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y is inversely proportion to the square of x. y=10 when x=5. Express y in terms of x.

y is proportion to 1/x 2 . This can be written as y=k/x 2 where k is a constant of proportionality. Given that y=10 when x=5 , k can be found as yx 2 which is equal to 25. Therefore; y=25/x 2 .
EH
Answered by Evan H. • Maths tutor
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The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x 2 -2ax+8. At point B , x=4 . This gives the relation 104=8a and thus gives a=13.
EH
Answered by Evan H. • Maths tutor
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How would one multiply out brackets?

If asked to multiply out a set of brackets, one must remember to multiply each term in a set of brackets by every term in the other set of brackets. For example, (x+2)(x-4) = x 2 +2x-4x-8 = x 2 -2x+8. An inc...
AR
Answered by Alden R. • Maths tutor
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find the inverse function of the following: f(x) = 3x-5

in an inverse function, simply put the x and y are inversed: meaning x becomes y, and y becomes x f(x): y=3x-5 f-1(x): x=3y-5 <=> x+5=3y <=> (x+5)/3 = y <=> (1/3)x + (5/3) = y answer
OT
Answered by Olivia T. • Maths tutor
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How do you integrate x* (exp(x))??

The easiest method to use in this incidence is integratation by parts. So let u=x and dv/dx=exp(x). Therefore du/dx=1 and v=exp(x). Then we use the formula where integral(u du/dx)=u v-integral(v*du/dx). So i...
HJ
Answered by Harmony J. • Maths tutor
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