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Where does the circle (x-6)^2+(y-7)^2=4 intersect with y=x+3

Where does the circle (x-6) 2 +(y-7) 2 =4 intersect with y=x+3We need to sub y=x+3 into the circle equation giving us an equation in just x:(x-6) 2 +(x-4) 2 =4Next we expand out the brackets:x 2 -12x+36+x 2 ...
NL
Answered by Nicola L. • Maths tutor
3503 Views

dh/dt = (6-h)/20. When t=0, h=1. Show that t=20ln(5/(6-h))

Part 1: This question requires us to first do some rearranging. The right hand side of the equation is in terms of h, and we are looking to find t in terms of h, so it won't be appropriate to simply integrat...
LA
Answered by Linetta A. • Maths tutor
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How do you integrate (sinx)^3 dx?

Firstly, we must use the special property of trig functions which means that (sinx) n is the same as sin n x. Likewise, (cosx) n =cos n x, (tanx) n =tan n x and so on. In this case, we need to start by repla...
SS
Answered by Shanti S. • Maths tutor
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Show that 2(1-cos(x)) = 3sin^2(x) can be written as 3cos^2(x)-2cos(x)-1=0.

Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let's t...
RS
Answered by Rebekah S. • Maths tutor
4341 Views

Given two functions x = at^3 and y = 4a, find dy/dx

Solution: Parametric Differentiation with utilisation of Chain Rule. By the chain rule: dy/dx = dy/dt * dt/dx Note: dt/dx = 1 / (dx/dt) So dy/dt = 0, dx/dt = 3at^2 So dy/dx = 0 * 1/(3at^2) and hence dy/dx = 0.
MP
Answered by Michele P. • Maths tutor
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