450 miles on 15 gallons of gas is what in a rate?

The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol

Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{7}{10}$

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{343}{1,000}$

Part c) The volume of the smaller pyramid is $4,116\ m^{3}$

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

so

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{21}{30}$

Simplify

$z=\frac{7}{10}$ -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

8 0

2 years ago

Write an inequality for the graph below.<br>please no links

PilotLPTM [1.2K]

Answer:

$x \geqslant - 6$

7 0

2 years ago

10 The table shows the cost of blueberries at a local farmer's

egoroff_w [7]

Answer:

This question needs rephrasing. It makes no sense.

Step-by-step explanation:

5 0

2 years ago

An amateur radio operator erects a 75-foot vertical tower for an antenna. A 117 guy wire is pulled from the top of the tower dia

vitfil [10]

Answer:

α=39.80°

Step-by-step explanation:

applying the law of sin and cos, we have:

$sin\alpha =\frac{75}{117}=0.6410\\\alpha =acs(0.64)= 39.79$

and to the nearest tenth of a degree

α=39.80°

3 0

3 years ago

7) First factor out the greatest common factor from each term. Then factor the remaining polynomial.

Stolb23 [73]

Answer: -138

Step-by-step explanation:

pls help me with this on my account

gaston is making a tent for boy scout camp. he has been instructed to use canvas on all of the sides except the bottom, which will be made out of a different material. how much canvas will gaston need?

6 0

2 years ago