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The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.

(a) If we consider the intersection of these two lines then, 3x-7=2px^2-6px+4p.This can be rearranged into the form ax^2+bx+c=0 such that, 2px^2+(-6p-3)x+4p+7, where a=2p, b=-6p-3 and c=4p+7.However, since t...
WG
Answered by Will G. • Maths tutor
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How do you differentiate using the chain rule?

The chain rule is used where the equation you are looking to differentiate is a function that is itself raised to a power. For example, we might have y = (x 2 -2) 3 and want to differentiate with respect to ...
OB
Answered by Oliver B. • Maths tutor
3901 Views

C and D are two events such that P(C) = 0.2, P(D) = 0.6 and P(C|D) = 0.3. Find P(D|C), P(C’ ∩ D’) & P(C’ ∩ D)

Here we use the formula for conditional probability:P(C|D)xP(D)=(𝑃(C∩D))= 0.3x0.6=0.18Note: 𝑃(C∩D)=𝑃(D∩C)=0.18Hence P(D|C)=𝑃(D∩C)/P(C) = 0.18/0.2 = 0.9P(C'∩D') = P(C'|D')xP(D')P(C'|D) = 0.7P(D')=0.4P(C')=0.8...
SV
Answered by Sunny V. • Maths tutor
11118 Views

Given that x = cot y, show that dy/dx = -1/(1+x^2)

Identify that we are looking at dy/dx, not dx/dy and realise the relationship that dy/dx=1/(dx/dy)2)Try find dx/dy;cot = 1/tan or (tan) -1 Hence, x=(tan y ) -1 implying dx/dy = (-1)(tan y) -2 (sec 2 y ) =(-1...
JF
Answered by Jacob F. • Maths tutor
12831 Views

Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.

To solve this problem we first must look into the given formula for time (T). It is stated, in the question, that the time taken is dependent on distance x. From this we can infer that the following problem ...
AH
Answered by Aziz H. • Maths tutor
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