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# Tutor profile: Heyley G.

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Heyley G.
Stetson University Student, Math and Comp Sci Double-Major
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## Questions

### Subject:Pre-Algebra

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Question:

Aliyah had \$24 to spend on seven pencils. After buying them she had \$10. How much did each pencil cost?

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Heyley G.

She has \$24 to spend = Bought 7 pencils of unknown cost + leaving her with \$10 \$24 = 7p + \$10 Now that you have your equation, solve for p (the price of each pencil). 24 = 7p + 10 ; Subtract 10 in each side. 14 = 7p ; Undo the multiplication with division (Divide 7 on both sides.) 2 = p Each pencil costs \$2!

### Subject:Calculus

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Question:

What is the 50th derivative of cos x?

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Heyley G.

Now, we are not just going to sit here and take 50 derivatives of cos x. That's ridiculous. If this is on your test, you wouldn't take 50 derivatives of cos x even if you wanted to because you wouldn't have the time to take 50 derivative of cos x. Instead, we're going to do what I love to do whenever solving problems in mathematics: recognize a pattern and take a shortcut. 1st derivative: -sin x 2nd derivative: -cos x 3rd derivative: sin x 4th derivative: cos x ; What??? That's the original equation!! After taking the 4th derivative of cos x, you end up the the same equation you started with. Therefore, the derivatives after that are going to be repeats of the first 4. In other words, the 5th derivative will be the same as the 1st derivative, the 6th derivative will be the same as the 2nd derivative, the 7th derivative will be the same as the 3rd derivative, the 8th derivative will be the same as the 4th, and so on and so forth. -sin x: 1 5 etc... -cos x: 2 6 sin x: 3 7 cos x: 4 8 We have found our pattern: after every 4 derivatives, the values/equations repeat. That also means that after ever multiple of 4, you will get back to the original equation. -sin x: 1 5 .... 49 -cos x: 2 6 .... 50!!!! sin x: 3 7 .... 51 cos x: 4 8 12 16 20 .... 44 48 52 The 50th derivative of cos x will be -cos x. Without doing the table, you could have divided 50 by 4. When you divide by 4, the remainder will be either 1, 2, 3, or no remainder which is means that you're back with the original equation. Dividing 5 by 4 will give you a remainder of 2 which means that the 50th derivative is the same as the 2nd derivative (-cos x). Either method works. If you're more visual and need to see the numbers changing, the table method is better for you! :)

### Subject:Algebra

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Question:

Solve for x in the following equation: y = 2x^2 - x - 1.

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Heyley G.

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