Tutor profile: Jesse M.

What is the derivative of 5y^3 + 8z^7 +90?

Derivatives involving variables follow this rule. Take the constant multiplied by the variable and multiply it by the power of the variable. Then subtract one from the power. Constants always derive to zero. This makes our answer 15y^2 + 56z^6 + 0 or 15y^2 + 56z^6

In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side? What about the medium leg?

The hypotenuse is the longest side, so we know no other side can be longer than 6. This means our answer must be shorter than 6. We also know that in a 30-60-90 triangle, the shortest leg will always be half of the hypotenuse. 6/2 = 3 so our answer is 3. The medium leg is always the length of the shortest leg time square root 3. This means the medium leg is 3 x square Root (3).

Why do you weigh less when going down in an elevator?

You only weigh less when the elevator is accelerating downward. This is because Force = mass X acceleration. This means to force the person presses down on the scale is equal to the mass of the person, times the acceleration. When you accelerate downward, you actually are applying less force to the scale, so the apparent weight is less.