The masses and volumes of eight bodies of the same material are measured. To do this, a balance that appreciates up to the tenth of a gram (o.1 g) and a graduated cylinder that appreciates up to two tenths of a cubic centimeter (0.2 cm^3) were used. The results are (see image) Calculate the density of the material using the method of least squares, and the value of the correlation coefficient. (Remember: plot of volume (abscissa) versus mass (ordinate), remembering that m=ρV.)

What is the volume of a hat box (cylinder) in liters, which is 60.0cm in diameter and 38.5cmtall ? (V = πr2h) Explain how you got your answer.

Note: a = 9 A piece of length (a + 142) cm was cut from a large board of length (02.3) m. What is the length of the board in millimeters after cutting?

A simple physics formula is density equals mass divided by volume. In problem 2 above, the density was δ(x,y,z) = e^((x^2+y^2+z^2)^3/2).The volume of the object could be calculated from the equations for volumes of spheres and cones with some simple subtraction. Why do we need to do a triple integral to find the mass of the solid? Why can’t we just use the physics formula M = ρ ·V ? Explain when we need a triple integral to calculate mass, and when we can get away with the simple physics formula. Most importantly, explain how the triple integral of p*dV uses the same physics formula and explain what the idea of an integral means.

PLEASE ANSWER SELECTIONS A AND B WITH ENCODED SOLUTIONS. THANK YOU!

Problem 2. 1-3

You are making a sculpture that is a pyramid with a square base . You want the height of the pyramid to be 4 inches less than the length of a side of the base . You want the volume of the sculpture to be 200 cubic inches . a . Let x represent the length ( in inches ) of a side of the sculpture's base . Draw a diagram of the sculpture , and label the dimensions in terms of x . b . Write a function that gives the volume V of the sculpture in terms of x .

A hot tub with a surface area of 28 ft2 is filled with water to a depth of 29 in . Hint: volume is calculated as area × height (A × h). A) What is the volume of water in the tub, in liters? Express your answer to two significant figures and include the appropriate units. B) How many kilojoules are needed to heat the water from 59∘F to 103 ∘F? Express your answer to two significant figures and include the appropriate units. C) If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 59∘F to 103∘F? Express your answer to two significant figures and include the appropriate units.

You will be using these rules in your calculations. As an example of a sample calculation, find the volume of a rectangular solid: V = Lx W x H V = (25.95 cm)(5.87 cm)(83 cm) V = 13000 cm³ = 1.3 x 10“ cm3 Note that when you do this calculation in your calculator, you will have an answer of 12643.0995. However, the 83 cm limits your answer to 2 significant figures, so you must round the final answer to 2 significant figures. Remember you need to keep the place value of the significant figures! The scientific notation helps clarify that none of the zeros are significant.

I recently asked this question, but the answers are not loading.  I don't understand part a, and the formulas used. I guess I don't understand how to derive the formulas into what you need. Could you explain, step  by step?