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Finding the length of the side opposite a known angle while having the hypotenuse length known

Sin x is equal to the length of the opposite side divided by the length of the hypotenuse. So, the length of the opposite side is Sin x multiplied by the length of the hypotenuse

AA
Answered by Amer A. Maths tutor
3859 Views

In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding ...

SW
Answered by Sam W. Maths tutor
5965 Views

The quadratic equation (k+1)x^2+12x+(k-4)=0 has real roots. (a) Show that k^2-3k-40<=0. (b) Hence find the possible values of k.

(a) There is a quadratic equation which should e solved using the delta andthe roots formulas.

delta=a2-4ab

delta=144-4(k+1)(k-4)

delta=-4k2+12k+160

Becau...

AB
13342 Views

You area told that y is proportional to x2 and that when y = 75, x = 5. a) Find a formula for y in terms of x. b) Find the value of y when x = 3. c) Find the value of x when y = 1200.

a) when y=75 x=5 and y is proportional to x^2, so the answer is y=___x^2
if x=5, then x^2 = 25, and 75/25=3, so the answer is y=3x^2

b) if x=3, x^2=9, if you multiply this by 3, you get the a...

MB
Answered by Millie B. Maths tutor
3350 Views

Express 3cos(theta) + 5sin(theta) in the form Rcos(theta - alpha) where R and alpha are constants, R>0 and 0<alpha<90. Give the exact value of R and the value of alpha to 2dp.

Write out identity:

Rcos(theta - alpha) = Rcos(theta)cos(alpha) + Rsin(theta)sin(alpha) from formula booklet

Write out in form of question so it's easier to compare:

3cos(theta) + 5si...

OS
Answered by Olivia S. Maths tutor
14404 Views

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