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Solnce55 [7]
3 years ago
7

If h(x) = 5 for the function h(x) = 2x + 1, what is the value of x?

Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0
If h(x)=5, and h(x)=2x+1 as well, then we can set the two expressions equal to each other.

5=2x+1
4=2x
x=2
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(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt

For the integral on the right, substitute

u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du

\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du

\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C

\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)

\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C

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Given that y(0)=12, we get

12=9+C\implies C=3

\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}

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