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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)r²and the area generated by R can be considered as an infinite number of circular areas.

Thus, we can write the area gene...

Answered by Stephen B. • Maths tutor

5375 Views

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 ...

Answered by Stephen B. • Maths tutor

5235 Views

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. ...

Answered by Hafsah K. • Maths tutor

17070 Views

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...

Answered by Hafsah K. • Physics tutor

17900 Views