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How does 125 thousandths equal 1 tenth and how many thousandths?
H
What is the speed if I travel 6 kilometres in 1 tenth of an hour?
60 km/h
What is the Proof of the derivative of the third root of x?
You can easily derive it from formula for the derivative of a power, if you remember that the cubic root of x is equal to x1/3. This question asks for the proof of the derivative, not the derivative itself. Using the definition of derivative, lim f(x) as h approaches 0 where f(x) = (f(a+h)-f(a))/h, we get the following: [(a+h)1/3 - a1/3]/h Complete the cube with (a2 + ab + b2) Multiply by [(a+h)2/3 + (a+h)1/3 × a1/3 + a2/3] / [(a+h)2/3 + (a+h)1/3 × a1/3 + a2/3] This completes the cube in the numerator, resulting in the following: (a + h - a) / (h × [(a+h)2/3 + (a+h)1/3 × a1/3 + a2/3]) h / (h × [(a+h)2/3 + (a+h)1/3 × a1/3 + a2/3]) h cancels 1 / [(a+h)2/3 + (a+h)1/3 × a1/3 + a2/3] Now that we have a function that is continuous for all h, we can evaluate the limit by plugging in 0 for h. This gives 1/[a2/3 + a1/3 × a1/3 + a2/3] Simplify a1/3 × a1/3 1/[a2/3 + a2/3 + a2/3] (1/3)a2/3 or (1/3)a-2/3 This agrees with the Power Rule.
What is one third of 40 hours?
1/3 x 40 h/1 = 40 h/3 = 13.333... h
Find the volume of each cone. Round your answer to the nearest tenth . Use 3.14 for pi?
To find the volume of a cone, you use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Calculate the volume of each cone by plugging in the given values for r and h into the formula. Round your final answers to the nearest tenth.
