This solution to this problem is predicated on the fact that the circumference is just:
. A straight line going through the center of the garden would actually be the diameter, which is well known to be two times the radius of the circle, so we can say that the circumference is just:
![d\pi](https://tex.z-dn.net/?f=%20d%5Cpi%20)
So, solving for both the radius and the diameter gives us:
![d\pi=8xy^2\pi\\ d=8xy^2\\ \\ 2\pi r=8xy^2\pi\\ r=4xy^2](https://tex.z-dn.net/?f=%20d%5Cpi%3D8xy%5E2%5Cpi%5C%5C%20d%3D8xy%5E2%5C%5C%20%5C%5C%202%5Cpi%20r%3D8xy%5E2%5Cpi%5C%5C%20r%3D4xy%5E2%20)
So, the length of thes traight path that goes through the center of the guardain is just
, and we can use the radius for the next part of the problem.
The area of a circle is
, which means we can just plug in the radius and find our area:
![A=\pi r^2 \implies \\ A=\pi (4xy^2)^2\implies \\ A= 16\pi x^2y^4](https://tex.z-dn.net/?f=%20A%3D%5Cpi%20r%5E2%20%5Cimplies%20%5C%5C%20A%3D%5Cpi%20%284xy%5E2%29%5E2%5Cimplies%20%5C%5C%20A%3D%2016%5Cpi%20x%5E2y%5E4%20)
So, we have found our area(
) and the problem is done.
Answer:
The year is 2020.
Step-by-step explanation:
Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.
Given:
Initial population is, ![P_0=450,000](https://tex.z-dn.net/?f=P_0%3D450%2C000)
Growth rate is, ![r=5\%=0.05](https://tex.z-dn.net/?f=r%3D5%5C%25%3D0.05)
Final population is, ![P=700,000](https://tex.z-dn.net/?f=P%3D700%2C000)
A population growth is an exponential growth and is modeled by the following function:
![P=P_0(1+r)^x](https://tex.z-dn.net/?f=P%3DP_0%281%2Br%29%5Ex)
Taking log on both sides, we get:
![\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}](https://tex.z-dn.net/?f=%5Clog%28P%29%3D%5Clog%28P_0%281%2Br%29%5Ex%29%5C%5C%5Clog%20P%3D%5Clog%20P_0%2Bx%5Clog%20%281%2Br%29%5C%5Cx%5Clog%20%281%2Br%29%3D%5Clog%20P-%5Clog%20P_0%5C%5Cx%5Clog%281%2Br%29%3D%5Clog%28%5Cfrac%7BP%7D%7BP_0%7D%29%5C%5Cx%3D%5Cfrac%7B%5Clog%28%5Cfrac%7BP%7D%7BP_0%7D%29%7D%7B%5Clog%281%2Br%29%7D)
Plug in all the given values and solve for 'x'.
![x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Clog%28%5Cfrac%7B700%2C000%7D%7B450%2C000%7D%29%7D%7B%5Clog%281%2B0.05%29%7D%5C%5Cx%3D%5Cfrac%7B0.192%7D%7B0.021%7D%3D9.13%5Capprox%2010)
So, for
, the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.
Therefore, the tenth year after 2010 is 2020.
Answer:
-4 1/4
Step-by-step explanation:
-7 3/4 + 3 1/2 = -4 1/4
Answer:
choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25
Step-by-step explanation:
75°+75°=150°
angles in a triangle add up to 180°
180°-150°=30°
c) x=30°