From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded up xi to make a box. Complete parts a through c below. a) Express the volume of the box as a function of the side x, in centimeters, of a cut-out square. V= 324x+4x-72x2 b) Find the domain of the function. (Type your answer in interval notation.)

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

A:

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: V=x(18-x)2 The length, width and height will…

Q: A wire length 23 is to be cut into two pieces and formed into a square and a circle. Let x represent…

A: Given that the total length of the wire is 23. That is, the perimeter of the wire is 23. Let x be…

Q: Determine the number at which the function f(x) = (2x - 3)/(3x3-24) is discontinuous. Answer:

A:

Q: Find the interval notation:

A: Given that:

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = 6x4 −…

A:

Q: The shaded set of numbers shown on the x-axis can be expressed in interval notation as________ .…

A:

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: From a 18 cm by 18 cm piece of cardboard, square corners are cut so that the sides can be folded up…

Q: Find the domain of f and write your answer in interval notation. f(x)%3D6/3-4z +7

A: Given function is: f(x) = 6 sqrt(3 - 4x) + 7 The above function is defined only when: 3 - 4x >= 0…

Q: Find the domain and express it by interval notation.

A: We have to find the domain .

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: " The domain of the function f(x) = Vx2 – 12x + 32 consists of one or more of the following…

A: Given function is, fx=x2-12x+32 We can write the given function as, fx=x-8x-4

Q: a. What is the domain of the function f(x)= (−4x) / √(5x−9)?  b. What is the domain of the function…

A:

Q: Give the domain of the function y = x/7, (Enter your answer using interval notation.)

A: The domain of a function is the possible set of input values where the function is defined.

Q: The perimeter of a rectangle is 422 inches. If the rectangle is x inches long, find a function for…

A: Let us assume a rectangle with length x inches and breadth y inches.

Q: Use the graph off to find the largest open interval on which f is increasing, and the largest open…

A: On observing curve we will find the interval.

Q: From a 24-cm by 24-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: in this first we will find side of the box and then  Volume of the box = length × breath× height

Q: The area of a rectangle is given by the function A(x) = 3x³ + 6x² + 4x + 8. If the length is defined…

A:

Q: Find the inflection points of f(x) = 3x4 + 17x³9x² + 4. (Give your answers as a comma separated…

A:

Q: A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four…

A:

Q: Write the domain of the given functions in interval notation:

A: here we have to find the domain of the given functions.

Q: Write the domain of the function in interval notation f(x)= 3squareroot x-12

A: Important: The value 'in the root' is always positive.

Q: Find the interval notation of the domain

A:

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

A:

Q: Write the domain of the function in interval notation.

A: The domain for any function is the values of x-axis covered by the function in its graph. And as per…

Q: From a 18-cm by 18-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: To find the volume of a box obtained by cutting squares so that the sides fold up to a box. Then…

Q: Find the domain of f and write your answer in interval notation. f(z) = 3/2 – 5z + 7 %3D

A:

Q: Find the domain and express it as an interval

A:

Q: For Exercise, write the domain of the function in interval notation. Зх — 5 p(x) 2x + 5x – 7

A:

Q: From a 27-cm by 27-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A:

Q: 6+ Write the domain of the function using interval notation.

A: Domain:- All possible value of x

Q: Write the domain of the function f(x) = arcsin(æ), using interval notation, in the space below.

A:

Q: Jared needs to lay out 550 chairs for a function on an open space 15m x 20m. Each chair occupies…

A: The area to be left for each chair can be calculated by adding the area of distance between 2 chairs…

Q: Indicate if the function is bijective from R to R, f (x) = −3x + 4, justify your answer

A: Given f : R→R, f(x)=-3x+4 Here the function is linear function. f'(x)=-3<0 for all x∈R Which…

Q: The area, A, in square feet, of a rectangular storage bin in a warehouse is given by the function…

A: Given data; The given expression for the area of the rectangular storage bin is A(x)=-2x2+36x. The…

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: Find the domain and range of f(x) = 3(9x +7)2 – 7. Express your answer in interval notation using…

A: Given: The function is,

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x)=6x4-x2

A:

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Please refer the attached image for complete solution.

Q: Let f(æ) be the function 10x2 – 6x + 3. Then the quotient f(2+h)-f(2) h can be simplified to ah + b…

A:

Q: Find the domain in interval notation

A: GivenS(x)=3x2+3x-4

Q: What is the area A of a circle expressed as a function of its circumference C?

A: Our Aim is to express the area A of a circle as a function of its circumference C=?

Q: Find Find the domain of (Enter your answer using interval notation.)

A:

Q: From a 6-cm by 6-cm piece of cardboard, square IX corners are cut out so that the sides can be…

A:

Q: Find the inflection points of f(x) = 2x* + 19x³ 15x2 + 11. (Give your answers as a comma separated…

A: Given: f(x)=2x4+19x3-15x2+11

Q: find the points of inflection and discuss the concavity of the graph of the function. f(x)=x…

A: Given, y=x9-x derivate both side  f'(x)=9-x+x29-x9-xf'(x)=18-x29-x3/2

Q: flx)= In (x-3) X1-16

A:

Q: Determine domain and range of quadratic function f(x)=-4(x+3)^2-9 answer in interval notation

A:

Q: what are the intercepts and asymptotes of the function 4x-8/(x-4)(x+1)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.