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Alik [6]
3 years ago
12

Evaluate the integral. (use c for the constant of integration.) 8 sin2(x) cos3(x) dx

Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0
Important formula we will use.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c

We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx

After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
= 4(- \frac{1}{5} cos5x-cosx)+c
= - \frac{4}{5} cos5x-4cosx+c
This is the answer.
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<u>Answer:</u>  

Broker1 with $66.

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Total number of shares Cindy have : 300

Market Price per share : $25  

Total price for the shares : 300 \times$25

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Now ,

<u>Case 1: </u>

Commission provided by broker1 = 0.75%

Online fees provided by broker1 = $ 10

Total price provided by broker1= \frac{75}{10000}\times7500 +$10

                                                =$66.25

<u>Case 2:  </u>

Commission provided by broker2= 0.5%

Online fees provided by broker2=$17

Total price provided by broker2= \frac{5}{1000}\times 7500 + $17

                                                =$54.5

<u>Case 3: </u>

Commission provided by broker 3= 0.6% for 100 0r few  

Not applicable because  the total shares are 300

For over 100 shares

Commission provided= 0.5%

Online fees = $10

Total price =  \frac{5}{1000}\times 7500 + $10

                =$47.5

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Online fees for buying and sharing= $50

Total price = $50

<u>Case5 : </u>

Commision for a share bought or sold = 0.05%

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Total Price= \frac{5}{10000}\times 7500 + $30

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Last month in the village of 125 people we’re issued a parking ticket. This month only 83 people were issued one. What was the p
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Answer:

the percent reduction is <u>33.6%</u> and the number of people who were issued a parking ticket are <u>42</u>.

Step-by-step explanation:

Given:

Last month in the village of 125 people were issued a parking ticket.

This month only 83 people were issued one.

Now, to find the percent reduction from this month to last month and the number of people who were issued a Parking ticket.

So, the reduction of the number of people who were issued a Parking ticket from this month to last month are:

125 people - 83 people = 42 people.

Thus, 42 people reduction from this month to last month.

Now, to get the percent reduction:

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