The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

Answer:

The new pyramid has a volume that is half the volume of the original pyramid.

Step-by-step explanation:

The volume of a pyramid is given by the following equation:

$V = \frac{h*l*w}{3}$

In which h is the height, l is the length and w is the width.

Modified volume:

height doubled, length and width cut in half. So

$h = 2h, l = 0.5l, w = 0.5w$

$V_{M} = \frac{2h*0.5l*0.5l}{3} = \frac{0.5*h*l*w}{3} = 0.5\frac{h*l*w}{3}$ = 0.5V[/tex]

That is

The new pyramid has a volume that is half the volume of the original pyramid.

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The birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)= 1450e0.018t people per year, fi

Cerrena [4.2K]

Answer:

38,674.This area represents the increase in population over a 10-year period.

Step-by-step explanation:

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.

The birth rate is graphed in green and the death rate is graphed in blue.

To find the area, take the integral of the difference of the functions:

$\int\limits^{10}_0 {2300e^{0.021t} - 1450e^{0.018t} } \, dt \\\\\frac{2300e^{0.021t}}{0.021} - \frac{1450e^{0.018t}}{0.018} \\\\(\frac{2300e^{0.21}}{0.021} -\frac{1450e^{0.18}}{0.018} ) - (\frac{2300}{0.021}- \frac{1450}{0.018} ) \\\\135117.12 - 96442.51 \\\\38,674$