1) use the distance formula to find that the radius (r) of the circle = 5
2) use the midpoint formula to find that the center of the circle (h,k) = (3, 0)
3) Now use the formula of a circle and input the (h,k) and r to create:
(x - 3)² + (y - 0)² = 5² → (x - 3)² + y² = 25
4) input the "x" value given in the question (x = 0) and solve for "y":
(0 - 3)² + y² = 25 → 9 + y² = 25 → y² = 16 → y = +/- 4
Since the question states that "b" must be positive, you can disregard the -4.
Answer: b = 4
Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: number of dimes in his pocket.
- Variable y: number of quarters in his pocket.
He has a total of 14 coins, hence:
x + y = 14 -> y = 14 - x.
They are worth $2.75, hence, considering the value of each coin(dimes $0.1 and quarters $0.25), we have that:
0.1x + 0.25y = 2.75
Since y = 14 - x:
0.1x + 0.25(14 - x) = 2.75
x = (0.25*14 - 2.75)/0.15.
x = 5.
y = 14 - x = 14 - 5 = 9.
There are 5 dimes and 9 quarters in his pocket.
More can be learned about a system of equations at brainly.com/question/24342899
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Answer:
3rd option: f(x)⇒ +∞ as x⇒-∞ and f(x)⇒ -∞ as x⇒ +∞
Step-by-step explanation:
This is a negative cubic graph, therefore:
Looking at the graph, as x goes towards negative infinity, the y values go toward positive infinity.
On the other hand, as x goes towards positive infinity, the y values go towards negative infinity.
Answer:
121/12
Step-by-step explanation:
1. 11/12 - (-10) = 11/12+10 = 131/12
2. 131/12-5/6 = 131/12 - 10/12 = 121/12
The formula
in solving the integral of the infinity of 3 is ∫3<span>∞?</span>(1<span>)÷((</span>x−2<span><span>)<span><span>(3/</span><span>2)</span></span></span>)</span><span>dx</span>
Substitute the numbers given
then solve
limn→inf∫3n(1/((n−2)(3/2))dn
limn→inf[−2/(n−2−−−−−√)−(−2/3−2−−−−√)
=0+2=2
Solve for the integral of 2 when 2 is approximate to 0.
Transpose 2 from the other side to make it -2
∫∞3(x−2)−3/2dx=(x−2)−1/2−1/2+C
(x−2)−1/2=1x−2−−−−√
0−(3−2)−1/2−1/2=2
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