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IrinaVladis [17]
2 years ago
14

99 POINT QUESTION, AND BRAINLIEST!!!

Mathematics
2 answers:
77julia77 [94]2 years ago
4 0
\displaystyle\int_{x=1}^{x=14}\frac{1-\cos4x}{4x-\sin4x}\,\mathrm dx

First, replace y=4x and \mathrm du=4\,\mathrm dx. Then you have

\displaystyle\frac14\int_{y=4}^{y=56}\frac{1-\cos y}{y-\sin y}\,\mathrm dy

If we take z=y-\sin y, then immediately we see a differential in the numerator in the form of \mathrm dz=(1-\cos y)\,\mathrm dy. So the integral becomes

\displaystyle\frac14\int_{z=4-\sin4}^{z=56-\sin56}\frac{\mathrm dz}z

and evaluates to

\dfrac14\ln|z|\bigg|_{z=4-\sin4}^{z=56-\sin56}=\dfrac14\left(\ln|56-\sin56|-\ln|4-\sin4|\right)=\dfrac14\ln\left|\dfrac{56-\sin56}{4-\sin4}\right|

making (A) the correct answer.
Gnesinka [82]2 years ago
3 0

This question is quite difficult but I've managed to solve it.

The correct answer is A.

You might be interested in
At a grocery store the manager randomly selects 20 cartons of eggs, he finds 3 cartons with at least 1 broken egg. If the refrig
ivann1987 [24]

Answer:

You would expect 75 cartons with at least 1 broken egg.

There are likely to be 222 DVD players that are defective.

Step-by-step explanation:

Both examples given in this question represent a ratio of broken or defective to a sample number of cartons or DVD players.  In order to find how many would be broken or defective overall, you can set up equivalent ratios, or proportions.

Egg Cartons: \frac{broken}{#cartons}=\frac{3}{20}=\frac{x}{500}

'x' represents the number of cartons out of 500 that would be expected to have at least 1 broken egg.  To solve for 'x' you can cross-multiply and divide, or you can find what factor you would multiply the denominator by to get 500 and then multiply the same factor by the numerator to find 'x'.  In this case 500/20 = 25, so the factor is 25.  3 x 25 = 75, so you have 75 expected cartons with a broken egg.

DVD Players:  \frac{defective}{#players}=\frac{3}{50}=\frac{x}{3700}

'x' represents the number of DVD players out of 3700 that would be expected to be defective.  To solve for 'x' you can cross-multiply and divide, or you can find what factor you would multiply the denominator by to get 3700 and then multiply the same factor by the numerator to find 'x'.  In this case 3700/50 = 74, so the factor is 74.  3 x 74 = 222, so you have 22 likely defective DVD players.

4 0
3 years ago
What is the quotient of 8 and 72.16
Wittaler [7]
72.16./8 is equal to 9.02. 

72 divided by 8 is 9.

,16 divided by 8 is .02.
8 0
3 years ago
Find the principal amount invested if there is $9300 in the account after 5 years and earned 4% simple interest per year.
Zielflug [23.3K]

Answer:

11314.87379 (This is still rounded).

Step-by-step explanation:

Year 1:

9300*4%=372. 9300+372=9672.

Year 2:

9672*4%=386.88. 386.88=10058.88.

Year 3:

10058.88*4%=402.3552. 402.3552+10058.88=10461.2352.

Year 4:

10461.2352*4%=418.449408. 418.449408+10461.2352=10879.68461

Year 5:

10879.68461*4%=435.1873843. 435.1873843+10879.68461=11314.87379.

4 0
2 years ago
Alyssa's team won 5 out of every 7 games this season. If the team played 28 games this season, how many games did they win?
sladkih [1.3K]

Answer:

Alyssa's team won 20 games.

Step-by-step explanation:

We can introduce a variable that represents how many games Alyssa's team won.

Let x<em> </em>represent how many games Alyssa's team won.

We can now create a expression, we know that her team won 5 out of 7 games which would be equivalent to the fraction 5/7. We also know her team has played 28 games and five sevenths (5/7) of those they won.

This would give us the expression 5/7 = x/28.

We need to do this because 5/7 is equivalent to x the numbers of games they won over 28 the number of games they played.

Solving for  5/7 = x/28 we have:

5/7 = x/28  

We need to isolate x on the right side to do so we can multiply both sides by 28.

5/7 * 28 = x/28*28     simplifying

20 = x.

Therefore the number of games Alyssa's team won is 20 games.

8 0
3 years ago
Find the difference.
MrMuchimi

To find the difference of the given expression, first step is to get rid of parenthesis. So, distribute negative sign to each terms of the second parenthesis. Hence,

(9x² + 10x + 4) - (9x² + 5x - 1)

= 9x² + 10x + 4 - 9x² - 5x + 1.

= (9x² - 9x²) +(10x - 5x) + (4 + 1) Group the like terms.

= 0 + 5x + 5 Combine the like terms.

= 5x + 5.

So, first choice is correct.

Hope this helps you!

3 0
3 years ago
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