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
A because the others are fractions and not a whole number
Examples of How to Find Unit Rate or Unit Price
Ryan purchased 3 apples for $1.80. What is the unit price, or the cost of one apple?
<span>We want to know the price per apple unit so we set up a ratio with the number of apples in the denominator. The total price goes in the numerator. So the fraction is 1.80/3.Complete the division: 1.80 ÷ 3 = .60. You can conclude that the per apple price unit rate is $0.60/1. Ryan paid a unit price of $0.60 per apple (60 cents per 1 apple = .60/1).</span>
The pottery store can make 176 coffee mugs in an 8 hour day. How many mugs can they make in one hour?
<span>We want to know the number of mugs made per hour unit so we set up a ratio with hours in the denominator. The total number of mugs made per day goes in the numerator. So the fraction is 176/8.Complete the division: 176 ÷ 8 = 22. You can conclude that the per hour mug-making unit rate is 22/1. The pottery store makes 22 mugs per hour (22 mugs per 1 hour = 22/1).</span>
Kylie can run 12 laps in 30 minutes. How many laps does she run per minute?
<span>We want to know the laps per minute unit so we set up a ratio with minutes in the denominator. The total laps goes in the numerator. So the fraction is 12/30.<span>Complete the division: 12 ÷ 30 = 0.4. You can conclude that the per minute lap unit rate is 0.4/1. Kylie can run 0.4 laps per minute (0.4 laps per 1 minute = 0.4/1).</span></span>
Answer:
![x > 4](https://tex.z-dn.net/?f=x%20%3E%204)
Step-by-step explanation:
X is greater than 4
Answer:
0.25*d = t
D= Amount of Quarters
T= The amount of Money.
Step-by-step explanation: