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Alex73 [517]
2 years ago
12

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

Mathematics
1 answer:
Soloha48 [4]2 years ago
8 0

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.

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Mary pays income tax according to the graduated schedule shown below. A 3-column table with 6 rows. Column 1 is labeled If taxab
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Answer:

$13564

Step-by-step explanation:

\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\%  of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\%  of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\%  of the amount over 77,100\end{array}\right|

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Mary’s taxable income= $68,562

From the table, If taxable income is over $31,850 but not over $77,100

The tax = $4386.25 + 25% of the amount over 31,850

Amount over $31,850=$68,562-$31,850

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Therefore:

Mary's tax = $4386.25 + (25% of $36,712)

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The area A (in square feet) of the rectangular shed is given by
a_sh-v [17]

This question is incomplete.

Complete Question

The area A (in square feet) of the rectangular shed is given by 6x³+7x²+11x+21.And one side of the rectangular is 2x+3. Use polynomial long division to find an expression for the length (in feet) of the shed.

Answer:

3x² - x +7

Step-by-step explanation:

Using the long division method:

We have :

Divisor : 6x³+7x²+11x+21

Dividend : 2x+3

Quotient : the length (in feet) of the shed = ???

Hence, we solve below

6x³+7x²+11x+21 ÷ 2x + 3

3x² -x + 7

______________________

2x+3 l 6x³+7x²+11x+21

6x³+9x²

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-2x²+11x

-2x²-3x

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14x+21

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0

Therefore, an expression for the length (in feet) of the shed is 3x² - x +7

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