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Given that x=3 is a solution to f(x)= 2x^3 - 8x^2 + 7x - 3 = 0, solve f(x)=0 completely.

As x=3 is a solution, (x - 3) is a factor of f(x) = 2x 3 - 8x 2 + 7x - 3 = 0 ie. 2x 3 - 8x 2 + 7x - 3 = (x - 3)(Ax 2 + Bx + C) where A,B,C are constants to be found. Expanding and then grouping terms by powe...
AS
Answered by Adrian S. • Maths tutor
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Express 3x+1/(x+1)(2x+1) in partial fractions

3x+1/(x+1)(2x+1)=A/(x+1) + B/(2x+1)Multiply equation by (x+1) and (2x+1) to get:3x+1= A(2x+1) + B(x+1)Let x=-1 (x+1=0 so x=-1) sub into new equation. -2= A(-1) + B (x+1)-2=-AA=2Let x=-1/2 and sub into same e...
NM
Answered by Niamh M. • Maths tutor
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Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.

theta/2pi x2pi r = length of ABso therefore simplifying gives... theta r = AB Perimeter = 2r+theta requate the answer of 4 AB to the perimeter.Solve for theta which eventually give 2/3then put theta in the e...
TD
Answered by Tutor460124 D. • Maths tutor
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What is the signed area between the curve y = x^2 - 4 and the x-axis?

The curve y = x^2 - 4 is a parabola that crosses the x axis at x = - 2 and x = 2, so the area that we are looking for is the area within the parabola when y <= 0 and -2<= x <= 2. So we expect our ar...
Answered by • Maths tutor
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Find the coordinates of the sationary points on the curve x^2 -xy+y^2=12

To find stationary points, we need to find dy/dx and set it equal to 0. Here we must use implicit differentiation: d/dx(x 2 ) + d/dx(-xy) + d/dx(y 2 ) = d/dx(12). Hence 2x - x(dy/dx) - y + 2y(dy/dx) = 0. Fac...
AB
Answered by Adam B. • Maths tutor
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