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Shruti J.

Experienced Math Tutor for three years at Umass Boston

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Applied Mathematics

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Question:

In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?

Shruti J.

Answer:

Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat. -4x + 4y + 2z = 560 : -9x + 9y + 6z = 1,290 -3x + 3y + 2z = 430 : divide all terms of equation C by 3 -x + y = 130 : subtract equation D from equation B -3(x + y) + 2z = 430 : equation D with factored terms. -3*130 + 2z = 430 -z = 20 : solve for z -x + y + z = 130 + 20 = $150

Pre-Calculus

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Question:

Your computer's screen saver is an expanding circle. The circle starts as a dot in the middle of the screen and expands outward, changing colors as it grows. With a twenty-one inch screen, you have a viewing area with a 10-inch radius (measured from the center diagonally down to a corner). The circle reaches the corners in four seconds. Express the area of the circle (discounting the area cut off by the edges of the viewing area) as a function of time t in seconds.

Shruti J.

Answer:

The radius is growing at a rate of (10 inches)/(4 seconds) = 2.5 inches per second. Then the equation of the radius r, as a function of time t, is: r(t) = 2.5t The formula for the area A of a circle is given by: A(r) = (pi) r^2 Then the area, as a function of time, is found by substituting the radius function in the area function and composing the two functions gives: A(t) = A(r(t)) = 6.25 (pi) t^2 Therefore the function that we are looking for is: A(t) = 6.25 (pi) t^2

Algebra

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Question:

Find the vertex, the focus, the axis of symmetry and the directrix of the parabola defined by the equation 2y 2 + 8y + x + 1 = 0

Shruti J.

Answer:

We first complete the square using the terms in y and y 2 and write the given equation in the form (y - k) 2 = 4a (x - h) where (h , k) is the vertex and the focus is at (h + a , k), the axis of symmetry is given by y = k and the directrix is given by x = h - a. 2(y 2 + 4y) + x + 1 = 0 2((y + 2) 2 - 4) + x + 1 = 0 (y + 2) 2= - (1/2)(x - 7) vertex at (7 , -2) -(1/2) = 4a , hence a = -1/8 focus at (7 - 1/8 , -2) = (6.875 , -2) axis of symmetry given by y = -2 Directrix is a vertical line given by: x = h - a = 7 + 1/8 = 7.125

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