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3 years ago

Need done ASAPppppppp

Mathematics

1 answer:

ladessa [460]3 years ago

4 0

Answer:

a. Yes it's a proportional relationship. It is because Distance is travelled uniformly.

b. Unit is m/min^2.

c. It means he is travelling in meters with minutes counting how far he have travelled.

Hope this helped. Dont forget to give thanks.

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3 years ago

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A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

Afina-wow [57]

Answer:

13.86 ft/sec

Step-by-step explanation:

If we let x = distance batter has run at time t and D = distance from second base to the batter at time t, then we know $\frac{dx}{dt}=31 ft/s$ and we want $\frac{dD}{dt}$ when he is halfway (at x = 45).

Using Pythagoras theorem

$D^2=90^2+(90-x)^2\\\text{Differentiating with respect to t}\\2D\frac{dD}{dt}=0+2(90-x)(-1)\frac{dx}{dt}\\2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}$

When x=45

$D^2=90^2+(90-x)^2\\D^2=90^2+(90-45)^2\\D^2=10125\\D=\sqrt{10125}$

$2D\frac{dD}{dt}=-2(90-x)\frac{dx}{dt}\\2\sqrt{10125}\frac{dD}{dt}=-2(90-45)(31)\\\frac{dD}{dt}=\frac{-2(45)(31)}{2\sqrt{10125}} =-13.86ft/s$

Thus, when the batter is halfway to first base, the distance between second base and the batter is decreasing at the rate of about 13.86 ft/sec.

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3 years ago