The diagram shows a sphere and a solid cylinder.

The sphere has radius 6 cm.
The solid cylinder has a base radius of 3 cm and a height of
h
cm.

The total surface area of the cylinder is twice the total surface area of the sphere.

Work out the ratio of the volume of the sphere to the volume of the cylinder. Give your answer in its simplest form.

(5 marks)

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Point a is located at (0, 4), and point c is located at (−3, 5). find the x value for the point b that is located one fourth the distance from point a to point c. −0.25 −0.5 −0.75 −1

How can the correlation in the scatter plot graph below best be described? positive correlation negative correlation both positive and negative no correlation