Top answers

Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.

y = (2x -3)^3 y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle. y = 8x^3 - 36x^2 + 54x - 27 dy/dx = 24x^2 - 72x + 54 at point (1,-1); dy/dx = 24 -72 + 54 = 6 Therefore tangent lin...
RS
Answered by Robert S. • Maths tutor
13345 Views

Find the first derivative of y=2^x

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question, is...
AM
Answered by Alex M. • Maths tutor
5232 Views

What is Pythagoras' Theorem and how do you use it?

Pythagoras' Theorem: a 2 + b 2 = c 2 where a, b, c relate to the sides of a right-angled triangle, and c is the hypoteneuse. Use the equation to find the length one side if you only know the lengths of two o...
HS
Answered by Hermione S. • Maths tutor
3899 Views

Find the general solution of 2 dy/dx - 5y = 10x

Try y=Ae bx diffrentiate this (dy/dx = Abe bx ) and sub into 2dy/dx -5y = 0 to find complementary function. 2Abe bx - 5Ae bx = 0 2b - 5 = 0 b = 2.5 Find the particular integral using trial solution y = Cx+D,...
AH
Answered by Amy H. • Maths tutor
5506 Views

Solve the equation for x: 3x^2 -5 = 22

x =3 or x= -3
RM
Answered by Rachel M. • Maths tutor
3945 Views