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Find the coordinates of the point of intersection of the lines 2x + 5y = 5 and x − 2y = 4.

Rearrange both equations to make y the subject:2x + 5y = 5 rearranges to y = -2x/5 + 1 and x - 2y = 4 rearranges to y = x/2 - 2Equate both the rearranged equations and solve for x:-2x/5 + 1 = x/2 - 2x = 10/3...
EO
Answered by Ethan O. • Maths tutor
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What is differentiation and integration?

An integral is an anti-derivative, meaning it will take the derivative we are assessing and return it back to its original function. Moreover, an integral is used to find the area under a curve. Differentiat...
OA
Answered by Othman A. • Maths tutor
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What is the product rule in differentiation?

The product rule is a special rule that exists for differentiating products of two (or more) functions. It states: If y= uv , then dy/dx= u (d v /dx) + v (d u /dx) . So when we have a product to differentiat...
IA
Answered by Ife A. • Maths tutor
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d/dx[sin(x) + cos(x)]

cos(x) - sin(x)
CM
Answered by Casimir M. • Maths tutor
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A particle of mass m moves from rest a time t=0, under the action of a variable force f(t) = A*t*exp(-B*t), where A,B are positive constants. Find the speed of the particle for large t, expressing the answer in terms of m, A, and B.

First, we need to find a formula for the speed of the particle, v, at a given time, t. Relate the speed, v, to the force f, using Newton's 2nd Law: f(t) = m dv/dt (remembering that acceleration is the time-d...
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