∫ √(4x - x²) dx
= 2[(4x - x²)^(3/2)] / 3(4 - 2x)
Answer:
Step-by-step explanation:
First convert the terms to fractional exponents
u = t^2/3 - 3t^3/2
differentiating
u' = 2/3 t^ (2/3 - 1) - 3* 3/2 t^(3/2 - 1)
= 2/3 t ^(-1/3) - 9/2 t ^(1/2)
= 2 / (3∛t) - 9 √ t / 2 in radical form
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
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<em>Additional comment</em>
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
