Answer: 8 centimeters
Step-by-step explanation: To find the radius of the circle, remember that the formula for the area of a circle is πr² and since we're given that the area of our circle is 64π, we can set up the equation 64π = πr².
To solve for <em>r</em>, we first divide both sides of the equation by π.
On the left side, the π's cancel and we're left with 64 and on the right side, the π's cancel and we're left with r².
So we have 64 = r².
Next, we take the square root of both sides to get 8 = r.
So the radius of our circle is 8 centimeters.
I think 6) is 17/25, 82%, 8,5, 8/5
Answer:
KL = 
= 17.93
MK = 
= 25.36
Explanation:
According to the Law of Sines:
where:
A, B, and C are angles
a, b, and c are the sides opposite to the angles
First of all, let's find m∠L: the sum of the angles of a triangle is 180°, therefore
m∠K + m∠L + m∠M = 180°
m∠L = 180° - m∠K - m∠M
m∠L = 180° - 105° - 30°
m∠L = 45°
Now, we can apply the Law of Sines to our case (see picture attached):
Let's solve one side at the time:
MK = 
= 25.36
Similarily:
KL = = 17.93
Answer:
Below.
Step-by-step explanation:
a) 5x-x² = x(5 - x).
b) x²-6x-27 = (x - 9)(x + 3).
c) x²+x-56 = (x - 7)(x + 8).
d) x³+8 = (x + 2)(x^2 - 2x + 4)
e) 3x⁴-54t = 3(x^4 - 18t)
f) x²+3x-10 = (x - 2)(x + 5)
g) 2(x⁴+x³-12x²) = 2x^2(x + 4)(x - 3)
h) 20(x³-1) = 20(x - 1)(x^2 + x + 1)
Answer:
![\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}](https://tex.z-dn.net/?f=%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
Step-by-step explanation:
Make use of the rules of logarithms:
log(a/b) = log(a) - log(b)
log(a^b) = b·log(a)
__
![5\log_5{x}-\dfrac{1}{4}\log_5{(8-x)}=\log_5{x^5}-\log_5{\sqrt[4]{8-x}}=\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}](https://tex.z-dn.net/?f=5%5Clog_5%7Bx%7D-%5Cdfrac%7B1%7D%7B4%7D%5Clog_5%7B%288-x%29%7D%3D%5Clog_5%7Bx%5E5%7D-%5Clog_5%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%3D%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
