What is the distance between the center of the circle with equation $x^2+y^2=6x-8y+24$ and the point $(-3,-12)$?
1 answer:
Answer:
The answer to your question is: 10 units
Step-by-step explanation:
P (-3, -12)
1.- Find the center of the circle
x² + y² = 6x - 8y + 24
x² - 6x + ( )² + y² + 8y + ( )² = 24
x² - 6x + (3)² + y² + 8y + (4)² = 24 + 9 + 16
(x - 3)² + (y + 4)² = 49
Center (3, -4)
2.- Find the distance between the center and the point given
Formula
d =
Substitution
d =
d =
d =
d =
d = 10 units
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Answer:
Probability that component 4 works given that the system is functioning = 0.434 .
Step-by-step explanation:
We are given that a parallel system functions whenever at least one of its components works.
There are parallel system of 5 components and each component works independently with probability 0.4 .
Let <em>A = Probability of component 4 working properly, P(A) = 0.4 .</em>
<em>Also let S = Probability that system is functioning for whole 5 components, P(S)</em>
Now, the conditional probability that component 4 works given that the system is functioning is given by P(A/S) ;
P(A/S) = {Means P(component 4 working and system also working)
divided by P(system is functioning)}
P(A/S) = {In numerator it is P(component 4 working) and in
denominator it is P(system working) = 1 - P(system is not working)}
Since we know that P(system not working) means that none of the components is working in system and it is given with the probability of 0.6 and since there are total of 5 components so P(system working) = 1 - .
Hence, P(A/S) = = 0.434.
Answer:
141
Step-by-step explanation:
1. The volume of a cylinder is , where r = radius and h = height. In this case, the height is 5 feet and the radius is 3 feet.
Solving Volume
Step 1: Plug in values
Step 2: Simplify.
- 141.3 ≈ 141
Therefore, the volume of the cylinder is 141 ft^3 (but don't put ft^3, as mentioned in the problem).
Have a lovely rest of your day/night, and good luck with your assignments! ♡