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Use the substitution u=4x-1 to find the exact value of 1/4<int<1/2 ((5-2x)(4x-1)^1/3)dx

We are required to solve this integral using integration by substitution, in which we assign a variable to equal a certain region of the integrated function in this case, 4x-1. The purpose of this is to remo...
TR
Answered by Taylor R. • Maths tutor
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If given two parametric equations for a curve, how would you work out an equation for the gradient?

Parametric equations will have both the x and the y coordinates expressed in terms of another paramater, usually t . Gradients of curves are expressed in the form of an equation of d y/ d x, in order to work...
MW
Answered by Mollie W. • Maths tutor
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Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)

Sec2A - Tan2A Definition of Sec and Tan = 1/Cos2A - Sin2A/Cos2A Combining Fractions = (1 - Sin2A) / (Cos2A) Apply Double Angle Formula = (1 - 2SinACosA) / (Cos 2 A - Sin 2 A) Make use of 1 = Cos 2 x + Sin 2 ...
JC
Answered by James C. • Maths tutor
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Solve: x^2-7x+6=0

Factorise the equation and then equate each set of brackets to 0 to obtain both possible solutions. By factorising: (x-6)(x-1)=0 Therefore: x=6 or x=1
PG
Answered by Phoebe G. • Maths tutor
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Line AB has equation 4x+5y+2=0. If the point P=(p, p+5) lies on AB, find P . The point A has coordinates (1, 2). The point C(5, k) is such that AC is perpendicular to AB. Find the value of k.

i) Well, if point P lies in AB, then the value of its x and y coordinates have to fulfill the condition imposed by equation AB. Therefore, substituting the x value p for x and the y value p+5 for y: 4(p)+5(p...
JL
Answered by Javier L. • Maths tutor
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