Answer:
either 20.25π or around 63.6173
Step-by-step explanation:
So first you find the side length of the square which is the perimeter/4 so in this case, 9. 9/2 will give you the radius of the circle and just solve for the area using the formula a=πr^2
Answer: The required factored form of the given expression is

Step-by-step explanation: We are given to find the factored form of the following algebraic expression:

We will be using the following formula:

Now, we have

Thus, the required factored form of the given expression is

We need to convert given value 465^8 as the base 5 number.
Let us assume x is the exponent of 5 when we take base 5.
We can setup an equation now.
5^x=465^8
Taking ln on both sides, we get





On simplifying, we get

Therefore,
.
Answer:
The integrals was calculated.
Step-by-step explanation:
We calculate integrals, and we get:
1) ∫ x^4 ln(x) dx=\frac{x^5 · ln(x)}{5} - \frac{x^5}{25}
2) ∫ arcsin(y) dy= y arcsin(y)+\sqrt{1-y²}
3) ∫ e^{-θ} cos(3θ) dθ = \frac{e^{-θ} ( 3sin(3θ)-cos(3θ) )}{10}
4) \int\limits^1_0 {x^3 · \sqrt{4+x^2} } \, dx = \frac{x²(x²+4)^{3/2}}{5} - \frac{8(x²+4)^{3/2}}{15} = \frac{64}{15} - \frac{5^{3/2}}{3}
5) \int\limits^{π/8}_0 {cos^4 (2x) } \, dx =\frac{sin(8x} + 8sin(4x)+24x}{6}=
=\frac{3π+8}{64}
6) ∫ sin^3 (x) dx = \frac{cos^3 (x)}{3} - cos x
7) ∫ sec^4 (x) tan^3 (x) dx = \frac{tan^6(x)}{6} + \frac{tan^4(x)}{4}
8) ∫ tan^5 (x) sec(x) dx = \frac{sec^5 (x)}{5} -\frac{2sec^3 (x)}{3}+ sec x
Answer:
72.25 ft
Step-by-step explanation:
The function that models the height of the ball is

The maximum height occurs at:


We substitute t=2.125 to get:


The maximum height is 72.25 feet