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Find the equation of the tangent to the unit circle when x=sqrt(3)/2 (in the first quadrant)

Unit circle: x 2 + y 2 = 1 when x = sqrt(3)/2: y 2 = 1 - (sqrt(3)/2) 2 y 2 = 1 - 3/4 y 2 = 1/4 y = 1/2 or -1/2 (first quadrant, so y is positive, i.e. y = 1/2) find gradient at (sqrt(3)/2, 1/2): x 2 + y 2 = ...
KJ
Answered by Kiran J. • Maths tutor
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Integral of (2(x^3)-7)/((x^4)-14x)

Set f(x)= (x^4)-14x. f’(x)=4(x^3)-14=2(2(x^3)-7). Thus we can write (2(x^3)-7)/((x^4)-14x)=(1/2)f’(x)/f(x). The integral of f’(x)/f(x)=ln|f(x)|+c. Thus the integral of (2(x^3)-7)/((x^4)-14x) is (1/2)(ln|f(x)...
IK
Answered by Issy K. • Maths tutor
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what is: a) 1/3 +1/4 ? b) 4/6 + 3/12?

a)First make the denominators the same by multiplying the 1/3 by 4 and 1/4 by 3. makesure top and bottom are multiplied then add the numerators together not denominators. answer should be 7/12. b) Do the sam...
CL
Answered by Charlotte L. • Maths tutor
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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...
RB
Answered by Robbie B. • Maths tutor
6200 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...
CG
Answered by Calin G. • Maths tutor
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