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Find the curve whose gradient is given by dy/dx=xy and which passes through the point (0,3)

First "Separate the Variables" by rearranging the equation to get the ys on the LHS and the xs on the RHS: (1/y) dy=x dx Now Integrate: Integral(1/y) dy = Integral(x) dx ln(y)=x 2 /2 + constant of ...
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Answered by Christian C. • Maths tutor
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Here are some fractions: 3/10, 2/8, 4/12, 12/40, 5/20. Which of these fractions are equivalent to 1/4?

Before we begin lets quickly do some reviewing. What are fractions and how can we write them? Fractions are often used when we don't want to write down numbers that are really long. A fraction , simply put i...
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Answered by Michael L. • Maths tutor
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Express 3/2x+3 – 1/2x-3 + 6/4x^2-9 as a single fraction in its simplest form.

First it is necessary to notice that 4x^2-9 can be written as (2x-3)(2x+3). To solve this question, you first have to write all the fractions in terms of their lowest common denominator. In this case that is...
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Answered by Dhian S. • Maths tutor
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By using partial fractions, integrate the function: f(x) = (4-2x)/(2x+1)(x+1)(x+3)

(4-2x)/(2x+1)(x+1)(x+3) = A/(2x+1) + B/(x+1) + C/(x+3) 4-2x = A(x+1)(x+3) + B(2x+1)(x+3) + C(2x+1)(x+1) let x = -1: 4-2(-1) = B(2(-1)+1)((-1)+3) 6 = B(-1)(2) B = -3 let x = -3: 4-2(-3)= C(2(-3)+1)((-3)+1) 10...
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Answered by Oliver F. • Maths tutor
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The velocity of a moving body is given by an equation v = 30 - 6t, where v - velocity in m/s, t - time in s. A) What is the acceleration a in m/s^2? B) Find the expression for the displacement s in terms of t given the initial displacement s(0)=10 m.

A) Acceleration is the rate of change of velocity with respect to time; therefore, in order to calculate it we need to differentiate the given equation of velocity v with respect to time t: a = dv / dt = d( ...
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Answered by Krisjanis P. • Maths tutor
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