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The equation f(x) =x^3 + 3x is drawn on a graph between x = 0 and x = 2. The graph is then rotated around the x axis by 2π to form a solid. What is the volume of this solid?

f(x) = x³+ 3x V = π ∫(f(x)²) dx V = π ∫₀²(x³+ 3x)(x³+ 3x) dx V = π ∫₀²(x⁶ + 6x⁴

Answered by Zac C. • Maths tutor

3390 Views

Jason and Mary leave their houses at the same time. They travel towards each other, Mary at 20km/h and Jason at 15km/h. They pass each other after an hour and a half. What was the original distance between them when they started?

Mary = 20km/h Jason = 15km/h s = d/t After 1.5 hours, Mary = 30km and Jason = 22.5km 30 + 22.5 = 52.5km

Answered by Zac C. • Maths tutor

2821 Views

Solve y = x^2 + 3x + 2 = 0

Factorising gives: y = (x+2)(x+1) = 0. y only equals 0 when (x+2)=0 or (x+1)=0. Therefore x=-2 or x=-1

Answered by Sean L. • Maths tutor

2831 Views

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

Differentiate wrt x. This leaves dy/dx = 3x^2 + 6x and equate this to 0 as we are looking for stationary points.So, 3x^2 + 6x = 0. Factorise to get x(3x +6) = 0. So x = 0 and x = -2 are the two solutions....

Answered by Tutor169411 D. • Maths tutor

3015 Views

Solve the simultaneous equations 3x +y =11 and 2x+y=8

Equation 1: 3x+y= 11, Equation 2: 2x+y=8. You want to find out what x is and what y is.In both equations there is only 1 unit of y therefore it is easiest to rearrange the first equation so that it equals...

Answered by Kathryn M. • Maths tutor

4479 Views