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tigry1 [53]
3 years ago
9

Can someone answer 15b

Mathematics
1 answer:
NISA [10]3 years ago
6 0
A)

well, we know the elevator's rate is -20 f/s, ok, so every second, is dropping 20 feet, therefore, "y" is "distance from the ground floor", so when y = 0, meaning the distance to the ground floor is 0, so you ARE at the ground floor then.

and "x" is how many seconds you've been in the elevator.

now, she got in the elevator for 6 seconds, so, the elevator went down by 20 * 6, or 120 feet down, reason why the slope is negative, when she stopped, she was 350 feet away from the ground floor still though.

if the elevator went down 120 feet, and she's still 350 feet from the ground floor, that means  she boarded the elevator at 120 + 350 feet, or 470 feet.

b)

\bf \begin{array}{lcccllll}
&\stackrel{\textit{elapsed seconds}}{x_1}&\stackrel{\textit{ft from ground-floor}}{y_1}\\
%   (a,b)
&({{ 6}}\quad ,&{{ 350}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies -20
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-350=-20(x-6)
\\\\\\
y-350=-20x+120\implies  y=-20x+\stackrel{y-intercept}{470}
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<h3>Volume:</h3>

With this prism, first separate it into a rectangular prism and a right triangle prism.

First, with the rectangular prism, it would have the units 5 * 5 * 6.3. Then with the right triangle prism, it would take the rest of the remaining space of it, being 3 * 5 * 6.3

The equation for the volume of a rectangular prism is L*W*H and the equation for the volume of a right triangle prism is (L*W*H) / 2.

With this, plug the numbers in for both prisms to get the volume of each of them:

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<u>Right triangle prism Volume</u>

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94.5 / 2

<em>47.25</em>

Lastly, combine these two values to get the total volume:

157.5 + 47.25 = 204.75 (Round Up) -->

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<h3>Surface Area:</h3>

Next, with the surface area of the prism. For this, lets combine all of the faces of the prism then add them all up.

First, lets do the bottom of the prism, or the base. It uses the lengths 8 cm and 6.3 cm. Lets do L * W to get the area of this face:

8 * 6.3 = 50.4

Next, lets do the slant side of it, which has the lengths 5.8 and 6.3.

5.8 * 6.3 = 36.54

Then, the top side with the lengths 5cm and 6.3 cm.

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5 * 6.3 = 31.5

Saving the most tedious part of it for last, the right trapezoids. Luckily, there is an equation for this:

<em>1/2 x (Sum of parallel sides) x (perpendicular distance between the parallel sides).</em>

<em>So, within each of these right </em>trapezoids, there's the parallel sides of 5 and 8. There's also a perpendicular side of 5cm. With this, we can plug this into the equation to solve for this part:

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Since there's two of them, times this by 2:

32.5 * 2 ---> 65.

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<em />

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