A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 18 in long and 8 in wide. He makes a fold along the two long sides a distance of x inches from the edge. 18 in 8 - 2x Part: 0/ 3 Part 1 of 3 (a) Write a function to represent the volume in terms of x. V (x) =O

Q: What is the volume of the box when x=3? V(3)= cubic centimeters

A: Solution: Volume of cube(V) = a3 where a is the length of side of the cube

Q: A rectangular box closed at the top has a fixed surface area S = 31. Find the dimensions that make…

A:

Q: ® Set up and evaluate Hhe intgral that jims Hhe velume of the salid formed ky aeling the the volume…

A: Set the volume of the region using Disk method

Q: Use the figure to the right to find its volume in cubic units.

A: The figure is given by ,

Q: Find the volume of the regular (hces - equilatoral A) Pyrawid. 10ft

A: Given Regular pyramid height 6 ft Face- equilateral triangle of side 10 ft To do Find the Volume…

Q: A spherical snowball is melting. Find the approximate change in volume if the radius decreases from…

A: Solve the following

Q: Determine (a) the volume and (b) the surface area of the three-dimensional figure. When appropriate,…

A:

Q: A landscaping company is hired to mow the grass for several large properties. The total area of the…

A: The regression equation is, y = 1350 – 1.2x, where x is the number of hours and y is the number of…

Q: Find the area of the stamp when / = 4x – 1 and w = 2x + 1. (Simplify your answer completely.) cm2 I…

A:

Q: A forest fire covers 1600 acres at timet = 0. The fire is growing at a rate of 2/t acres per hour,…

A: Initially, Forest fire covers 1600 acres. Fire grows at the rate of 2t acres per hour. Find the…

Q: A solid with volume 12 cubic units is dilated by a scale factor of K. Find the volume of the image…

A: Volume, V=12×k3 Since, k=14, we have  V=12×14×14×14

Q: A box without a top is to be made from a rectangular piece of cardboard, measuring 1.5 yd by 3.2 yd,…

A:

Q: 5 ft 3 ft

A: We have been given a prism where the base is a rectangle and the sides are of right triangles.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.