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A curve has parametric equations: x = 3t +8, y = t^3 - 5t^2 + 7t. Find the co-ordinates of the stationary points.

First differentiate: dx/dt = 3, dy/dt = 3t 2 - 10t + 7 Using the chain rule: dy/dx = dy/dt * dt/dx = (3t 2 - 10t + 7)/3 At stationary points, the gradient is equal to zero: 3t 2 - 10t + 7 = 0 Solve for t usi...
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Answered by Robbie B. • Maths tutor
6109 Views

Amber earns £7 for each hour she works from Monday to Friday. She earns £10 for each hour she works on Saturday. One week Amber worked for 4 hours on Saturday. That week she earned a total of £180 (a) How many hours did Amber work that week?

We know Amber worked 4 hours on a Saturday, so she earned 4*£10= £40 that day. The rest of the money, which is £180-£40=£140, she must have earned it during the week. Knowing she earns £7 per hour, this will...
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Answered by Calin G. • Maths tutor
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Solve 5x-2>3x+11

5x-3x>11+2 2x>13 x>13/2 or x>6.5
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Answered by Hamza H. • Maths tutor
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There is a bag of blue, red, and white counters. 1/6 of the bag is blue counters. 1/4 of the bag is red counters. What is the smallest number of white counters that could possibly be in the bag.

6 and 4 are common factors of 24. 1/6 = 4/24, and 1/4=6/24. 4/24+6/24 =10/24 of the bag is blue and red counters. Therefore, 24/24-10/24=14/24 of the bag is white counters. 14/24 can be simplified to 7/12. A...
AC
Answered by Alex C. • Maths tutor
6578 Views

A triangle has 3 angles of 60 degrees, (5y-40) degrees, and (2y+20) degrees. Show that the triangle is equilateral.

All the angles in a triangle add up to 180 degrees. Therefore, 60 + (5y - 40) + (2y + 20) = 180. This can be simplified to 7y +40 = 180. And simplified again to 7y = 140, which then means y = 140 / 7 = 20 de...
AC
Answered by Alex C. • Maths tutor
7418 Views