Aboat at anchor is bobbing up and down in the sea. the vertical distance, y, in feet, between the sea floor and the boat is given as a function of time, t, in minutes, by y=15+sin(2πt).
(a) find the vertical velocity, v, of the boat at time t.
(b) make rough sketches of y and v against t.

Step-by-step explanation:

Given

(a)Vertical velocity v at time t

graph of y is similar to sin x but is it shifted by a unit of 15 units and repeat itself after 1 s

Graph of v(t) is similar to cos x but it is amplified by a factor of

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!