A baseball is hit along the third base line with a speed of 100 ft/s. At what rate is the balls distance from first base changing when it crosses third base?

Answers

Answer 1

Solution :

From the triangle,

[tex]$x^2 = s^2 + 90^2$[/tex]

[tex]$x = \sqrt{s^2 + 90^2}$[/tex]

Now differentiating w.r.t "t", we get

[tex]$\frac{dx}{dt}=\frac{d}{dt}\left(s^2 +90^2 \right)^{1/2}$[/tex]

    [tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{\frac{1}{2}-1} \cdot 2s \cdot \frac{ds}{dt}$[/tex]     [chain rule]

    [tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{-\frac{1}{2}} \cdot 2s \cdot \frac{ds}{dt}$[/tex]

    [tex]$=\frac{s}{\left(s^2 + 90^2\right)^{\frac{1}{2}}} . \frac{ds}{dt}$[/tex]  

But given that [tex]$\frac{ds}{dt}$[/tex] = 100 ft/s

When all the ball crosses the third base, this means that s = 90. So substituting the value of s and [tex]$\frac{ds}{dt}$[/tex]  in [tex]$\frac{dx}{dt}$[/tex] , we get

[tex]$\frac{dx}{dt} = \frac{90}{\left(90^2 +90^2\right)^{1/2}} \times 100$[/tex]

[tex]$\frac{dx}{dt} = \frac{90}{\sqrt{8100+8100}} \times 100$[/tex]

[tex]$\frac{dx}{dt} = 50\sqrt2$[/tex]

    = 70.710 ft/s    


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Answers

Answer:

Slope = 2

Step-by-step explanation:

Answer:

is this what youre looking for ?

Step-by-step explanation:

Input Data :

Point A  ( x A , y A )  = (3, 2)

Point B  ( x B , y B )  = (7, 10)  

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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The solution to the equation 7x = 105 is x = 15.

We have the equation: 7x= 105

To solve for x in the equation 7x = 105, we need to isolate x on one side of the equation.

Divide both sides of the equation by 7:

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Answers

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

You are finding the intersection point of the system of linear equations.

Step-by-step explanation:

You can use methods like substitution, elimination, and/or equal values to find the solution for the system of linear equations.

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Answer:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Item 6 A rectangular prism has a length of 8 meters, a width of 4 meters, and a height of 5 meters. Which equations could be used to determine the volume, V, of the prism? Select each correct answer. V = 12 × 5 V = 5 × 4 × 4 V = 8 × 4 × 5 V = 32 × 5

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

x = 30

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Answers

Answer:

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Answers


2
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Step-by-step explanation:

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1) given

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Step-by-step explanation:

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