Find the volume and centroid of the solid generated when the indicated region is revolved about y axis and revolved about x axis

Please help

Region 1 is bounded by the x axis, the line x=1 and the curve y=x^2.find the volume and centroid of the solid generated when the indicated region is revolved about y axis and revolved about x axis

How to obtain the equation of cost of laying cables and what is the amount of least cost?

Point A and B are opposite to each other on the shores of a straight river 5km wide. point F is on the same shore as B but K kilometers down the river from B. Atelephone company wishes to lay a cable from A to f where the cost per km of the cable on land is 10,000 US dollar and under the water is 12,500 US dollar. Let P be a point on the same shoreas B annd Fso that the cable runs from A to P to F.(a)if X kilometer is the distance from B to P obtain an equation defining (x) if C(x) dollars is the total cost of laying cable and state the domain of C.

Find the volume of solid generated using disc and shell methods, as the region bounded by y^2=8x, x-axis, and latus rectum is revolved.

Find the volume and centroid of the solid generated using disc and shel methods,as the region bounded by the curve y^2=8x, the x axis and the latus rectun of the curve is revolved about:
A. The x axis
B. The y axis
C. The latus rectum

Elementary Applications

Newton's Law of Cooling

Newton's Law of Cooling states that the temperature of a body changes at a rate proportional to the difference in temperature between its own temperature and the temperature of its surroundings.
 

We can therefore write

$\dfrac{dT}{dt} = -k(T - T_s)$

where,
T = temperature of the body at any time, t
Ts = temperature of the surroundings (also called ambient temperature)
To = initial temperature of the body
k = constant of proportionality
 

Find when the reading, to the nearest degree, will show the correct (70°F) indoor temperature.

Need help on this one. DE Newton's Law of Cooling

At 9 A.M., a thermometer reading 70°F is taken outdoors where the temperature is l 5°F. At 9: 05 A.M., the thermometer reading is 45°F. At 9: 10 A.M., the thermometer is taken back indoors where the temperature is fixed at 70°F. Find

  1. the reading at 9: 20 A.M. and
  2. when the reading, to the nearest degree, will show the correct (70°F) indoor temperature.