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The gradient of a curve is given by dy/dx = 3 - x^2. The curve passes through the point (6,1). Find the equation of the curve.

Since we differentiate a function to find the gradient of a curve at any point, we need to reverse that to find the equation of the curve. We do this by integrating with respect to x:If you have a constan...

Answered by Darya N. • Maths tutor

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Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.

Formula for a straight line y-y₁=m(x-x₁), where m is the gradient substituting in the values given to find the gradient we get 4-1=m(3+2), therefore m= 3/5the midpoint of the two poi...

Answered by Paige M. • Maths tutor

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Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2

When a function is increasing, it’s derivative is positive. So first let us differentiate f(x). To differentiate xⁿwe multiply by n and then reduce the power by 1. So f’(x)=8-2*2x=8-4x. We wan...

Answered by Ruby L. • Maths tutor

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Benjamin has a 0.7 chance of passing his driving test the first time and a 0.85 chance of passing the second time. What is the probability of his passing on either the first or second try?

The probability of passing at either the first or second time round is P(passing first time) + P(taking the test for a second time then passing)
= 0.7 + (0.85 x 0.3)= 0.7 + 0.255= 0....

Answered by Rob F. • Maths tutor

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Expand the brackets (2x + 3)(3x - 1)

Use the crab claw method to expand the bracket. Draw two lines above the equation from the 2X, one to the 3X and one to the -1. Draw another two lines below the equation from the +3, one to the 3X and one...

Answered by Caitlin M. • Maths tutor

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