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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
12761 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
3102 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
13518 Views

how to write down the differential equation from a word problem, involving rate of change.

Read the word problem more than once to make sure you fully understand what is being asked and write down the variables involved. Then try to write down all the derivatives in terms of each other, using t...

CG
2758 Views

Differentiate: y = 2 ^ x

y = 2 ^ x

take ln of both sides

ln( y) = ln (2 ^ x)

using the log rules we can bring the power of x down in front of the ln

ln( y ) = x*ln(2)

differentiate both sides wr...

SH
Answered by Shantu H. Maths tutor
52451 Views

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