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What is the gradient of the quadratic function y=3x²?

The gradient of a function with variable x is found by applying the differential operator to it. The differential operator is commonly written as d/dx. Hence the differential operator applied to the funct...

Answered by Matthew C. • Maths tutor

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There are two lines in the x-y plane. The points A(-2,5) and B(3,2) lie on line one (L1), C(-1,-2) and D(4,1) lie on line two (L2). Find whether the two lines intersect and the coordinates of the intersection if they do.

We first want to find the equations of the lines. The general equation of a line is: (y-y₁)=m(x-x₁) where (x₁,y₁) are the coordinates of a point on the line and...

Answered by Zsofia S. • Maths tutor

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Express 2Cos(a) - Sin(a) in the form RCos(a+b) Give the exact value of R and the value of b in degrees to 2 d.p.

R = 5^0.5

b = 26.57 degrees

Answered by William F. • Maths tutor

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How to find the reciprocal of a graph, such as y=cos(x)?

To find the reciprocal of any graph, first consider the key points, in this case: (0,1), (90,0), (180,-1), (270,0) and (360,1). Since we are finding the reciprocal in the y-axis, we can find the reciproca...

Answered by Aqeel A. • Maths tutor

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Let f(x) = x * sin(2x). Find the area beneath the graph of y = f(x), bounded by the x-axis, the y-axis and the line x = π/2.

After short consideration, we see that we must integrate f(x) with respect to x, between 0 and π/2, using integration by parts. Taking the formula for integration by parts, we set u = x and dv/dx = sin(2x...

Answered by Benjamin C. • Maths tutor

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