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Two functions, y1 & y2, are given by y1=x^2+16x+4; y2=2(3x+2). Find analytically the volume of the solid created by revolving the area between the two curves by 2pi radians around the x-axis. N.B. y2>y1 on the interval between the points of intersection.

Setting the two equations equal to one another to find the intersection boundaries:x^2+16x+4=6x+4; x^2+16x+4-6x-4=0; x^2+10x=0;x(x+10)=0; x=0, x=-10. Setting up the volume of revolution (N.B. Due to typing r...
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Answered by Filippos G. • Maths tutor
2526 Views

Find exact solution to 2ln(2x+1) - 10 =0

Isolate the 'ln term' 2ln(2x+1) = 10ln(2x+1) = 5 Take to the exponential power form e^(ln(2x+1)) = e^52x+1 = e^5 Simplify 2x = e^5 -1x = (e^5-1)/2
JD
Answered by Johnny D. • Maths tutor
4484 Views

A roll of card has an area of 43 m^2. A postcard has an area of 125 cm^2. How many post cards can be cut from the roll, assuming there is no wastage? (calculator question)

This question is assessing your knowledge of units and their conversion. Notice that the area units of the roll of card and the postcard are different, so it is important that before we carry out any calcula...
HG
Answered by Hafsah G. • Maths tutor
3500 Views

The point P, (-1,4) lies on a circle C that is centered about the origin. Find the equation of the tangent to the circle at point P.

The most important fact to remember with this question is that two perpendicular straight lines have gradients related by m 1 = -1/m 2. This can then be used to find the gradient of the tangent by first find...
JA
Answered by James A. • Maths tutor
5182 Views

Solve "x^2 - 12x - 45 = 0" by completing the square

The equation is of the formx 2 +bx+c=0This means it can be rearranged to(x+(b/2)) 2 =(b/2) 2 -cTaking the square root of both sides leaves us with x. x 2 -12x-45=0(x-(12/2)) 2 -(12/2) 2 -45 = 0(x-6) 2 -6 2 -...
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Answered by Elsa J. • Maths tutor
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