Area

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Evaluate the integrals for f(x) shown in the figure below. The two parts of the graph are semicircles. a. \int_0^2 4 f(x) dx b. \int_0^6 5 f(x) dx c. \int _1^4 3 f(x) dx d. \int _1^6|5f(x)|dx
Find the area under the curve y=2x-3 from x=0 to x=6 using the right endpoints of 4 subintervals of equal width.
Given that Area = 15x^3 + 25x^2 what is the length and width of the rectangle?
A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are used, what is the maximum area that can be enclosed?
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. \int_0^2 f(x) dx b. \int_0^5 f(x) dx c. \int_5^7 f(x) dx d. \int_0^9 f(x) dx
Jose is planning to spread fertilizer on his rectangular yard. His yard has a length of 40 ft and a width of 25 ft. How much fertilizer does he need?
The area of a rectangle is 72 square inches and the perimeter is 44 inches. Find its dimensions.
The width of a rectangle is 3 less than twice the length of x. if the area of a rectangle is 43 in sq ft. which equation can be used to find length in feet a. 2x(x-3) = 43 \\b.2x + 2(2x-3) = 43 \\c.
The area of a rectangle is 21 ft^2,and the length of the rectangle is 1 ft less than twice the width. Find the dimensions of the rectangle.
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions of the rectangle in centimeters?
The dimensions of a rectangle are such that it's length is 9 inches more than its width. If the length were doubled and if the width were decreased by 4 inches, the area would be increased by 110 in^2
The area of a rectangle painting is given by the trinomial a^2-14a+45. The painting length is (a+2). What is the painting width?
The sides of a rectangle were 5cm { \times } 9cm. When both dimensions were increased by an equal amounts the area of the rectangle increased by { 120 cm^2 } find the dimensions of the new rectang
Kevin is installing a carpet in his home. The cost of the carpet he selected is $5 per square foot. How much will it cost to carpet a room that measures 34 feet { \times } 21 feet?
The dimensions of a playground are 50 feet { \times } 75 feet. You want to double its area by adding the same distance x to the length and width. Find x and the new dimensions of the playground.
A rectangular garden has a walk around it of a width x. The garden is 20 ft by 15 ft. Write a function representing the combined area, A(x), of the garden walk. Write as a polynomial in standard form.
If the dimensions of a room are 10 ft. by 20 ft., what is its approximate area in square meters?
A wooden fence 6 ft. high and 300 ft. long is to be painted. How many gallons of paint are needed if one gallon covers 400 sq. ft.?
Determine the value of a that makes F(x) an antiderivative of f(x). f(x) = 9x^2, F(x) = ax^3
An aquarium 5 ft long, 2 ft wide and 3 ft deep is full of water. a. Find the hydrostatic pressure on the bottom of the tank. b. Find the hydrostatic force at the bottom of the tank. c. Find the hydrostatic force on one end of the aquarium.
Find the area between the curves. y = x ^\frac{15}{14} , y = 13x ^\frac{1}{14}
A lot is 50 m by 40 m. A house 29 m by 9 m is built on the lot. How much area is left over?
Todd has a rectangular garden with an area of 30 square feet. If the garden is 13 feet longer than it is wide, what is the perimeter of the garden (in feet)?
I have 104 feet to build a dog pen. What is the largest width to maximise the area? What is the area? A=52x-x^2 x=width
The perimeter of a rectangle is 80 x. The base is 7 times the height. In terms of x, what are the dimensions of the rectangle. What is the area?
A rectangular pen for a pet is 5 feet longer than it is wide. Give the possible width of the pen if its area must be 204 and 750 square feet, inclusively.
Evaluate: \int_0^1 c^{k+1} (1-c)^{n-k}dc
A regular region of length x and width y has an area of 493 square meters. Write the width y as a function of x .
Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute an answer to three decimals, if necessary. y = 5e^x - 3; y = 0; 0 less than or equal to x less than or equal to 2.
The length of a rectangle is 5 yd more than twice its width and area of the rectangle is 42 yd ^2, find the dimensions.
The area of a rectangle of length x is given 3x^2 +5x. Find the width of the rectangle.
The area of a rectangle is 72 cm^2. The length l, of the rectangle, is 6 cm longer than the width, w. What is the width of the rectangle? a) 10 cm b) 8 cm c) 6 cm d) 2 cm
A rectangle has a width of 2(sqrt 5) cm and an area of 50 cm^2. Find the length of the rectangle.
One side of a rectangle is 10 m longer than the adjacent side. The area is 231 m^2. What are the dimensions of the rectangle?
A rectangular garden plot is to be enclosed with 40 meters of fences and find the area of the garden as a function of the demensions of the recangle.
A room is 18 feet long and 14 feet wide with walls 10 feet high. If one can of paint covers 450 square feet, how many cans of paint would be needed in order to paint the four walls?
The opposite sides of a rectangle are each of length x. If the perimeter of the rectangle is 16, then the area, as function of x, is?
carpet costs $3 per square yard. the room that will be carpeted is 12 feet x 18 feet. how much will the carpet cost?
A rectangle field is 130 m by 420 m. a rectangle barn 19 m by 25m is built in the field. how much area is left over?
A rectangular garden is 6 ft longer than it is wide. its area is 520 ft^2. What are its dimensions?
How long is the shorter side of a rectangle when one side is 2 times longer than the other and the area is 15 sq. in?
Write a polynomial for the length of the rectangle given the following: Area= -7x^4 - 14x\\ Width= 7x
The length of the top of a table is 6 m greater than the width, the area is 91 m^2. Find the dimensions of the table.
The length of a rectangle is 5 in. longer than its width. If the perimeter of the rectangle is 50 in., find its area.
The area of the rectangular athletic field is represented by the expression 25 y^2 - 4 z^2 square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense,
The length of a rectangle is 4 inches more than twice the width. If the area of the rectangle is 48 square inches, what is the length of the rectangle? Show work.
The length of a rectangle is 5ft less than twice its width. The area of the rectangle is { 75ft^2 }. Find the length of the rectangle.
Lisa is cutting carpet for a rectangular room. The area of the room is { 324 ft^2 }. The length of the room is 3 feet longer than twice he width. What should the dimensions of the carpet be?
The length of a certain rectangle is 4 cm longer that's it's the width and the area exceeds 7 times its width by 18 find the dimensions?
The length of a rectangle is the width minus 5 units. the area of the rectangle is 14 units. what is the width, in units, of the rectangle?
How many 8-inch squares will it take to tile a rectangular floor that measures 18 feet by 24 feet?
A family is building a new house on a rectangular lot of land. The lot measures 7x by 11x and the house will be 2x by 3x. How much land will be left for their yard after the house is built?
Louis wants to carpet the rectangular floor of his basement. The basement has an area of 864 square feet. The width of the basement is 2/3 its length. What is the length of Louis's basement?
What is the area of a rectangle that's 15 feet long and 20 feet wide?
The length of the rectangle is greater than its breadth by 2 cm. If the length is increased by 4 cm and the breadth decreased by 3 cm , the area remains the same. Find length and breadth of the rectan
Set up a triple integral to find the mass of the solid tetrahedron bounded by the xy-plane, the yz-plane, the xz_plane, and the plane \frac{x}{6} + \frac{y}{5} + \frac{z}{30} = 1. If the density funct
If you have a rectangle and increase the length by 20% while decreasing the width by 20%, what is the change in area?
The area of a 12-cm-wide rectangle is 252 cm^2. What is its length? please show steps on how you get the answer.
Find the area of the bedroom in square feet if the bedroom is 11' x 13' 10".
If the size of a rectangle's area is twice as large as the size of it's perimeter, and the length of one of its sides is 4.5, what is the length of the other side?
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