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A rectangle has a total perimeter of 32cm with sides of length '3x' and 'x+8'. Solve for x.

3x + x+ 8 + 3x + x + 8 = 328x + 16 = 328x = 16x = 2
SP
Answered by Sai P. • Maths tutor
3589 Views

Differentiate cos(2x^3)/3x

Using quotient rule y = u/v - dy/dx = (v.du/dx - u.dv/dx)/v 2 .u = cos(2x 3 ) , a = 2x 3 . du/da = -sin(a), da/dx = 6x 2 . From chain rule, we know that du/dx = du/da . da/dx, so du/dx = -6x 2 sin(2x 3 ). We...
CW
Answered by Charlie W. • Maths tutor
10134 Views

Differentiate x^2 ln(3x) with respect to x

This question requires the use of differentiation by product rule. First differentiate the first term, whilst keeping the second term the same, i.e. we get 2xln(3x). Secondly we keep the first term the same,...
RF
Answered by Ricky F. • Maths tutor
15169 Views

When solving two simultaneous equations, when should you use the method of elimination and when would you use the method of substitution?

I would first always label the two equations as equation 1 equation 2. I would then look to see if you can cancel one of the variables out by adding or subtracting the two equations together. If this is poss...
RC
Answered by Reece C. • Maths tutor
3938 Views

The line y = (a^2)x and the curve y = x(b − x)^2, where 0<a<b , intersect at the origin O and at points P and Q. Find the coordinates of P and Q, where P<Q, and sketch the line and the curve on the same axes. Find the tangent at the point P.

Firstly, for the points of intersection we need to equate the two expressions for y. Since we know that they intersect at the origin, we can immediately cancel the x values and then solve the quadratic for t...
JB
Answered by Josh B. • Maths tutor
7291 Views