When a ship is sailing, the total cost per hour includes a fixed part p and the fuel cost q that is proportional to the cube of its speed, that is q=kv3.) Determine the minimum value of the total cost per 1 mile.

Q: 4. A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle.…

A:

Q: A body is thrown at an angle α with the horizontal. Neglecting air resistance, determine the angle…

A:

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the…

A: Total distance travel by the women if she row from A to C and walks from C to B. Total distance…

Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: An architetect wants to design a semicircular tunnel so that two average trucks measuring 8 feet…

A: Given: Dimension of the truck is 8 feet wide and 12 feet tall. Horizontal distance between two truck…

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: (a) If you can throw a baseball with an initial speed of 40 meters per second, at what angle of…

A:

Q: a. A water tank has the shape of an upright cylinder with radius r = 1 meter and height 10 meters.…

A: Work needed = 37500 N m

Q: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a…

A: Calculate the curved surface area of hemisphere and cylinder.

Q: 2. A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle.…

A:

Q: A student presses a book between his hands, as the drawing indicates. The forces that he exerts on…

A: Given that  A student presses a book between his hands, as the drawing indicates. The forces that he…

Q: The shape for a building that is to become a wheat silo is created by rotating the region bounded by…

A: Given : the shape for a building that is to become a wheat silo is created by rotating the region…

Q: Fruit juice will be packaged in cylindrical cans with a volume of 40 in each. The top and bottonm of…

A: Fruit juice will be packaged in cylindrical cans with a volume of 40 in3 each. The top and the…

Q: Full working plz, Thank you.

A: Suppose, I is the real image of an object O and let d be distance between the image and the…

Q: The shape of the cable in a suspension bridge is parabolic when it is suspended between two towers…

A:

Q: Two railroad tracks intersect at right angles. At noon there is a train on each track approaching…

A: Consider the given information. Let's draw the figure for the given information and mention the…

Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If…

A: Let x be the length and width, and y be the height of the rectangle box with square base.Therefore,…

Q: Suppose that the temperature in degrees Celsius at a point (x, y) on a flat metal plate is T (x, y)…

A:

Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

A:

Q: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral…

A: The radius of metal bases = 1 in. The height of cylindrical container = 3 in. So the total area of 2…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find the dimensions of a cylinder of volume 1 m 3of minimal costif the top and bottom are made of…

A: Given: Find the dimensions of a cylinder of volume 1 m 3of minimal cost if the top and bottom are…

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: the maximum area for the rectangular whic

A:

Q: A company wishes to manufacture a box with a volume of 44 cubic feet that is open on top and is…

A: Let the length of box is l=2x. The company wishes the box open on top and is twice as long as it is…

Q: A coast artillery gun can fire at any angle of elevation between 0° and 90° in a fixed vertical…

A: A coast artillery gun can fire at any angle of elevation between 0° and 90.

Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

A:

Q: A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If…

A: Given,Volume of the rectangular box = 147 ft3The cost of the bottom = $6 per ft2The cost of the…

Q: Diagram 4 shows a solid that consists of a cylinder, of radius r cm, surmounted by a hemisphere. The…

A: Volume of cylinder(Radius is r, height is h)=πr2hCurved surface area of a cylinder(Radius is r,…

Q: Exercise 10. A wire of length 28 m is to be cut into two pieces. One of the two pieces is to be made…

A: Concept: Maximum and minimum value: To find the maximum and minimum value of a function using first…

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: A worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If…

A: Consider the given information about the box:

Q: A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle.…

A: In this we have to find the area formula with the angle thetha then the find the value of thetha for…

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: We wish to empty a hemispherical tank full of water out the top. Which should entail the larger…

A:

Q: shows an offshore oil well located at a point W that is 5 km from the closest point A on a straight…

A:

Q: A closed box with a square base is to be built and the volume fixed at 30 m3. Determine the minimum…

A: To determine the minimum cost of the box.

Q: A manufacturer needs to make a cylindrical can that uses 100 square centimeters of material.…

A:

Q: If an open box has a square base and a volume of 103 in.3 and is constructed from a tin sheet, find…

A:

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: If the velocity through rack at max design DWF is 0.58 m/s, and the velocity through rack at peak…

A: Use the given values and proper formula to solve the following question. First, determine the…

Q: A worker is to construct an open rectangular box with a square base and a volume of 48 ft3. If…

A: Note: Please check the material cost for side. Because the dimension seems to be unrealistic since…

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Q: The arm of a boom crane is 12 m long. Because of the location of the construction site, the angle of…

A: Topic = Trigonometry

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.