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A curve is defined by parametric equations: x = t^(2) + 2, and y = t(4-t^(2)). Find dy/dx in terms of t, hence, define the gradient of the curve at the point where t = 2.

dy/dx = (dy/dt)/(dx/dt) y = t(4-t 2 ), then using differentiation of y with respect to t, dy/dt = 4 - 3t 2 x = t 2 + 2, then using differentiation of x with respect to t, dx/dt = 2t Find dy/dx by dividing dy...
MW
Answered by Micah W. • Maths tutor
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Solve x^2 - 6x + 8 < 0

To see the answer more clearly, we can sketch the function. First, we start by sketching the parabola (curve). If we have a positive x^2 term then we have a U shaped parabola and if it is negative, i.e. -x^2...
RW
Answered by Rachel W. • Maths tutor
15946 Views

Evaluate 3 /5 + 1/ 4

5×4=20 common denominator what did you do to 5 to get to 20? X4, therefore you have to 3x4=12what did you do to 4 to get to 20? X5, therefore you have to 1x5=5 12/20 + 5/20= 17/20
VK
Answered by Vickie K. • Maths tutor
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Express 3sin(2x) + 5cos(2x) in the form Rsin(2x+a), R>0 0<a<pi/2

Start by expanding out Rsin(2x+a) using the addition formula for sin, sin(A+B) = sin(A)cos(B)+cos(A)sin(B). Substituting 2x = A and a= b, we get that Rsin(2x+a) = R(sin(2x)cos(a) + cos(2x)sin(a)) = Rcos(a)si...
MF
Answered by Michael F. • Maths tutor
10408 Views

Harry drives from Exeter to London in 4 hours at an average speed of 70km/h. Ron drives from Exeter to London in 5 hours. (a) Assuming Ron took the same route as Harry, calculate Ron's average speed.

The distance from Exeter to London can be calculated using the information about Harry's journey. Average speed = Distance/Time so Distance = Average speed x Time. This means that the distance from Exeter to...
JF
Answered by James F. • Maths tutor
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