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Adrian B.

In-person tutor for three years

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Pre-Calculus

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Question:

Find the exact value of cos 15° without using a calculator.

Adrian B.

Answer:

cos(15°) = cos(45° - 30°) ----Law of Cosines: cos(A + B) = cos(A) * cos(B) + sin(A) * sin(B) cos(45°) * cos(30°) + sin(45°) * sin(30°) (√2/2)*(√3/2) + (√2/2)*(1/2) (√6/4) + (√2/4) ***cos(15°) = (√6/4) + (√2/4)***

Trigonometry

TutorMe

Question:

A man is on the beach standing 50 ft from a lighthouse. He looks at the top of the lighthouse at an angle of elevation of 60º. How tall is the lighthouse?

Adrian B.

Answer:

A triangle is being made out of three numerical values: the distance from the lighthouse (50 ft), the height of the lighthouse (x ft), and the distance from the man to the top of the lighthouse, which is not needed since we have the distance from the lighthouse. In addition, the angle of elevation is known to be 60º. To find x, use tan(A), where "A" is the angle of elevation. tan(A) = Opposite/Adjacent ------ Substitute all known variables tan(60º) = x/50 ------------------------ Multiply both sides by 50 to isolate "x" 50 * tan(60º) = x ---------------------- Solve for "x" 86.6025... = x *The lighthouse is approximately 86.6 feet tall.*

Algebra

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Question:

Travis and his band are planning to record their first CD. The initial start-up cost is $1500, and each CD will cost $4 to produce. They plan to sell their CDs for $10 each. How many CDs must the band sell before they make a profit?

Adrian B.

Answer:

First is to find the equations needed. Let: x= Number of CDs and y= Number of dollars y= Cost per CD(x) + Start-up Cost y= Price per CD(x) y= 4x + 1500 y= 10x Second, since both equations are equal to "y", set them equal to each other and solve for "x". 4x + 1500 = 10x -------Subtract 4x from each side of the equation 1500 = 6x ---------------Divide both sides by 6 to isolate "x" 250 = x *Travis and his band will have to sell 250 CDs to break even. If Travis sells more than 250 CDs, he will be making a profit.*

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