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polet [3.4K]
2 years ago
9

A point moves along the curve y = √ x in such a way that the y-component of the position of the point is increasing at a rate of

2 units per second. At what rate is the x-component changing for each of the following values?
Mathematics
1 answer:
Eduardwww [97]2 years ago
5 0

Answer:

The value of x component changes at a rate of \frac{dx}{dt}=4\sqrt{x} units per second

Step-by-step explanation:

We are given that y=x^{\frac{1}{2}}

Differentiating on both sides with respect to time we get

\frac{dy}{dt}=\frac{d\sqrt{x}}{dt}\\\\\frac{dy}{dt}=\frac{1}{2}x^{\frac{-1}{2}}(\frac{dx}{dt})\\\\\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}

It is given that \frac{dy}{dt}=2units/sec

Solving for \frac{dx}{dt} we get

\frac{dx}{dt}=\frac{dy}{dt}\times 2\sqrt{x}\\\\\frac{dx}{dt}=4\sqrt{x}

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At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,
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Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

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Let linear function to calculate total cost of gym be:

c(n)=mn+b

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For Gym 2

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In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months (n)

20n+12=22n+4

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So,

In 4 months the cost of both gyms will be the same.

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