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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
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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
5487 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
5652 Views

There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet from the bag and eats it. Hannah then takes at another sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0

P(2 orange sweets) = P(orange sweet) * P(orange sweet) (6/n) * (5/(n-1)) = 1/3 30/(n(n-1)) = 1/3 90 = n(n-1) 90 = n 2 -n n 2 -n-90=0 as required
TV
Answered by Tim V. • Maths tutor
17021 Views

What is the quadratic formula and how do I use it?

The quadratic formula is a way of solving quadratic equations of the form: ax 2 +bx+c=0. By plugging in the values a,b and c into it, the solutions for x can be obtained:x = [-b +/- sqrt(b 2 -4ac)]/2a For ex...
PM
Answered by Patrick M. • Maths tutor
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