Answer:
(16, 30)
Step-by-step explanation:
First the equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2, where (h,k) - the center.
We rewrite the equation and set them equal :
(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2− 32x − 60y +1122=0
x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0
We solve for each coeffiecient meaning if the term on the LHS contains an x then its coefficient is the same as the one on the RHS containing the x or y.
-2hx = -32x => h = 16.
-2ky = -60y => k = 30. => the center is at (16, 30)
The calculation of the integral will give us the answer.
Amount = Int (2000e^(-0,2t))dt
With t = 0 to t = 10
A = 2000.In(e^(-0,2t))dt
Making U = -0,2t
U = -0,2t
dU/dt = d(-0,2t)/dt
dU/dt = -0,2
dU = -0,2dt
dt = dU/-0,2
_______________
Then,
A = 2000.Int (e^U).dU/-0,2
A = -10.000.Int(e^U)dU
A = -10.000.e^U
A = -10.000.e^(-0,2t) | (0,10)
A = -10.000.(e^(-2)) - [ -10.000.e^(0)]
A = -10.000.e^(-2) + 10.000
A ~ 8,646 Gallons
The probability that the number of spoiled eggs among the 3 selected is 2 will be 0.57.
<h3>What is probability?</h3>
The probability of favorable events to the total number of occurrences.
A really bad carton of 7 eggs contains 5 spoiled eggs. An unsuspecting chef picks 3 eggs at random for his "Mega-Omelet Surprise".
Then the probability that the number of spoiled eggs among the 3 selected is 2 will be
The total number of the event will be
Total = ⁷C₃
Total = 35
Then the probability will be
P = (⁵C₂ x ²C₁) / 35
P = 10 x 2 / 35
P = 20 / 35
P = 0.57
More about the probability link is given below.
brainly.com/question/795909
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Answer:
2m/s² ; - 2m/s²
25m ; 50m ; 25m
6.67 m/s²
Step-by-step explanation:
The acceleration and deceleration :
Both rates are the Same from the graph ;
According to scenario described, acceleration = 2m/s²
Deceleration occurred in equal time interval = - 2m/s
Distance covered during each stage:
Stage 1 : area of triangle
0.5 * base * height
0.5 * 5 * 10 =25 m
Stage 2: area of rectangle :
Length * breadth = 5 * 10 = 50 m
Stage 3 : area of triangle
0.5 * base * height
0.5 * 5 * 10 =25 m
Average Velocity :
Total distance / time = (25 + 50 + 25) / 15 = 100/ 15 = 6. 67 m/s