The equation of a circle centered at the origin is x² + y² = r², where r is the radius.
Because we know that the circle goes through point (0, -9), we know that the radius of the circle is 9, so the equation of the circle is x² + y² = 9² = x² + y² = 81.
Therefore, to see if the point (8, √17) lies on the circle, we need to substitute these coordinates into the equation:
x² + y² = 81
8² + (√17)² = 81
64 + 17 = 81
81 = 81
So this confirms that the point (8, √17) lies on the circle.
I hope this helps!
Answer:
3.4 × 10^25
Step-by-step explanation:
First number has to be less than 10 so 3.4.
Count how many decimal places the decimal needs to move.
Answer:
0.4
Step-by-step explanation:
Use the formula for conditional probability.
P(B|A) = P(A&B)/P(A) = 0.20/0.50 = 0.4
Answer:
The time now is 7 pm
Step-by-step explanation:
Suppose that now is the time T.
We know that:
"if time is four hours from now, the time left till midnight would be a quarter that if it is one hour from now".
Then:
if we define midnight as 12, and we assume that T is in the pm range.
Then the "time left till midnigth, assuming that the time is four hours from now" will be written as (12 - (T + 4))
With this in mind, we can write the problem as:
12 - (T + 4) = (1/4)*( 12 - (T + 1))
Now we can solve this for T.
12 - T - 4 = (1/4)*(12 - T - 1)
8 - T = (1/4)*(11 - T)
4*(8 - T) = 11 - T
32 - 4*T = 11 - T
32 - 11 = -T + 4*T
21 = 3*T
21/3 = T
7 = T
Then T = 7 pm
The time now is 7 pm
