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Show the curve y = 4x^2 + 5x + 3 and the line y = x + 2 have exactly one point of intersection

The curve and the line will intersect when the two expressions are equal, so:4x²+ 5x + 3 = x + 2 (eliminating y and putting the expressions in terms of one variable).4x²+ 4x + 1 = 0(...

Answered by Jacob H. • Maths tutor

2858 Views

Factorise and find the solutions of the equation 6x^2 + 4x -10 = 0

6x² + 4x - 10 = 0
6x² + 10x - 6x - 10 = 0
2x(3x + 5) - 2(3x + 5) = 0
(2x - 2)(3x + 5) = 0
Case 1:
2x - 2 = 0
2x = 2
x = 1
Case 2:
3x +...

Answered by Cathy H. • Maths tutor

4212 Views

Simplify the expression: (2a + a)x(5a - a)

Evaluate each bracket first. We have:(2a + a)x(5a - a) = (3a)x(4a)Then, multiply both brackets.(3a)x(4a) = 12a²

Answered by Jonas O. • Maths tutor

4446 Views

Solve 6/(x-3) + x/(x+4) = 1

(6(x+4) + x(x-3) )/ ((x-3)(x+4)) = 1 obtain a common denominator and write as one fraction. (6x+24+x²-3x ) /( x²-3x+4x-12) = 1 multiply out the brackets. (x²+3x+24)/ (x

Answered by Jana R. • Maths tutor

2424 Views

Find an antiderivative to the function f(x) = e^x cos(x)

We see a product of two things, so we should consider integration by parts (IBP). IBP is usually useful when either 1) you can differentiate or integrate one of the two things repeatedly to eventually get...

Answered by Christoffer A. • Maths tutor

1220 Views