3 years ago

Which equations would you use the subtraction property of equality to solve?

Mathematics

1 answer:

arlik [135]3 years ago

8 0

The ones that subtract are 76=d+4, h+2=54.Because 76-4=72 which 72+4=76 and 54-2=52 and 52+2=54.

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<u>Solution-</u>

The two parabolas are,

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By solving the above two equations we calculate where the two parabolas meet,

$So \ 16x^2-c^2 = c^2-16x^2 \Rightarrow 32x^2=2c^2 \Rightarrow x=\frac{1}{4}c$

Given the symmetry, the area bounded by the two parabolas is twice the area bounded by either parabola with the x-axis.

$\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}$

$So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68$

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