Please help and explain!

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

I think I'm not sure sorry if it's wrong

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Find the integral, using techniques from this or the previous chapter.<br> ∫x(8-x)3/2 dx

Soloha48 [4]

Answer:

$\int x(8-x)^{3/2}dx= -\frac{16}{5} (8-x)^{\frac{5}{2}} +\frac{2}{7} (8-x)^{\frac{7}{2}} +C$

Step-by-step explanation:

For this case we need to find the following integral:

$\int x(8-x)^{3/2}dx$

And for this case we can use the substitution $u = 8-x$ from here we see that $du = -dx$ , and if we solve for x we got $x = 8-u$ , so then we can rewrite the integral like this:

$\int x(8-x)^{3/2}dx= \int (8-u) u^{3/2} (-du)$

And if we distribute the exponents we have this:

$\int x(8-x)^{3/2}dx= - \int 8 u^{3/2} + \int u^{5/2} du$

Now we can do the integrals one by one:

$\int x(8-x)^{3/2}dx= -8 \frac{u^{5/2}}{\frac{5}{2}} + \frac{u^{7/2}}{\frac{7}{2}} +C$

And reordering the terms we have"

$\int x(8-x)^{3/2}dx= -\frac{16}{5} u^{\frac{5}{2}} +\frac{2}{7} u^{\frac{7}{2}} +C$

And rewriting in terms of x we got:

$\int x(8-x)^{3/2}dx= -\frac{16}{5} (8-x)^{\frac{5}{2}} +\frac{2}{7} (8-x)^{\frac{7}{2}} +C$

And that would be our final answer.

8 0

3 years ago

PLEASE HELP ME!!! THE RIGHT ANSWER WILL GET THE BRAINIEST!

Lina20 [59]

Answer:

$\sf D) \quad s=8 \frac{1}{4}t$

Step-by-step explanation:

t = time (in hours) → this is the independent variable
s = total area cleaned (in square feet) → this is the dependent variable (as the number of square feet cleaned depends on the number of hours worked)

Therefore, if the rate of cleaning is 8 1/4 square feet per hour, the relationship between s and t is:

$\sf s=8 \frac{1}{4}t$