The figure below shows cost (blue) and revenue (black) functions over the domain 0 < q < 15 (in thousands of uni (Click on the graph to get a larger version.)

Q: The absolute minimum value of the function f(x) = 9x² – 18x + 8 over the interval [0, 10] O 1 O 8 -1…

A: Find the minimum value of the given function.

Q: The region between the graphs of f(x)=x^2+3 and g(x)=−x+5 has ____________area square units.

A:

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: 3/2 3. Estimate (3cos x)dx using five subintervals and right endpoints. Sketch the graph and shade…

A:

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y x³ on the interval 0 0 and p and q are…

A: step:- 1 Generalization using nature of graph In interval (0,1) First draw graphs of x13,x12,x,x2,x3…

Q: (b) Find the absolute minimum value of f correct to four decimal places.

A:

Q: 21. Find the quadratię function y = ax² + bx + c whose graph passes through the points (-1,0), (1,…

A:

Q: The absolute minimum value of the function f(x) = 7x2 - 14z +9 over the interval [0, 8] O 10 O 2 O…

A:

Q: The goal of this problem is to find the maximum area of a rectangle whose lower-left vertex is at…

A:

Q: A rectangular billboard 9 feet in height stands in a field so that its bottom is 6 feet above the…

A: To maximize the function, we have to differentiate the function first and then equate with zero.

Q: Find the absolute minimum and absolute maximum values of fon the given interval. Rx) = x- In(7x), 2…

A: The given function is fx=x-ln7x,  12,2.

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: GivenLet x be the distance point PSmall island is 2 miles from the nearest point PWoman on the…

Q: Look at the given graph of the function V(x) from question 1 above. 150- -140+ -10- -120 -110 -100-…

A: By observing the graph ;

Q: ) Suppose we shift the graph of f vertically downwards by h units such that the maximum turning…

A: Given, the function f and g are defined by              f(x)=acosk(t-b)and              g(x)=mcsc…

Q: A piece of cardboard measuring 10 inches by 13 inches is formed into an open-top box by cutting…

A:

Q: A piece of cardboard measuring 12 inches by 9 inches is formed into an open-top box by cutting…

A: Given: Cardboard having length 12 inches. and width 9 inches. and cutting square with side length x…

Q: Two nonnegative numbers whose product is 36a? (where a > 0) and whose sum is a minimum, are

A: Now we will solve the problem.

Q: A picture with dimensions 10 cm by 8 cm is drawn on a rectangular cardboard leaving a border of…

A: We have to  denote the area of the border in terms of the width x,   find the value(s) of x if…

Q: The following graph shows the rate of inhalation of oxygen (in liters per minutes) by a person…

A: Solution: from the given data and graph, we can use Riemann mid-point sum: each width =1

Q: 2. Sketch the parabola: f(x) = x² - 2x - 3. Graph -6 Domain Range (Label x and y intercepts and…

A:

Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: Find the quadratic approximation to g(x) = 1/x at x = 1. Graph g and its quadratic approximation…

A: Given function is,

Q: sketch the graph of each function and determine whether the function has any absolute extreme values…

A:

Q: (a) If you can throw a baseball with an initial speed of 40 meters per second, at what angle of…

A: As per our guidelines, answer first three subpart of multipart question. So please resubmit the…

Q: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6 mi from…

A:

Q: 3. Find the number in the interval E,2] such that the sum of the number and its reciprocal is (a) a…

A:

Q: Consider the graph of f'(x) = . At what value(s) of x does f(æ) have a local maximum? y4 4. 3 2- -1+…

A: f(x) will local maxima or local minima at the points where f'(x)=0 Maxima points: points at which…

Q: Consider the function in the graph to the right. The function has a relative maximum of at x =

A: The function has a relative maximum of  2      or x = 0the function has a relative minimum of -6…

Q: I am stuck on the maximum and minimum values of y and corresponding x.  Will you please assist on…

A:

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

Q: A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15 mi from…

A: Given- A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15…

Q: Solve the given equation by selecting the graph of two related functions and finding their polnts of…

A: 3(x-3)2-147=0

Q: A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 12 mi from…

A: Given a boat in the ocean is 5 mi from the nearest point on a straight shoreline that point is 12 mi…

Q: A sheet of paper 82 cm-by-84 cm is made into an open box (i.e. there's no top), by cutting x-cm…

A:

Q: A rectangle is constructed under the graph of f(1) = 4x with one corner at (8, 0) and one corner on…

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Q: 4. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions…

A:

Q: 12. The graph on the right is NOT differentiable at x = 1. For what reason is it not differentiable?

A: Yes, given graph is correct.Given function:f(x) = x-1f(x) = -x+1        x&lt;1x-1           x≥1

Q: Find the absolute maximum and minimum values of the function g(x) = 2x− 4sin(x) on the interval [0,…

A:

Q: During this pandemic Mary and her friends decided to take a break from schoolwork and go on a hike…

A: Let the cubic equation for mountain is f(x)=(x-2)(x+3)(x-1) or f(x)=x3-7x+6…

Q: A boat on the ocean is 2 mi. from the nearest point on a straight shoreline; that point is 13 miles…

A: According to the question, x is the distance between the nearest point on a shoreline and the point…

Q: 4 is the cube root of 64.Use linear approximation for cube root function @ a = 64 with AX=0.5 to…

A:

Q: Use a graph of  f to estimate the maximum and minimumvalues. Then find the exact values.(b) Estimate…

A:

Q: The annual revenue and cost functions for a manufacturer of precision gauges are approximately R ( x…

A: Given Revenue function Rx=500x-0.02x2 Cost function Cx=120x+100,000

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: In an economic enterprise, the total amount T that is produced is a function of the amount n of a…

A: (a) The graph of the function is as follows: (b) Here, T(1.02)=-2(1.02)3+3(1.02)2+1.02…

Q: Using the techniques described in section 2.6.4 of the Course Notes, find the global extrema of the…

A:

Q: Find the x value where the function g(x) = xe-lx attains a local maximum. Enter the exact answer. If…

A: Differentiate y and by solving y'=0 obtain critical points. Check sign of y'' on critical points -…

Q: The demand for face masks is given by p =-3 In(x) + 10 with domain [1, 28] where x is the number of…

A: Given: The demand for face masks is given by, p=-3 lnx+10, with domain 1, 28 where x is the number…

Q: 3. Find the number in the interval ,2] such that the sum of the number and its reciprocal is (a) a…

A: Let number = x,  It is given that, the function is = sum of number and its reciprocal

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.