4 Current Attempt in ProgressDetermine whether the solution space of the system Ax = 0 is a linethrough the origin, a plane through the origin, or the origin only. If itis a plane, find an equation for it. If it is a line, find parametricequations for it, using t as parameter.1-31(c) A =2 -6 23-9 3The solution space is Choose one1 -1 1O Links is a plane, find an equation for it. If it is a line, find parametricequations for it, using t as parameter.1-31(c) A =2 -6 2%3D3.-9 3The solution space is Choose one v1-11(d) A =2 -143111The solution space is Choose one v

Statement used :- If dimension of a null space is 1 then its solution space is a line. And if…

Answered: Current Attempt in Progress Determine…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 29E

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By definition, a hyperbola is the locus of points whose positive difference of distances from two fixed points F1 and F2 called foci is constant. In the grid provided, find points whose difference of distances from points F15, 0 and F2-5, 0 is 6. That is, locate some points for which PF1-PF2=6 or PF2-PF1=6; point P3, 0 is one such point. Then sketch the hyperbola.
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuration. Centerville is located at (15,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at (0,-3). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. (Draw a picture of this situation).It costs $1000 per unit to lay cable along the x-axis and $1250 per unit otherwise. Write a function for the total cost of laying the cable in terms of x.Cost(x)=__________ Take the derivative of your cost function by carefully applying the chain rule.dCost/dx=__________ To find the x location that yields a minimum cost we need Calculus! Recall that if the derivative of the cost function is zero then the x is…
2. The orthogonal trajectory of y= cex is a parabola of the form y = ax+b. Find the values of a & b so that the vertex is at (3,0).
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be the cable connecting Centerville to both towns. The idea is to save on the cost of the cable by arranging the cable in a Y-shaped configuration.Centerville is located at (7,0) in the xy-plane, Springfield is at (0,5), and Shelbyville is at (0,−5). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. 1). To solve this problem we need to minimize the following function of x:f(x)=? a). We find that f(x) has a critical number at x=? b). To verify that f(x) has a minimum at this critical number we compute the second derivative f′′(x) and find that its value at the critical number is =? (positive…
(a) Beginning with the general solution of the systemx' = -2y, y' = 2x , calculate x2 + y2 to show that the trajectories are circles. (b) Show similarly that the trajectories of the system x' = 1/2y, y' = -8x are ellipses with equations of the form 16x2 + y2 =C2.
The equation of the Plane in the form of Ax+By+Cz+D=0 that passes through points (3,1,-2), (-1,2,4) and (2,-1,1). Which of the following is the possible sum of A,B and C.
2.4(2) With the equations of three plans (shown in the image) A) Demonstrates that the three planes intersect into a single point. B) Determines the coordinates of the intersection point.
Find an equation of a sphere with radius r and center C(h, k, l). SOLUTION By definition, a sphere is the set of all points P(x, y, z) whose distance from C is r. (See the figure.) Thus, in terms of r, P is on the sphere if and only if |PC| = . Squaring both sides, in terms of radius r, we have |PC|2 = . In terms of Cartesian coordinates and radius r, the equation of a sphere is (x − )^2+ (y − k)^2+ (z − )^2 =
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation.Centerville is located at (7,0) in the xy-plane, Springfield is at (0,5), and Shelbyville is at (0,−5). The cable runs from Centerville to some point (x,0) on the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of xx:f(x)= ?We find that f(x) has a critical number at x=?To verify that f(x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is ? , a positive number.Thus the…
The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A tourist moves up a hillside such that the projection of his route on the XY plane is a straight line with equation y=x-1 . Determine the coordinates of the highest point of the tourist's route.
14.1 Find the equation for the plane through the points P0(−4,3,2), Q0(1,−3,0), and R0(0,−5,0). The equation of the plane is =
The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so that the vertex is at (-3,0)

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