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Morgan A.

Can Tutor Pre-Algebra or College Algebra

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Pre-Calculus

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Question:

Prove the identity sin^2 θ + cos^2 θ = 1.

Morgan A.

Answer:

Per the unit circle, sin θ = y/r while cos θ = x/r. Plugging both ratios into our identity, we now have: (y/r)^2 + (x/r)^2 = 1, or y^2/r^2 + x^2/r^2 = 1. Multiplying both sides of the equation by r^2, we have y^2 + x^2 = r^2, or x^2 + y^2 = r^2. This is the standard form for the unit circle.

Pre-Algebra

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Question:

Missy currently has $750 in her bank account. During the work week, she wrote checks in the amounts of $213.00, $75.00, $44.00, and $26.00. On Friday, her paycheck of $2332 was deposited (via Direct Deposit) into her account. As of Friday, how much does Missy have left in her account?

Morgan A.

Answer:

Add the checks together to get $358. Subtract $358 from $750 to get $392. Add $2332 to $392 to get Missy's current balance, or $2724.

Algebra

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Question:

George rented a car from the Save-A-Bunch car place. George had to put down a $50 deposit. Plus, he will be charged $.15 per mile traveled. If George traveled 400 miles, how much will the rental cost him?

Morgan A.

Answer:

Let x equal the number of miles. Setting up an algebraic equation, we have C (for cost) = 50 + .15x. To find the total cost, replace x with 400 to get the following: C = 50 + .15(400) = 50 + 60 = 110 Therefore, it will cost George $110 total.

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