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Ashley S.

Undergraduate Mathematics Student

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Geometry

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Question:

Find whether 2x+3y=4 and 4x+6y=8 intersect.

Ashley S.

Answer:

4x+6y-8=0 can be written as 2 (2x+3y-4=0). Hence these lines are parallel and parallel lines never intersect)

Basic Math

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Question:

If y = |x|; x €R (real number) and y is a positive integer. If y is a function of x, what type of function is that?

Ashley S.

Answer:

Since y = |x| and y is positive while x is both positive and negative, for each value of y we have two values in x. For eg: f (-1,1) = 1 ; x = -1, 1 and y = 1. At the same time every element y has a pre image x, for eg: $$f^-1$$ (7) =(7, -7) ; x=7, -7, y = 7 Therefore it is an onto function

Calculus

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Question:

Find the area between the parabola, $$3y^2 = 25x$$ and $$5x^2 = 9y $$

Ashley S.

Answer:

$$\int_0^3$$ $$\int_{5/9 x^2}^{5\sqrt{x/3}}$$ dydx integrating $$dy$$ part to $$y$$ and substituting the limits =$$\int_0^3$$ $$(5\sqrt{x/3} - 5/9 x^2)$$ dx Integrating the $$dx $$ part into $$x $$ and substituting the limits 3,0 =5 Sq.units

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