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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=a 2 -4ab delta=144-4(k+1)(k-4) delta=-4k 2 +12k+160 Because the problem tells us that the roots are real, ...
AB
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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 answer of 27. c)i...
MB
Answered by Millie B. • Maths tutor
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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) + 5sin(theta) = R[cos(alpha)c...
OS
Answered by Olivia S. • Maths tutor
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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 the ...
CG
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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 wrt x ( 1 / y ) * dy / dx = ln(2) dy / d...
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Answered by Shantu H. • Maths tutor
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