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3 years ago

Find integral∫cos³x dx) )?

Mathematics

2 answers:

atroni [7]3 years ago

8 0

cos³(x) = cos(x) cos²(x)

… = cos(x) (1 - sin²(x))

Substitute u = sin(x) and du = cos(x) dx. Then in the integral, you get

∫ cos³(x) dx = ∫ (1 - u ²) du

… = u - 1/3 u ³ + C

… = sin(x) - 1/3 sin³(x) + C

son4ous [18]3 years ago

4 0

Answer:

sin(x)−1/3(sin3(x))+C

Step-by-step explanation:

use u substitution method to integrate

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Use the binomial series series to expand the function as a power series. 3/((6+x)^3)

Degger [83]

= 3/(6^3*x^0 + 3*6^2*x^1 + 3*6^1*x^2 + 6^0*x^3)
= 3/(216 + 108x + 18x^2 + x^3)

6 0

4 years ago

If a triangle has side lengths 7, 10, and 12, is it a right triangle??

Vesnalui [34]

Answer:

No. Remember, a right angle must have a 90 degree angle. We can find the lengths with the Pythagorean Theorem.

Step-by-step explanation:

Given the length 7, 10, and 12, we can assume that 12 is the hypotenuse (it is the longest length).

- we can use 7 and 10 interchangeably.

Fill in the equation, $a^2 + b^2 = c^2$

where c = 12, and a or b = 7 or 10.

To indicate if the given lengths would form a right angle, we can only input 7 or 10, not both.

Therefore, $7^2 + b^2 = 12^2$ or $10^2 + b^2 = 12^2$

$7^2 + b^2 = 12^2$ ==> 49 + b^2 = 144 ==> b= $\sqrt{95$ ==> 9.746

b= 9.7, not 10.

$10^2 + b^2 = 12^2$ ==> 100 + b^2 = 144 ==> b = $\sqrt{44$ ==> 6.633 

b= 6.6, not 7.

Therefore, the lengths 7, 10, and 12, does NOT make a right triangle.

Hope this helps!

5 0

3 years ago

the length of a rectangle is two more than it's width. If the area of the triangle is 48cm squared, what is the length of the re

svet-max [94.6K]

Answer:

Step-by-step explanation:

Let the width of the rectangle be x. Then the length would be x+2

Area=(length)*(width)

48=x(x+2), => x=6. Width is 6 and length is 8

8 0

3 years ago

5) A theatre can be rented for different hours. The cost is $100 for deposit and $200 per hour. Write a function rule to find th

IgorLugansk [536]

Answer:

Step-by-step explanation:

Since the cost is $100 for deposit and $200 per hour, the function rule to find the total cost of renting the theatre for 'n' hours will be:

= 100 + 200(n)

= 100 + 200n

The total cost if you rented the theatre for 4 hours will be gotten by replacing n with 4. This will be:

= 100 + 200n

= 100 + 200(4)

= 100 + 800

= $900

6 0

3 years ago

Match the verbal expression (term) with its algebraic expression (definition).

AnnyKZ [126]

Answer:

4 less than an unknown value-c

quotient of a variable and 4-e

some #to the power of 4-d

4 times a unknown value-b

4 more than some #-a

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find integral∫cos³x dx) )?​

Find integral∫cos³x dx) )?