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Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.

Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(the...
JW
Answered by Joe W. • Maths tutor
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Find dy/dx for y=5x^3−2x^2+7x−15

'Find dy/dx' means it wants us to differentiate. The rules for this are multiply the coefficient (number before x) by the current power, then decrease the power by 1.In this example:5x 3 would become 15x 2 ,...
GS
Answered by Georgia S. • Maths tutor
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y= arcos(x). Find dy/dx in terms of x.

Rearrange the expression to create a familiar function with a known differencial: arcos(x)=y x= cos(y) Differenciate x with respect to y: dx/dy= -sin(y) We know that dy/dx= 1/(dx/dy), so rearange to find an ...
DK
Answered by Danyal K. • Maths tutor
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Find the derivative of x^3 - (y^2)x =3

Differentiating with respect to x gives:3x^2 -y^2- x 2y(dy/dx) = 03x^2 -y^2 = x2y(dy/dx)dy/dx = (3x^2 - y^2)/2xy
NH
Answered by Nims H. • Maths tutor
3617 Views

Can you explain what a logarithm is?

We can think of taking the logarithm base a of a number b (log a b) as &quot;the number of times we need to multiply a by itself to get b&quot;. So for example, log 2 16 = 4, since we need to multiply 2 by i...
DH
Answered by Daniel H. • Maths tutor
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