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What if my equation doesn't factorise?

For all quadratic equations, you can use the quadratic formula . Given an equation of the form ax 2 +bx+c , you can plug those values into this formula: x 1 , x 2 = (-b +/- sqrt(b 2 - 4ac)) / 2a Note: the te...
HM
Answered by Hayden M. • Maths tutor
4955 Views

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

y = e 2x (x 2 +1) 5/2 The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation: y = uv where u = e 2x and v = (x 2 +1) 5/2 . We now diffe...
AS
Answered by Adam S. • Maths tutor
13483 Views

Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Recall that for two lines to be skew they must satisfy two conditions: 1) They must not be parallel. 2) They must not intersect. We shall check each condition individually. Condition 1 The general vector equ...
DA
Answered by Dorian A. • Maths tutor
12241 Views

How do you use Pythagoras' Theorem?

Pythagoras' Theorem states that h 2 = a 2 + b 2 . This is where you have a right angled triangle, with sides a, b and h where h is the hypotenuse. For example, if we had a triangle with sides of length 3 and...
RB
Answered by Ryan B. • Maths tutor
5408 Views

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

The first step to solving this problem is to treat it as a normal quadratic equation; if you are struggling with comparing our equation to a normal quadratic, try substituting sin(x) = y into the equation as...
KS
Answered by Kirsten S. • Maths tutor
5574 Views