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The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.

For the line and the curve to intersect we need the for the following system of equations to have a solution. y = 3x AND y = x² - aThe solutio...

Answered by Hasnat K. • Further Mathematics tutor

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prove by induction that, f(n) = 2^(3n+1) + 3(5^(2n+1)) is divisible by 17 for all n>0.

With induction we start with the base case n = 1. So setting n=1 we find that f(1) = 391 which is equal to 17x23. So indeed the base case holds.We assume that for positive integers k, f(k) is divisible by...

Answered by Matt B. • Further Mathematics tutor

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How do you solve, dy/dx=(x^2+y^2)/xy?

Substitute y/x = z then separate the variables and integrate.

Answered by • Further Mathematics tutor

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Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

Base case - First let us consider the base case where n=1. Then the left hand side of the equation becomes 1 and the right hand side is (1/6)12*3=6/6=1. Thus LHS=RHS and we are d...

Answered by Anna R. • Further Mathematics tutor

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Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1

As is the case with all induction questions, we first need to show that the result is true for the base case, in this case n = 1.If n = 1, we have that the LHS = 6¹ + ...

Answered by Adam B. • Further Mathematics tutor

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