Constructing a storage tank Refer to Example 8. A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 10 feet with a hemisphere attached to each end. The radius r is yet to be determined. Express the surface area S of the tank as a function of r.

Q: Find the global maximum and global minimum values of the function `g(theta) = 6 theta - 7 sin(theta)…

A:

Q: Temperature during an illness. The temperature of a person during an intestinal illness is given by…

A:

Q: 9x Let/(x) = + 14. V- 5 The tangent line to the graph of f at the point (6, f(6)) intersects the…

A: Here we find the tangent line then we find y intercept.

Q: A rectangular box has a square base. Its height is half the width of the base.Find a function that…

A: Let the length of the box= w So the width=length = w (because square base) So, height = w/2

Q: Question Suppose that the length I, width w, and area A = lw of a rectangle are differentiable…

A: l=7 , w= 9A = lw differentiate w.r.t tdAdt=l dwdt+ wdl dt

Q: Inscribing a Cylinder in a Sphere Inscribe a right circularcylinder of height h and radius r in a…

A: Given: Radius of sphere is R. Radius of cylinder is r. Height of cylinder is h. Provided figure is

Q: An airplane is flying at an altitude of 30,000 feet. The distance, d, in feet, from an observer on…

A:

Q: 不y y =x5 (0, у) (х, у) (0, 0) A right triangle has one vertex on the graph of y = x°, x>0, at (x,…

A: GivenA right tringle has one vertex on the graph of y=x5, x>0Another vertex is at the origin.and…

Q: closed aluminum can of volume is to be in the form of a right-circular cylinder. Find a mathematical…

A: A closed aluminum can of volume is to be in the form of a right-circular cylinder. Find a…

Q: Please help me

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: A right cylinder with height y and radius x is used to store wheat. The top and bottom of the…

A:

Q: Find all functions f having the indicated property. (Enter your solution as an equation.) The…

A: The tangent to the graph of f at the point (x, y) intersects the x-axis at (x + 17, 0) We need to…

Q: A rectangular box has total surface area of 2 ft². Express the volume of the box as a function of…

A: Express the volume of the box as a function of the dimensions x and y of the base of the box.…

Q: A thin observatory probe having the shape of a plate is probing a volcano in an xy −plane at a point…

A:

Q: 71. Volume of a Cylinder The volume V of a right circular cylinder of height h and radius r is V =…

A: Given the volume V of aright circular is V=πr2h. where h is the height of the cylinder and r is the…

Q: eal function f(r) = a2, th Ibe 20. 2+1 (c) f(x) = 3- a=

A:

Q: function f(x) = x² ose x-coordinates are -2 , 0, and 1. 2x and draw the tangent lines to the gr 10 4…

A: We will draw the graph and the tangents.

Q: An open rectangular box with volume 6 m3 has a square base.(a) Express the surface area of the box…

A: Let the side of the square base be x and the height of the box be h.

Q: Linear approximationa. Find the linear approximation to the function ƒ at the point (a, b).b. Use…

A: The linear approximation of f(x, y) at (a, b) is the linear function L(x, y)=f(a, b)+fx(a,…

Q: . Inscribing a Cylinder in a Cone Inscribe a right circularcylinder of height h and radius r in a…

A: Here we have to  Express the volume V of the cylinder as a function of r.

Q: An open box is to be made out of a 12-inch by 16-inch piece of cardboard by cutting out squares of…

A: We find V(x) in step 2

Q: wing function: f(x) = x² – 7x +10 the coordinates for the v-intercent.

A:

Q: A television camera at ground level is filming the lift-off of a rocket at a point 800 meters from…

A:

Q: 11. At noon, a car leaves town A on a street road, heading south at 60 km/h, and a plane 4 km above…

A:

Q: In the problem you are asked to find a function that models a real life situation. Use the…

A: Given: Volume of a rectangular box is 60 ft3and the rectangular box has square base with length of…

Q: Use the integration capabilities of a graphing utility to approximate the work done by a press in a…

A:

Q: Filling a Conical Tank Water is poured into a containerin the shape of a right circular cone with…

A: The height and radius of the right circular shape container as shown in the figure: R=4 feetH=16…

Q: An airplane is flying at a speed of 450 mi/h at an altitude of one mile. The plane passes directly…

A: (a) The horizontal distance d , altitude 1 mi and the distance between radar station and plane s…

Q: can you help me step by step please

A: To determine the ordered pair (x ,y) where tangent line is horizontal to the graph of the function y…

Q: A ladder 22 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: We use Pythagorean theorem for given problem.

Q: 4. A cone is inscribed in a sphere of radius 5. Express the volume of the cone as a function of the…

A: To express the volume of cone as a function of height

Q: (a) Use implicit differentiation to find if  x2+ x   y + y 2 +1 = 0 (b) Plot the curve in part (a).…

A:

Q: When gas expands in a cylinder with radius r, the pressure at any given time is a function of the…

A: Consider a cylinder of radius r. The force exerted by the gas on the piston is as follows.…

Q: An open-top box is created by cutting out corners from a piece of cardboard as pictured below. Find…

A: An open-top box is created by cutting out corners from a piece of cardboard as pictured below. Find…

Q: Graph of / The graph of a differentiable function fis shown in the figure above Which of the…

A: Explanation of the answer is as follows

Q: - When gas expands in a cylinder with radiusr, the pressure at any given time is a function of the…

A: As shown in the figure , when the piston is at a distance x ,the volume inside the cylinder is…

Q: ) Material Needed to Make a Drum A steel drum in the shape of a right circular cylinder is required…

A:

Q: A rectangular box with a volume of 60 ft3 has a square base. Find a function that models its surface…

A: The volume of the rectangular box with a square base is, V=60 ft3. One side of the base is x. Thus,…

Q: A segment line AB crosses the curve of f(x) at the given points A and B. Write an equation for the…

A:

Q: f(x) = 2 cos x - cos 2x.

A: Given function f(x) =2 cos x - cos 2 x    ; [0, 2π]

Q: A thin observatory probe having the shape of a plate is probing a volcano in an xy −plane at a point…

A: The objective is to represent the temperature as the function of x and y.

Q: The graph of a function of two variable is O A volume in the 3D space O A surface in the 3D space O…

A:

Q: An open rectangular box (no top) with volume 4 cubic meters has a square base. Express the surface…

A:

Q: A right cylinder with height y and radius x is used to store wheat. The top and bottom of the…

A: The figure of a cylinder that has its top and bottom in the shape of a hemisphere can be represented…

Q: est value of the function 1.1) is

A:

Q: Distance between cars At noon, car A is 10 feet to the right and 20 feet ahead of car B, as shown in…

A: Pythagoras theorem states that the square of hypotenuse is equal to the sum of square of the other…

Q: Describing the closed interval and determining the function values The range R of the projectile…

A:

Q: Express the function by a formula. 3. The height of a cylindrical can as a function of the base, if…

A: The objective is to express the function by a formula. The height of a cylinder can as a function of…

Q: a cardboard box manufacturer wishes to make open boxes from regular pieces of cardboard with…

A:

Q: Question A tank contains 3 kg of salt dissolved in 430L of water. A salt solution of 0.01 kg salt/L…

A: Assume U(t) be the amount of salt and C be the capacity of the tank. Ut=salt amountdUdt=rate of…