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Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.

The area of a circle is given by (pi)r 2 and the area generated by R can be considered as an infinite number of circular areas. Thus, we can write the area generated by R as the integral of (pi)(x 3 ) 2 betw...
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Answered by Stephen B. • Maths tutor
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Does the equation: x^2+5x-6 have two real roots? If so what are they?

Having two real roots is equivalent to having two intersections with the x axis. The equation is a parabola (a U shape) so, having two real roots is equivalent to having the lowest point of the curve below t...
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Answered by Stephen B. • Maths tutor
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Differentiate a^x

Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. Using the...
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Answered by Hafsah K. • Maths tutor
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Explain what is meant by resonance.

Resonance occurs when a driving frequency is similar to the natural frequency of the system. The system is forced to vibrate at its natural frequency and therefore absorbs maximum energy, which means that th...
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Answered by Hafsah K. • Physics tutor
20101 Views

Solve 13+4x=7-4x

Collect like terms on one side: 4x+4x=7-132. Simplify: 8x=-63. Divide to find the solution for x: x=-6/84. Simplify again for the answer: x=-3/4
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Answered by Hafsah K. • Maths tutor
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