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Solve algebraically the simultaneous equations: x^2 + y^2 = 25, y - 3x = 13

Steps:Number both equationsUsing equation 2, solve for y in terms of x.Substitute this answer into equation 1 so that your equation only includes x terms and no y terms.Solve equation 1 for x. (This will be ...
RM
Answered by Rowena M. • Maths tutor
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A cricket player is capable of throwing a ball at velocity v. Neglecting air resistance, what angle from the horizontal should they throw at to achieve maximum distance before contact with the ground? How far is that distance?

Assume angle of throw theta. Resolving vertical and horizontal components: Vvert=v.sin(theta) and Vhoriz=v.cos(theta).From 'suvat' equations, time to vertical stationary t=v/a. This must be doubled to find t...
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Answered by Benjamin W. • Maths tutor
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3 teas and 2 coffees have a total cost of £7.80. 5 teas and 4 coffees have a total cost of £14.20. Work out the cost of one tea and the cost of one coffee.

This is a typical simultaneous equations question. Using the information in the question we can write down two equations in two unknowns (let's say T=tea and C=coffee).(1) 3T + 2C = £7.80(2) 5T + 4C = £14.20...
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Answered by Emily P. • Maths tutor
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how do you work out the gradient and point of interception of a linear graph given some coordinates

plot the coordinates to obtain a straight line graphcalculate the gradient by using the equation m=change in y/change in xfind the point of interception by seeing where the line crosses the y axis, where x=0
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Answered by Katrina P. • Maths tutor
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f(x) = e^(sin2x) , 0 ≤ x ≤ pi (a). Use calculus to find the coordinates of the turning points on the graph of y = f(x)

First, understand the concept of a turning point (zero gradient, implying first derivative is zero at the turning point)How do we differentiate exponentials ( if f(x) = e^g(x) then f'(x) = g'(x)*e^g(x) ) Oka...
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Answered by Marco W. • Maths tutor
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