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o-na [289]
1 year ago
11

Answer the question below. Be sure to show your work

Mathematics
1 answer:
likoan [24]1 year ago
5 0

ANSWER:

We have to find new side-lengths of PQR triangle.

Original sides are.

\begin{gathered} PQ\text{ = 8cm} \\ QR=17\operatorname{cm} \\ RP=15\operatorname{cm} \end{gathered}

After multiplying by 2.5 we get

\begin{gathered} PQ^{\prime}=2.5\times PQ=(8\times2.5)cm=20\operatorname{cm} \\ QR^{\prime}=(17\times2.5)cm=42.5\operatorname{cm} \\ RP^{\prime}=(15\times2.5)cm=37.5\operatorname{cm} \end{gathered}

These are the new sides of the P'Q'R' triangle.

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Answer:

\frac{16\pi}{3}.

Step-by-step explanation:

I graphed the region in the image below. The blue line is y=3, the purple line is x=1 and the green curve is y = 4x-x^{2}. The shaded region in blue is the region we are going to rotate.

Now, to find the volume  v= 2\pi \int\limits^a_b {p(x)h(x)} \, dx where a=1, b=3 (left and right points of the region), p(x) is the distance from the rotation axis to the diferential Δx, we say p(x)=x and h(x) is the height of the region, in this case is h(x)= 4x-x^{2}-3. Then,

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= 2\pi*\frac{8}{3}

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Step-by-step explanation:

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