Since the circle is centered at the origin, we can use the equations
x² + y² = r²
x = r cos θ
y = r sin θ
We know y = 8 and r = 10. Solving for x
x² + 8² = 10²
x = 6
From this equation:
x = r cos θ
6 = 10 cos θ
cos θ = 6/10 = 0.6
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
So for 1, the way to find one 'part' of the ratio, is to add up the ratio and divide the number from 180 (180 degrees in a triangle). So you would do 7 + 13 + 16 = 36. 180 divided by 36 = 5. Each part represents '5'. So to find the angles, you would do the coefficient multiplied by 5. Therefore, angle DEA is 13 * 5, which is 65 degrees, angle DFA is 16 * 5 = 80 degrees, and angle FDE is 7 * 5, which is 35. You know this is correct because 80 + 35 + 65 = 180 degrees.
For 2, you just have to set up a ratio. So we know that there are 320 cookies for 16 students, so the ratio would be set up as 320:16. So the cookie:student ratio, a.k.a, the number of cookies for each student is going to be the entire ratio divided by 16. We do this because there are 16 students, so to find the amount of cookies for 1 student, we do 16 / 16, which is 1. But of course, this affects the first part of the ratio too, so you do 320 divided by 16, which is 20. So the cookie:student ratio is 20:1. Every 1 student gets 20 cookies.
For 3, you just have to set up another ratio. If he finds 2 clovers in the first 12 minutes, the clover:minute ratio will be 2:12, or 1:6. This means that for every 6 minutes spent searching, 1 clover will be found. If he spends a total of 180 minutes searching, we can predict the number of clovers he will find by doing a proportion calculation. 180 / 6 = 30. That means we have to multiply 1:6 by 30 to find the number of clovers he will find. We multiply by 30 because 6 * 30 is 180 minutes, and obviously, this will affect the first part of the ratio too. 1 * 30 = 30. So that means the ratio is now 30:180. He will find 30 clovers in 180 minutes.
I hope you get it by now, but if you don't let me know. I'll help you answer the rest of the questions :)
4 bc I’m smart and I passed
