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monitta
4 years ago
15

99 POINT QUESTION, PLUS BRAINLIEST!!!

Mathematics
2 answers:
MArishka [77]4 years ago
5 0
The first solution:
\int\limits^8_0 {\frac{16x}{1+x^2}} \, dx=8log(65)

The second solution:
\int\limits^2_{-6}{(-36-12x-x^2+8(6+x))} \, dx=\frac{256}{3}
kicyunya [14]4 years ago
4 0
4.
first one, since the lower bound is y=0

so what we do is just inetgrate from x=0 to x=8


\int\limits^8_9 { \frac{16x}{x^2+1} } \, dx
find an antiederivitive

use u subsitution
u=x²+1
du=2x dx
so factor out the 8

8 \int\limits^8_9 { \frac{2x}{x^2+1} } \, dx
8 \int\limits^8_9 { \frac{1}{u} } \, du
and we know that the antideritivitve of 1/u is ln|u|
8ln|x²+1| is an antideritivive
now
[8ln|x^2+1|]^8_0
8ln|8^2+1|-8ln|0^2+1|
8ln|65|+8ln|1|
8ln65+0
the aera is 8ln65
A is the answer





6.
find where they intersect to find the area bounded
f(x)=g(x) at x=-6 and x=2
and g(x) is on top (we can see that because g(0)>f(0))
so we integrate from -6 to 2
\int\limits^2_{-6} {g(x)-f(x)} \, dx
\int\limits^2_{-6} {8x+48-(x^2+12x+36)} \, dx
\int\limits^2_{-6} {8x+48-x^2-12x-36)} \, dx
\int\limits^2_{-6} {-x^2-4x+12)} \, dx
this is easy
use reverse power rules
remember that \int\limits^a_b {f(x)+g(x)} \, dx = \int\limits^a_b {f(x)} \, dx + \int\limits^a_b {g(x)} \, dx
the antiderivitive is
\frac{-x^3}{3} -2x^2+12x
so
 [\frac{-x^3}{3} -2x^2+12x]^2_{-6}=
(\frac{-2^3}{3} -2(2)^2+12(2))-(\frac{-(-6)^3}{3} -2(-6)^2+12(-6))=
({-8}{3} -8+24)-(72 -72-72)=
({-8}{3}+ 16)-(-72)=
{-8}{3}+ 16+72=
{-8}{3}+ 88=
\frac{-8}{3} + \frac{264}{3}=
\frac{256}{3}

answer is C
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In the first 25% of the produce, 7% of that is defective. Which means that 25%*93% is not defective.

=20.75% not defective.

In the second 30% of the produce, 6% is defective Which means that 30%*94%

=28.2% not defective

Now for the 3rd 45% of the produce, 4% is defective which means that

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7 0
3 years ago
What is the slope of a line passing through (3, 4) and (5,8)?
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Answer:

2

Step-by-step explanation:

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8 0
2 years ago
The machinist's goal was to increase his production by at least 10% each day. Assume he achieved his goal. If he was able to mac
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Step-by-step explanation:


3 0
3 years ago
Jessica, Lauren and Kimmie were paid a total of $120 for babysitting in a ratio of 2:3:5. How much less did Jessica make than Ki
Tju [1.3M]

Answer:

Jessica makes $36 less than Kimmie  

Step-by-step explanation:

Let

x -----> amount paid to Jessica

y  ----> amount paid to Lauren

z ----> amount paid to Kimmie

we know that

x+y+z=120 ------> equation A

\frac{x}{y}=\frac{2}{3}

x=\frac{2}{3}y -----> equation B

\frac{y}{z}=\frac{3}{5}

z=\frac{5}{3}y -----> equation C

substitute equation B and equation C in equation A and solve for y

\frac{2}{3}y+y+\frac{5}{3}y=120

\frac{10}{3}y=120

y=120(3)/10

y=36

<em>Find the value of x</em>

x=\frac{2}{3}(36)=24

<em>Find the value of z</em>

z=\frac{5}{3}(36)=60

therefore

The  amount paid to Jessica was $24

The amount paid to Lauren was $36

The amount paid to Kimmie was $60

To find out how much less Jessica did than Kimmie, subtract the amount paid to Jessica from the amount paid to Kimmie.

\$60-\$24=\$36

therefore

Jessica makes $36 less than Kimmie

7 0
3 years ago
8. If3:8=c:56, the value of c will be
adelina 88 [10]

The scale for the second values is 56/8 = 7

C = 3 x 7 = 21

C= 21

6 0
3 years ago
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