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Vaselesa [24]
2 years ago
12

3. The table of values represents a polynomial function f(x). How much greater is the average rate of change over the interval [

6, 8] than the interval [4, 6]?
x f(x)
4 105
5 384
6 945
7 1920
8 3465
9 5760
Mathematics
1 answer:
Ymorist [56]2 years ago
3 0

Answer:

367

Step-by-step explanation:

##CARRYONLEARNING

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Evaluate the integral. (sec2(t) i t(t2 1)8 j t7 ln(t) k) dt
polet [3.4K]

If you're just integrating a vector-valued function, you just integrate each component:

\displaystyle\int(\sec^2t\,\hat\imath+t(t^2-1)^8\,\hat\jmath+t^7\ln t\,\hat k)\,\mathrm dt

=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k

The first integral is trivial since (\tan t)'=\sec^2t.

The second can be done by substituting u=t^2-1:

u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C

The third can be found by integrating by parts:

u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t

\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8

\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C

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3 years ago
What is the surface area of a cylinder with base radius 3 and height 6?
Nikolay [14]

Answer:

I think the answer is 169.65

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I didn't get how you wrote 1.75 like how did it come there?
sertanlavr [38]

Answer:

Uhh what??

Step-by-step explanation:

Do you mean like 1.75 in a decimal form??

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