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Nadya [2.5K]
3 years ago
11

Evaluate the indefinite integral. (Use C for the constant of integration.) sin(10x) 1 cos2(10x) dx

Mathematics
1 answer:
Schach [20]3 years ago
5 0

Answer:

The result of the integral is -\frac{\cos^3{10x}}{30} + C

Step-by-step explanation:

We are given the following integral:

\int \sin{(10x)}\cos^{2}{(10x)} dx

I am going to solve by substitution, using u = \cos{10x}, so du = -10\sin{10x}dx, dx = -\frac{du}{10\sin{10x}}. So, we have

-\frac{1}{10} \int u^2 du

Which has the following result:

-\frac{u^3}{30} + C

Going back to x, the result of the integral is

-\frac{\cos^3{10x}}{30} + C

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At Polynomials Pizza, a large cheese pizza costs $6.50. Each additional topping for the pizza costs $1.45. The total for a large
dangina [55]

Answer:x

=

5

toppings

Step-by-step explanation:Total cost of cheese pizza:  

$

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Any additional topping adds:  

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So a cheese pizza with  

1

additional topping is:

$

10.75

+

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1.25

=

$

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A cheese pizza with  

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additional toppings is:

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10.75

+

$

1.25

+

$

1.25

=

$

10.75

+

2

×

$

1.25

=

$

13.25

A cheese pizza with  

3

additional toppings is:

$

10.75

+

$

1.25

+

$

1.25

+

$

1.25

$

10.75

+

3

×

$

1.25

=

$

14.50

If you pay attention to the pattern you can see that, for any number of toppings, say  

x

toppings, the price is going to be:

$

10.25

+

x

×

$

1.25

We are told the final cost is  

$

17.00

. That is

$

10.25

+

x

×

$

1.25

=

$

17.00

Subtract  

$

10.25

from both sides

$

10.25

−

$

10.25

+

x

×

$

1.25

=

$

17.00

−

$

10.25

x

×

$

1.25

=

$

6.25

Divide both sides by  

$

1.25

x

×

$

1.25

$

1.25

=

$

6.25

$

1.25

x

=

5

4 0
3 years ago
Read 2 more answers
How many centimeters long is a leg of an isosceles right triangle if its hypotenuse has a length of 8√2 centimeters?
andrew-mc [135]

Answer:

The leg is 8 cm long

Step-by-step explanation:

An isosceles right triangle has the length of its hypotenuse and opposite equal

Let us call the length x

From Pythagoras’ , the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have ;

x^2 + x^2 = (8 √2)^2

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x= √64

x = 8 cm

7 0
3 years ago
Need help answering this
Alla [95]
The answer is “=“. Both are different representations of the same fraction.
8 0
3 years ago
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