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Trigonometry
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Question:

In a right triangle ABC with angle A equal to 90o, find angle B and C so that sin(B) = cos(B).

Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse. sin(B) = b/h and cos(B) = c/h sin(B) = cos(B) means b/h = c/h which gives c = b The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45 degrees.

Basic Math
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Question:

A scale of 1:20 is used to make the drawing of a car. If the length of the drawing is 10 inches, what is the real length of the car?

Length according to scale= 10 inches=1/(20+1)=1/21 of the real length of the car Therefore, real length=10/(1/21)=210 inches.

Algebra
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Question:

f(x) is a quadratic function such that f(1) = 3 and f(5) = 3. Find the x coordinate of the vertex of the graph of f.

f(x) = ax2 + bx + c f(1) = 3 which give 3 = a + b + c f(5) = 3 which gives 3 = 25a + 5b + c 24a + 4b = 0 : subtract equation B from equation C x coordinate of vertex = -b/2a = 3 : from above equation

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