Write each formula as an English phrase using the word varies or ...

Question

Write each formula as an English phrase using the word varies or proportional. 
V = 1/3 πr^2h, where V is the volume of a cone of radius r and height h

Accepted Answer

Hey, everyone here we are given for the following formula use the term varies or proportional to write them as word statements here. The given formula is E is equal to one half M V squared. Where E is the kinetic energy of a body with mass M and velocity V. Here we have four answer choice options. Answer choice A, the kinetic energy of a body is directly proportional with its velocity and one half of its mass. Answer B the kinetic energy of a body is inversely proportional with its mass and the square of its velocity answer C the kinetic energy of a body varies jointly as the square of its velocity and its mass. And lastly answer choice D the kinetic energy of a body varies jointly as the square of its mass and its velocity. So here looking at the formula that describes kinetic energy, we see that we have a constant of one half times a product M V squared. Well, since we have a constant times a product, we know that the kinetic energy of a body varies jointly. So because we have varies jointly. In our statement, we narrow it down to answer choices C and D. So we see A and B are out of the picture now, so now we can look closely at the variables here, we have mass on its own times velocity, which is squared. And since velocity is squared, we know in our statement that we will have the square of its velocity. And so we see that answer choice D is incorrect because it says we have the square of its mass. But that is just incorrect since we are again squaring the velocity. So with this, we are left with answer choice C, the kinetic energy of a body varies jointly as the square of its velocity and its mass. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write each formula as an English phrase using the word varies or proportional. V = 1/3 πr^2h, where V is the volume of a cone of radius r and height h

Key Concepts

Volume of a Cone

Proportional Relationships

Mathematical Translation

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