An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made with the smallest amount of material.

Q: The area of the rectangular piece of cardboard shown below is 209 square inches. The cardboard is…

A: Given problem:- The area of the rectangular piece of cardboard shown below is 209 square inches. The…

Q: A frame for a picture is 2 inches wide (see figure). The picture inside the frame is 4 inches longer…

A: As shown in the figure, the Frame has a 2-inch border on each side,

Q: A gardener has 1120 feet of fencing to fence in a rectangular garden. One side of the garden is…

A:

Q: The rectangular playground is 80m long. Its length is 38m longer than its width. Find the perimeter…

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Q: A farmer has to enclose a pasture for his cows. He has 1160 yards of fencing for the perimeter of…

A: according to the question 2(a+b) = 1160⇒a+b = 1160/2⇒b = 580-a⇒b= 580-aArea A = ab⇒A = a(580-a)⇒A =…

Q: Find the dimensions of the box described. The length is twice as long as the width. The height is 2…

A: We know, Volume of the cuboid = (length)×(width)×(height)

Q: Three water storage containers have the same volume in the shape of a cylinder, a cone, and a…

A: Given three water storage containers have the same volume in the shape of a cylinder, a cone and a…

Q: and the dimensions of the rectangle The area is 23 square inches. (3a + 5)

A: Given query is to find the dimensions of the rectangle.

Q: A rectangular room is 33 meters longer than it is wide, and its perimeter is 26 meters. Find the…

A: Let w be the width of the room. Then the length will be w + 3 (as it is 3 meters longer than it is…

Q: 10) A norman window has the shape of a rectangle surmounted by a semicircle (similar to older…

A:

Q: A gardener has 1200 feet of fencing to fence in a rectangular garden. One side of the garden is…

A:

Q: A rectangular poster is to contain 800 square centimeters of print. The margins at the top and…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: US Postal Service regulations state that the length plus the girth of a package cannot exceed 108…

A: Given that US Postal Service regulations state that the length plus the girth of a package cannot…

Q: A gardener has 920 feet of fencing to fence in a rectangular garden. One side of the garden is…

A:

Q: The area of a certain rectangle is 52 square yards, and its perimeter is 34 yards. Find the…

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Q: A rancher has 120 feet of fence with which to enclose three sides of a rectangular pasture (the…

A:

Q: The length of a rectangular parking lot is 8m longer than its width. The area of the parking lot is…

A:

Q: A rectangular picture frame has a perimeter of 7 meters. The height of the frame is  2 3  times its…

A:

Q: The floor of a conference room can be  covered completely with tiles. It's length is 26ft longer…

A: Given length is 26 ft. longer than it's width. Let width be x ft. So, the length=x+26 ft. Now, it is…

Q: Four hundred eighty dollars are available to fence in a rectangular garden. The fencing for the…

A: Four hundred eighty dollars are available to fence in a rectangular garden. The fencing for the…

Q: A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is…

A:

Q: farmer has to enclose a pasture for his cows. He has 720 yards of fencing for the perimeter of the…

A:

Q: A rancher has 220 meters of fence with which to enclose three sides of a rectangular meadow (the…

A: Proceed as shown below...

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 2580 yd of fencing to enclose a…

A: The owner of the Rancho Los Feliz has 2580 yd. of fencing to enclose a rectangular piece of grazing…

Q: A gardener has 1080 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: x=shorter side y=longer side total fencing length is 1080 feet in this case, the perimeter is given…

Q: A gardener has 720 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: Fencing available =720 feet fencing is available for 3 sides find out the greatest possible area

Q: A gardener has 800 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: to find the area.

Q: A gardener has 920 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: Find the dimension and gretest possible area

Q: A rancher has 220 meters of fence with which to enclose three sides of a rectangular meadow (the…

A:

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

A: Solve for least dimensions

Q: Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle…

A:

Q: An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide…

A: We have, An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3…

Q: Find the dimensions of a rectangle with an area of 288 square cm. The length is twice the width

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Q: feet. The fence along three sides is to be A fence is to be built to enclose a rectangular area of…

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Q: b) and 10 inches. Find the dimensions of the rectangle with the greatest area assuming the A…

A: Given problem:- A rectangle is to be inscribed in a right triangle having sides of length 6 inches,…

Q: Postal regulations specify that a parcel sent by priority mail may have a combined length and girth…

A: 4x + l = 102 l = 102 - 4x Volume = x*x*h in3  = x2 (102 - 4x)                              = 102x2 -…

Q: A cone has a volume of 100 cubic inches and base area of 25 square inches. Malik is making a square…

A: The volume of a cone with base radius r and height h is given by the formula Vc=13πr2h. The base…

Q: A gardener has 480 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: Consider that the shorter side is x and the longer side is y. Then, the perimeter is,…

Q: The width of a photo is 5 inches less than its length. A border of 2 inches is placed around the…

A:

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 3540 yd of fencing to enclose a…

A: Given : Fencing is equal to 3540 yd . To find : Value of x & y and area of rectangular piece of…

Q: The height of a triangle is 3 inches less than 5 times the length of its base. The area is 34 square…

A:

Q: A gardener has 1000 feet of fencing to fence in a rectangular garden. One side of the garden is…

A:

Q: volume of 64 cubic feet. A larger cube has sides Make Sense and Persevere A small cube has a that…

A: Let the length of side of small cube is a

Q: A gardener has 640 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: Let the smallest side of the garden be ‘x’ and the longest side of the garden be ‘y’. So, the total…

Q: A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: Let two sides are of x feet and one side is of y feet  So perimeter: x+x+y=520 Or, 2x+y=520 Or,…

Q: A tennis court an area of 312 yd^2. If length is 2 yd more than twice the width, find the dimension…

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Q: A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the…

A: Hair we use the second derivative test If second derivative of function is negative at critical…

Q: A box with an open-top has a square base and four sides of equal height. The volume of the box is…

A:

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 3120 yd of fencing to enclose a…

A:

Q: An open box is formed by cutting equal squares out of the corners of a rectangular piece of…

A: An open box is formed by cutting equal squares out of the corners of a rectangular piece of…

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.