Ryan S.

Graduate Student at Lehigh University

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Calculus

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Question:

Find the equation of the tangent line to the graph x*y=y^{2}*x^{2}+y+x+2 at the point (0,-2).

Ryan S.

Answer:

Use implicit differentiation to find y' and then plug in the point (0,-2) to find the slope of the tangent line at that point. Taking the derivative gives y+x*y'=2y*y'*x^{2}+y^{2}*(2*x)+y'+1 Plugging in (0,-2) gives -2+0=0+0+y'+1, or y'=-3, Thus, the slope of the tangent line to this graph at the point (0,-2) is -3. Since we have a point and the slope of the tangent line, we will use the point-slope form of the line. The equation of the tangent line at (0,-2) is y-(-2)=-3(x-0), or y+2=-3x,

Algebra

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Question:

Solve the following equation -> 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Ryan S.

Answer:

1) 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 2) 15x - 10 - x + 3 = -16x - 20 +13 3) -16x - 7 = -16x - 7 4) 0=0 5) the above statement is true for all values of x and therefore all real numbers are solutions to the given equation.

Physics

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Question:

The density of a uniform cylinder is determined by measuring its mass, length, and diameter. Calculate the density. mass = m = 47.36 g length = l = 15.28 mm diameter = d = 21.37 mm

Ryan S.

Answer:

Calculate the density using the following formula: density = p = (4*m)/(pi*l*d^2) = 8642 kg*m^-3

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