

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