Hi hi I hope you understand your beautiful message
Answer:
C. √2 - 1
Step-by-step explanation:
If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)
Let r = the radius of the small circle
Using Pythagoras' Theorem ![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
to find the diagonal of the square:
![\implies r^2 + r^2 = c^2](https://tex.z-dn.net/?f=%5Cimplies%20r%5E2%20%2B%20r%5E2%20%3D%20c%5E2)
![\implies 2r^2 = c^2](https://tex.z-dn.net/?f=%5Cimplies%202r%5E2%20%3D%20c%5E2)
![\implies c=\sqrt{2r^2}](https://tex.z-dn.net/?f=%5Cimplies%20c%3D%5Csqrt%7B2r%5E2%7D)
So the diagonal of the square = ![\sqrt{2r^2}](https://tex.z-dn.net/?f=%5Csqrt%7B2r%5E2%7D)
We are told that the radius of the large circle is 1:
⇒ Diagonal of square + r = 1
![\implies \sqrt{2r^2}+r=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7B2r%5E2%7D%2Br%3D1)
![\implies \sqrt{2r^2}=1-r](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7B2r%5E2%7D%3D1-r)
![\implies 2r^2=(1-r)^2](https://tex.z-dn.net/?f=%5Cimplies%202r%5E2%3D%281-r%29%5E2)
![\implies 2r^2=1-2r+r^2](https://tex.z-dn.net/?f=%5Cimplies%202r%5E2%3D1-2r%2Br%5E2)
![\implies r^2+2r-1=0](https://tex.z-dn.net/?f=%5Cimplies%20r%5E2%2B2r-1%3D0)
Using the quadratic formula to calculate r:
![\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cimplies%20r%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}](https://tex.z-dn.net/?f=%5Cimplies%20r%3D%5Cdfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%281%29%28-1%29%7D%7D%7B2%281%29%7D)
![\implies r=\dfrac{-2\pm\sqrt{8}}{2}](https://tex.z-dn.net/?f=%5Cimplies%20r%3D%5Cdfrac%7B-2%5Cpm%5Csqrt%7B8%7D%7D%7B2%7D)
![\implies r=-1\pm\sqrt{2}](https://tex.z-dn.net/?f=%5Cimplies%20r%3D-1%5Cpm%5Csqrt%7B2%7D)
As distance is positive,
only
Y = 2/3x + -5
That is ur equation
follow Y = Mx + b
slope is M
and B is y intercept
Your Welcome I hope it worked<
Ashlin Monington
Your answer would be 5,290
Answer:
a) 1.6 x 10 ^6 dollars.
Step-by-step explanation:
since President Ronald Reagan served for 8 years. So the total amount of money that he earned is 2 x 10^5 x 8 = 16 x 10 ^ 5 = 1.6 x 10^6 dollars.