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n200080 [17]
3 years ago
8

The table below shows the cube roots of different numbers

Mathematics
1 answer:
siniylev [52]3 years ago
8 0
Part A :  Yes, it represents y as a function of x. There are not 2 different y values for the same x value.
f ( x ) = ∛ x   ( or : y = ∛x  )
Part B : f ( x ) = 10 + 20 x
f ( 100 ) = 10 + 20 · 100 = 10 + 2,000 = 2,010
f ( 100 ) represents the total cost for renting a bike for 100 hours.
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Step-by-step explanation:

z = 2 - x^2 - y^2.........(1) \\\\z = 1.............(2)  

Let add equation 1 and 2:

Using formula: x^2+y^2=1 \\\\

convert to polar coordinates

r=2

\theta \varepsilon (0=\pi)=z\\\\V=\int^{2\pi}_{\theta=0}\int^{1}_{\pi=0}\int^{z_{2}}_{z_1} r \ dr \d \theta\\\\

    =\int^{2\pi}_{0}\int^{1}_{0}  (Z_2-z_1)r  \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} 1- (-1-x^2-y^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (+1 \pm r^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (-r^3 + r)  \ dr \d \theta\\\\=\int^{2\pi}_{0} (-\frac{r^4}{4}+\frac{r^2}{1})^{1}_{0}  \d \theta\\\\=\int^{2\pi}_{0} (\frac{1}{4})  \d \theta\\\\=(\frac{2 \pi}{4}) \\\\=(\frac{\pi}{2}) \\\\

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