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Express 3cos(theta) + 5sin(theta) in the form Rcos(theta - alpha) where R and alpha are constants, R>0 and 0<alpha<90. Give the exact value of R and the value of alpha to 2dp.

Write out identity: Rcos(theta - alpha) = Rcos(theta)cos(alpha) + Rsin(theta)sin(alpha) from formula booklet Write out in form of question so it's easier to compare: 3cos(theta) + 5sin(theta) = R[cos(alpha)c...
OS
Answered by Olivia S. • Maths tutor
15620 Views

how to write down the differential equation from a word problem, involving rate of change.

Read the word problem more than once to make sure you fully understand what is being asked and write down the variables involved. Then try to write down all the derivatives in terms of each other, using the ...
CG
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Differentiate: y = 2 ^ x

y = 2 ^ x take ln of both sides ln( y) = ln (2 ^ x) using the log rules we can bring the power of x down in front of the ln ln( y ) = x*ln(2) differentiate both sides wrt x ( 1 / y ) * dy / dx = ln(2) dy / d...
SH
Answered by Shantu H. • Maths tutor
55460 Views

The points A and B have coordinates (2,4,1) and (3,2,-1) respectively. The point C is such that OC = 2OB, where O is the origin. Find the distance between A and C.

To find the distance between the points A and C, we want to find the magnitude of the vector AC. In order to do this, we must first find the vector AC, which we do by using their position vectors. We are giv...
SW
Answered by Sophie W. • Maths tutor
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what is the equation of the normal line to the curve y=x^2-4x+3 at the point (5,8)?

first we need to work out the gradient of the tangent at (5,8). so first differentiate the equation once with respect to x. this gives is dy/dx=2x-4. so at (5,8) the gradient of the tangent is 6. this means ...
MC
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