Consider all rectangles with an area of 200 m². Let x be the length of one side of the rectangle. a) Express the perimeter as a function of x. b) Find the dimensions of a rectangle whose perimeter is 70 m.

Q: 59. Express the area of an equilateral triangle as a function of the length of a side.

A:

Q: Express the length plus the girth in terms of x and h.

A: Given: length l and the girth xie., length =l and sides of a square=x

Q: Consider the function: 81x2 + 16 f(x) = Ston 1 of 2. Cind alL cciticaL Soparats pauleiple with

A:

Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

A:

Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: Consider the function defined on the indicated interval. f(x) = 2x – 30x + 144x – 220, [5, 8] %3D…

A: To find maximum and minimum of the given function in interval [5, 8] fx=2x3−30x2+144x−220

Q: volume

A: Please refer to the image below

Q: A goat is tethered to a stake In the ground by a rope that is 10 feet long in terms of pi, what is…

A:

Q: Is it possible for a function to satisfy f(x) > 0, f′(x) > 0, andf ″(x) < 0 on an interval?…

A: We want function that is: 1. positive on interval I since fx>0   2. increasing on interval I…

Q: ch brick is 2" x 8", what is the peri

A: Given that if each brick 2"×8".

Q: Enter an eqvation_for the line of symmetry for the function flx)=4x²+[6X-9 %3D

A: The function is given by f(x) = 4x2+16x-9 To evaluate : Equation of the line of symmetry

Q: ■ Find a formula for the described function and state its domain Express the area of an equilateral…

A:

Q: Consider the function f (x) = 3x² + 2x – 4 What is the exact value of Cin the interval [-2, 4] such…

A: By using Mean Value Theorem for Integrals f(x)=3x2+2x-4 find c over interval [-2 , 4] = ?

Q: Express the set x 0 using interval notation.

A: topic - inequality

Q: Express the set W = {r |x 8} using interval notation. Use "U" for or

A: Sets problem

Q: Find the length of f(r) = on the interval [1, 2]. Show all calculations. %3D

A:

Q: functions f1(x) = ex+2, f2(x) = ex-3 linearly dependent or linearly independent on (−∞, ∞)? Explain.

A:

Q: Express the interval using two different representations. x 9

A:

Q: For Exercise, write the domain of the function in interval notation. h(a) = Va – 5 %3D

A:

Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

A:

Q: Use the Second Fundametal Theorem of Calculas to find F'(x)

A: The second fundamental theorem of calculus is as follows.Let f be continuous on [a,b] then,

Q: A pool measuring 20 meters by 10 meters is surrounded by a path of uniform width, as shown in the…

A: Given information: A pool of rectangle size of length 20 m and breadth 10 m, Surrounded by a path of…

Q: Interpret the Mean Value Theorem when it is applied to any linear function.

A: Interpret the Mean Value Theorem when it is applied to any linear function.

Q: . By law, a wheelchair service ramp may be inclined no more than 4.76°. If the base of a ramp begins…

A:

Q: If a gun is fired with and a =30o and V0 = 500m/s, whenwill the bullet hit the ground? How far from…

A:

Q: a box with a square base and no top has a volume of 100cubic cm. If the material for the 4 sides…

A: Given that, the volume of the box is 100 cubic cm, the material cost for the 4 sides is 8 cents per…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 36…

A: Given that:   (1)                                                (2)

Q: Find the average of the function h (x) = 4x² – x + 5 on the interval [-2,3]. %3D Average=

A: h(x)=4x2-x+5 on the interval -2, 3

Q: A closed rectangular box with a square base has a volume of 8000 cubic centimeters. Express the…

A:

Q: Find the domain of the function and express as an interval

A: In the question it is asked to calculate the domain of the function f(x)=x+6-2.

Q: Is the domain of y = 4' all real numbers? (ie) continuous

A:

Q: A once-popular dog’s chew toy is slowly declining in popularity. The quartic function…

A: Given that x is the number of years since 1993 So 2001 means x=2001-1993=8

Q: Express the volume of a cube as a function of the length of an edge.

A: Cube:

Q: Find the averuge valuc of the function fcx)-4x4 on the interval [2,6],

A: Given : fx = 4x4

Q: Express the set W = {r|x < 2} using interval notation. %3D

A: W={x | x&lt;=2}

Q: What is the domain of the function that defines the actual distance (in miles), dd, in terms of nn,…

A: Domain is the input value that can be given to a function. The distance on the map varies with the…

Q: 4.x2 – 7 x -1 бх + х2

A: Given

Q: Find the average of the function h (x) == 4x² – x + 5 on the interval [-2,3]. %3D Average=

A: Given query is to find the average value of the function for the interval [-2,3]

Q: Is the distance between any two different real numbersalways positive?

A: State whether the distance between any two different real numbersalways positive or not

Q: Find the domain of the function f(x) = √7x − 3 - In interval form, the domain of fis Cubr

A:

Q: -20 in.- 14 in.

A: Question is solved.

Q: How many axes (or how many dimensions) are needed to graph the function z = ƒ(x, y)? Explain.

A: How many axes (or how many dimensions) are needed to graph the function z = ƒ(x, y)? Explain.

Q: Find the values for each of the dimensions of an open-top box of length x, width y, and height…

A:

Q: An open-top box is made by cutting equal squares of side x out of the corners of a piece of carboard…

A: Given that an open top box is made by cutting equal squares of side x out of the corners of a piece…

Q: Estimate the area under the graph of f, the x-axis, and the lines x = −1 and x = 2 using three…

A: In this question, we have to find the area bounded by the given curves. We need to approximate the…

Q: f(x, y) = 500 4+x² + y²

A:

Q: ind the maximum product of two positive numbers given that the sum of the umber and twice the second…

A: Please refer to the image below