# Tutor profile: Jonathan N.

## Questions

### Subject: Geometry

Lets say you have two different size basketballs. One has a radius of 12 inches, and one has a radius of 7 inches. What is the difference in the volume of both basketballs (assuming they are spheres)?

Using the equation for volume of spheres and plugging in the radius for 'r' which is: 4/3 * pi*r^2 We find that the volume of the 12 inch radius basketball is 7238.23 inches^3 And the volume of the 7 inch radius basketball is 1436.76 inches^3 The difference between the volume of both basketballs would be 7238.23 - 1436.76 Which gives us 5801.47 inches^3

### Subject: Calculus

Find the derivative of: 2cos(4x^3)

The first step is to take the derivative of the term inside of the cos expression. The derivative of 4x^3 is 12x^2. Then you multiply that by the derivative of cos, which is negative sin. This gives you -12x^2 * sin(4x^3). Lastly, multiply that whole expression by the 2 that was in front of cos, giving you your final answer. -24x^2 * sin(4x^3).

### Subject: Algebra

Suppose you have just opened up a lemonade stand. For supplies, you spent 3 dollars on ice, 10 dollars on lemons, 3 dollars on sugar, and 4 dollars on plastic cups. If you are selling each cup of lemonade for 50 cents, then how many cups of lemonade do you need to sell to break even with your supplies costs? How many cups of lemonade do you need to sell to earn 5 dollars (This is including the supplies costs)?

The first step to solving this problem is to find the total supplies cost, which turns out to be 20 dollars. Next, we can set up an equation to solve for how many cups of lemonade must be sold in order to break even. In order to break even, this equation can be written, 20.00 = 0.50*x . In order to earn 5 dollars, we have to earn five more dollars than the supplies cost, which gives us the following equation, 25.00 = 0.50*x. Solving the two equations for 'x' would give us 40 cups of lemonade to break even, and 50 cups to earn five dollars.

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