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avanturin [10]
3 years ago
7

A model car travels around a circular track with radius 5 feet. Let Z denote the distance between the model car and a fixed poin

t that is 20 feet to the left of the center of the circular track. The diagram above indicates the fixed point at the origin, the center of the circular track at the point (20,0), and the position of the car at the point (x,y). Z is the length of the line segment from the origin to the point (x,y). If x and y are functions of time t, in seconds, what is the rate of change of Z when x=23, y=4, and dxdt=2 ?
Mathematics
1 answer:
Eddi Din [679]3 years ago
5 0

Answer:

\frac{dZ}{dt}= \frac{40}{\sqrt{545} } , so the model car is moving away from the fixed point at a rate of approximately 1.7 feet per second.

Step-by-step explanation:

The functions x and y satisfy (x−20)^2+y^2=25 and differentiating gives 2(x−20)dx/dt+2y dy/dt=0. Substituting the three known values and solving for dy/dt yields dy/dt=−32. Since Z=x^2+y^2−−−−−−√, dZ/dt=(2x ^ dx/dt+2y^dy/dt) / 2x2+y2√. Substituting Since Substituting for x, y,\frac{dx}{dt} , and \frac{dy}{dt} gives \frac{dZ}{dt}= \frac{40}{\sqrt{545} } ,

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The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume th
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Answer:

a) f(x) = \frac{1}{25.9}

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Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

P(X < x) = \frac{x - a}{b - a}

The probability of finding a value between c and d is:

P(c \leq X \leq d) = \frac{d - c}{b - a}

The probability of finding a value above x is:

P(X > x) = \frac{b - x}{b - a}

The probability density function of the uniform distribution is:

f(x) = \frac{1}{b-a}

The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.

This means that a = 284.7, b = 310.6.

a. Give a mathematical expression for the probability density function of driving distance.

f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}

b. What is the probability the driving distance for one of these golfers is less than 290 yards?

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2 years ago
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The terms of this expression are ...

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The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

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Answer:

3)  y=\dfrac35x+\dfrac25

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