the amount of gasoline used by a car varies jointly as the distance traveled and square root of the speed. suppose a car used 25 liters on a 100 km trip at 1000 kph. about how many liters will it use on a 1000km trip at 64 kph?

**Answer:**

To find out the amount of gasoline used by a car on a 1000 km trip at 64 kph, we need to use the formula that relates the distance traveled, speed, and the amount of gasoline used.

Given the formula: V = kd^(1/2)

Where V is the amount of gasoline used, k is a constant of proportionality, and d is the distance traveled.

Since we know that the car used 25 liters on a 100 km trip at 1000 kph, we can use this information to find the value of k.

25 = k * 100^(1/2) * 1000^(1/2)

Solving for k:

k = 25 / (100 * 1000)^(1/2)

Now that we have the value of k, we can use it to find the amount of gasoline used on a 1000 km trip at 64 kph.

V = k * 1000 * 64^(1/2)

V = k * 1000 * 8

V = 25 * 1000 * 8 / (100 * 1000)^(1/2)

V = 200 liters

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