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Mike C.

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Trigonometry

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Question:

A person is standing 90 feet from the base of a building and observes that the angle between the ground and the top of the building is 26 degrees. Estimate the height of the building to the nearest tenth of a foot.

Mike C.

Answer:

The answer 43.9 feet. Here is how to solve this question: 1) Draw a picture of the given information in the problem in order to better understand the situation. 2) Notice that the given lengths of the triangle are adjacent and opposite to the given angle. 3) Remember SOH CAH TOA, and understand that we must use TOA because we are given the opposite and adjacent side lengths. This means we will be using tangent. 4) Plug in the given angle and side lengths. We will get tangent(26) = height/90. 5) In order to get height alone, multiply both sides of the equation by 90 to get 90tangent(26) = height. 6) Use your calculator, making sure it is in degrees, and solve for the left side of the equation. This will bring you to 43.8959 = height. 7) Round to the nearest tenth of a foot to get the answer 43.9 feet.

Calculus

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Question:

What is the limit as x approaches 1 of: 1 - x^2 / x^2 - x?

Mike C.

Answer:

The answer is -2. Here is how to solve this question: 1) Plug in 1 to all of the x's in the equation. You will find that the limit becomes 0/0, which is an indeterminate form. 2) In order to solve this, we must use L'Hopital's rule and differentiate both the bottom and the top separately. This will give us 0 - 2x / 2x - 1. 3) We plug in 1 again to the equation to find the limit is 0 - 2(1) / 2 (1) - 1. 4) This simplifies to -2/1, therefore the answer is -2.

Algebra

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Question:

The lines y = 2x and 2y = - x are: A. Parallel B. Perpendicular C. Horizontal D. Vertical E. None of the Above

Mike C.

Answer:

The answer is (A) Perpendicular. Here is how to solve this question: 1) You first want both lines to be in the form y = mx+b, so we divide both sides of the second equation by 2. We now have the equations y = 2x and y= -x/2. 2) We notice that the slopes (coefficient of x) are negative reciprocals of each other. 3) Since the slopes of the two equations are negative reciprocals, we know the equations must be perpendicular to each other.

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