Setup Average Equation:
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Average=Sum of our 4 numbers + unknown number of x
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Total Numbers
15 = 3 + 19 + 8 + 32 + x
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5
Cross Multiply
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3 + 19 + 8 + 32 + = 15 x 5
x + 62 = 75
Subtract 62 from both sides of the equation to isolate x:
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x + 62 - 62 = 75 - 62
x = 13
Answer:
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Step-by-step explanation:
The slope of the tangent line to the curve at (8, 2) is given by the derivative
at that point. By the chain rule,

Differentiate the given parametric equations with respect to
:


Then

We have
and
when
, so the slope at the given point is
.
The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation

Alternatively, we can eliminate the parameter and express
explicitly in terms of
:

Then the slope of the tangent line is

At
, the slope is again
, so the normal has slope +4, and so on.
Circumference of circular track, C = 0.5 miles = 0.5×5280 feet = 2640 feet.
We know, circumference in circle is given by :

( Here, r is radius i.e distance of centre from track )
Putting values in above equation :
2 × 3.14 × r = 2640
6.28 × r = 2640
r = 420.38 feet
Therefore, distance between centre and track is 420.38 feet .
Hence, this is the required solution.