14 in USE 3.14 for pi

Mathematics

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Gnesinka [82]3 years ago

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The triangular prism and the triangular pyramid shown have the same base and the same height. Use the drop-down menus to complet

Mila [183]

A triangular prism Vol. = area (A) of the triangular base × height (h) of prism
A triangular pyramid V = A × 1/3 h
So since they have same base A and h, the V of the pyramid will be exactly 1/3 the V of the prism

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3 years ago

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A pumpkin is launched from the top of a 20 foot tall platform at an initial velocity of 84 feet per second. The height, h, of th

Gennadij [26K]

<h2>Explanation:</h2>

In this problem we have a pumpkin is launched from the top of a 20 foot tall platform at an initial velocity of 84 feet per second. So the height, h, of the pumpkin at time t seconds after the launch can be modeled by the equation:

$h(t) = -16t^2 + 84t + 20$

So this is the equation of a parabola. The maximum of this parabola occurs at its vertex. So let's find this vertex:

$\text{The x-value of the vertex is}: \\ \\ t=-\frac{b}{2a} \\ \\ \\ Where: \\ \\ a=-16 \\ \\ b=84 \\ \\ c=20 \\ \\ \\ t=-\frac{84}{2(-16)} \\ \\ t=-\frac{84}{-32} \\ \\ t=\frac{21}{8}=2.625 \\ \\ h(2.625)=-16(2.625)^2+84(2.625)+20 \\ \\ h(2.625)=-110.25+220.5+20 \\ \\ h(2.625)=130.25m$