17. Area A rectangle is inscribed in a semicircle of radius 10, as shown in the figure. Find a function that models the area A of the rectangle in terms of its height h. h A h 10

Q: A rectangle is inscribed in a semicircle of radius r= 6, as shown in the figure. Find a function…

A: For the given semi circle, radius is r=6.

Q: *****.. ......... During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the…

A: If snow falls of t hours at the speed of a inches per hour, then the depth of snow is given as at…

Q: 1. The number of bacteria in a culture begins with approximately 10,000 organisms at the start of an…

A: Given  P(t)=10000(2)t5 P0=10000Now plug in 5 for t and find P(5)P(5)=10000(2)55P(5)=20000(5,20000)…

Q: The volume of a sphere, V(r), is a function if its radius r given by 4 V(+) = r %3D (a) Complete the…

A: Put r=1, 3,5,7 in v(r).  According to guidelines we solve only first three parts.

Q: 3. In Einstein's theory of special relativity the mass of an object moving with velocity v is given…

A: The above binomial expansion formula can also be written as, (x+y)n=xn+n·xn-1 y1 +n(n-1)2!·xn-2…

Q: 1) A circle with a radius of 5cm is removed from a circle with radius r. i) express the shaded area…

A: In question (a) we will find the function and find the domain of the function keeping in mind that…

Q: (2) An open metal pan is to be made by cutting out squares of the same size from the corners of a…

A: the volume of a rectangular box  domain  the check function is continuous of not

Q: Let P = (x, y) be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the origin…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The given figure shows an open box with a square base. The box is to have a volume of 4 cubic feet.…

A: Box: length, l =  x  breadth, b = x  height, h = y Volume of box (cuboid) = length . width . height…

Q: A hemispherical bowl of radius 8 inches is filled to a depth of h inches, where 0 … h … 8. Find the…

A: A hemispherical bowl of radius 8 inches is filled to a depth of h inches, where 0 ≤ h ≤ 8. To find…

Q: 126. Given a circle with radius r, diameter d, circumference C, and area A, a. Write C as a function…

A:

Q: Let P = (x, y) be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point…

A: y=x2-8

Q: Sketch the graphs of the functions.   f(x)=square root of x and g(x)=x^2         Find the area of…

A:

Q: Area A rectangle is inscribed in a semicircle of radius 10, as shown in the figure. Find a function…

A: Given Data The radius of the semicircle is R=10. The width of the rectangle is h.   Consider the…

Q: 1 Consider all rectangles with perimeter equa to 20 cm. Let the base of the rectangle be x cm and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A box without a lid is constructed from a 34-inch by 34 inch piece of cardboard by cutting x in.…

A: Given,  A box without a lid is constructed from a 34-inch by 34 inch piece of cardboard by cutting x…

Q: 14) Marginal Productivity: A company's productivity is given by the Cobb-Douglas function P(L, K) =…

A: The solution is given below

Q: A rectangle has a perimeter of 30 ft. Find a function that models its area A in terms of the length…

A: Given the length of one side of the rectangle is x. Let the length of other side of the rectangle be…

Q: 1) Write a function returns the area of a circle with radius 3cm. The area of circle is claculated…

A: Given: Radius = 3cm

Q: (b) Determine what type of function best models the data. o linear O power O quadratic O cubic O…

A:

Q: 19. The temperature in degrees Farenheit at a given location goes through a similar cycle each day.…

A:

Q: A box without a lid is constructed from a 20 inch by 20 inch piece of cardboard by cutting z in.…

A: (a) Here, length of the box(l)=(20-2x) in         width of the box(w)=(20-2x) in        height of…

Q: A box without a lid is constructed from a 24 inch by 24 inch piece of cardboard by cutting r in.…

A: Given Length of cardboard=24 inch Width of cardboard=24 inch

Q: In this problem you are asked to find a function that models a real-life situation and then use the…

A: A box with an open top is to be constructed from a rectangular piece of  cardboard with dimension 14…

Q: During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 4 hours, at a…

A: Given that during a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 4…

Q: 126. Given a circle with radius r; diameter d, circumference C, and area A, a. Write C as a function…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 1. In how many point(s) does a vertical line intersect the graph of a function? A. at least one…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 2. A ladder that is 10 feet long is leaning vertically against a wall. A carpenter slides the bottom…

A: (a). Height of wall = y Width of the foot of ladder from the wall = x

Q: Let P = (x, y) be a point on the graph of y = 1/x.(a) Express the distance d from P to the origin as…

A: (a) The distance between two points x1, y1 and x2, y2 is given by the following formula.…

Q: 5. A fence is to be built against a concrete wall to form a rectangular lot. Only three sides of the…

A:

Q: 2. A rectangle is inscribed in a semicircle of radius 10, as shown in figure below. Find a function…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only the first…

Q: The formula for area of a square is A = s 1. Fill in the missing parts of the table. 9 16 100 2. Is…

A:

Q: Let P = (x, y) be a point on the graph of y = √x.(a) Express the distance d from P to the point (1,…

A: The graph given to us is y = √x.

Q: A wire 14 cm long is cut into two pieces, one of length x and the other of length 14 – x, as shown…

A: Given: A wire 14 cm long is cut into 2 pieces ,one of length x and the other of the length 14-x.…

Q: A certain state taxes the first $500,000 in property value at a rate of 1%; all value over $500,000…

A: Explanation: Given that,  First $500000; rate = 1%Over $500000; rate = 1.25%

Q: Towns A and B are located 6 miles and 3 miles, respectively, from a major expressway. The point on…

A: Pythagorean theoremSum of squares of legs=hypotenuse square

Q: - (a) What is an even function? How can you tell that a func- tion is even by looking at its graph?…

A: a)We know, A function f(x) is said to be even if it satisfies the equation ,f(-x)=f(x) For all x…

Q: A semicircle of radius r= 4x is inscribed in a rectangle so that the diameter of the semicircle is…

A:

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A:

Q: 3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine…

A: We need to use given data to sketch the graph . Use relation between degree and radian to get angles…

Q: 2. A ladder that is 10 feet long is leaning vertically against a wall. A carpenter slides the bottom…

A: Here, x be the horizontal distance of the bottom from the wall and y be the vertical  distance of…

Q: An isosceles triangle has a perimeter of 8 cm. Find a function that models its area A in terms of…

A: given that an isosceles triangle has a perimeter of 8 cm.

Q: 33-34 Locate the discontinuities of the function and illustrate hy graphing.

A:

Q: 11) This is a function written in vertex form. F(x) = 2(x- 3)² + 4. %3D Describe the number of units…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 1. On a piece of graph paper, draw the graph of the function y = −1 over 2 x + 1. What is thedomain…

A: (A)We can use graphing calculator and draw graph

Q: 3. Write the coordinates of the local and the absolute extrema of the function whose graph is shown…

A: (1) From the given plot, see the coordinate (-6,0). It can be observed that the value of the…

Q: 8. A ladder of length L is placed so that it rests on top of a 4-foot wall and leans against a…

A: Given: BE= 8 feet DE= 4 feet CE= x feet Let height of building = AB= h feet To find length of…

Q: 5- What kind of functions is the function shown in this figure? c) Neither odd nor even 3- 2 a) Even…

A: To check whether the graph is even or odd find out if the it is symmetrical to x or y axis.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.