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Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)

First we subtract ln(2-y) from both sides to get "ln(4y+7) - ln(2-y) = 3". By applying the laws of logs from C2, we have "ln[(4y+7)/(2-y)] = 3". Therefore, if we put them as exponents of ...
DB
Answered by Danielle B. • Maths tutor
4579 Views

Find the differential of y(x)=(5x*Cos(3x))^2

Firstly I would state the substitution rule, letting 5x Cos(3x)=w(x), and differentiating with respect to w(x). This gives y'(x)=2 w'(x) (w(x)).I would then demonstrate the product rule stating where u and v...
HL
Answered by Harry L. • Maths tutor
4032 Views

If x is a real number, what are the solutions to the quadratic: 4*x^2- 4*x+1 = 0

You first calculate the delta of the equation: delta = b^2-4 a c = 16 - 16 = 0 => the solution is double.x1,2 = (-b±sqrt(delta))/2/a = 4/2/4 = 1/2 which is real.so the solutions are 1/2 and 1/2.
MI
Answered by Maria I. • Maths tutor
3602 Views

The equation x^2+ kx + 8 = k has no real solutions for x. Show that k satisfies k^2 + 4k < 32.

If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac&lt;0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^2 +...
TD
Answered by Tutor91955 D. • Maths tutor
15864 Views

Find the equation of the tangent to the curve y^3 - 4x^2 - 3xy + 25 = 0 at the point (2,-3).

This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us 3y...
TJ
Answered by Tanmayi J. • Maths tutor
5035 Views