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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...

Answered by Andreea-Irina B. • Maths tutor

12697 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...

Answered by Olivia S. • Maths tutor

13409 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...

Answered by Christoforos G. • Maths tutor

2729 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...

Answered by Shantu H. • Maths tutor

52294 Views

The points A and B have coordinates (2,4,1) and (3,2,-1) respectively. The point C is such that OC = 2OB, where O is the origin. Find the distance between A and C.

To find the distance between the points A and C, we want to find the magnitude of the vector AC. In order to do this, we must first find the vector AC, which we do by using their position vectors. We are ...

Answered by Sophie W. • Maths tutor

10584 Views