Given points a=(−3,0), b=(0,6), c=(3,0) and P is somewhere on the y-axis. Determine the coordinates of P so that it minimizes the total distance to all three other points.

Q: Please

A:

Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

A:

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Find the slope and concavity of the curves at the given points. r = θ, θ = 0, π/2

A: Consider the formula for the derivative for polar curve. The slope is equal to the derivative at…

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

A:

Q: 2) If you are given two points in space, P1 (X1,yı) and P2 (X2,yz), demonstrate why the distance…

A:

Q: find the distance d between the points P1 and P2. P1 = ( - 1, 0); P2 = (2, 4)

A: P1-1, 0  &  P22, 4

Q: Find all points on the y-axis that are a distance 6 from P(5,3).

A: A point on the y axis is of the form (0,k) , where k= real number. Let (0,k) is 6 units away from…

Q: The maximum value of Duf(x, ys / f2 (x, y) + f (x, y) V O True False

A: We have to check whether the maximum value of Dufx,y=fx2x,y+fy2x,y.

Q: A car leaves Smogtown at noon, heading west at a speed of 60 km/h. Another car heads south at a…

A:

Q: Find the closure of a straight line in R x R_.

A: Given: Straight line in ℝ×ℝ. To find: Closure of straight line in ℝ×ℝ.

Q: Find the point on the graph of y = 2x that is closest to the point (3, 1). Use distancefrom and…

A: Let the point on the graph of y = 2x be (a,2a). Now, Using the Distance formula between two points…

Q: Find the exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

A:

Q: (b) Find the value of r that minimizes V(r).

A: 8(b) The expression for Morse potential is given by Vr=e-r-Ae-ar, r>0, where A and a are positive…

Q: Find the minimum value of xy, when p²x* + q²y* = r². %3D

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

A:

Q: Given that f is a quadratic function with minimum f(x) = f(1) = 3, find the axis, vertex, range and…

A: Given, f is a quadratic function with minimum f(x) = f(1) = 3. We have to find the axis, vertex,…

Q: For what minimum integer value of a, will the line ax+(a+1),y=18 (a> 0) have two intersection points…

A:

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

A:

Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

A:

Q: Find all points on the x-axis that are a distance 5 from P(−2, 3)

A: Given,P (-2, 3) and distance,d = 5

Q: Find all points on the x-axis that are a distance 5 from P(−2, 4)

A: Given,           All points on the x-axis that are a distance 5 from  P(−2, 4)

Q: find the distance d between the points P1 and P2.

A: We know, By distance formula, distance d between two points (a,b) and (c,k) is given by:…

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: Given points ? = (−3,0), ? = (0,6), ? = (3,0) and P is somewhere on the y-axis. Determine the…

A: Finding critical points by equating first derivatives of distance with y coordinate to zero.

Q: A. Find the shortest distance between the point A (3, 10) and the line y=x+1.

A:

Q: x = t³, y = t²,0 <t < v3

A:

Q: A company that produces cell phones has a cost function of C the cost in dollars and x is the number…

A: Let's find critical points. The derivative of the cost function is  C'(x) = 20x - 189 The derivative…

Q: What values of a and b, with a < b, minimize the value of (x* – 2r?) dr?

A: The given integral is ∫abx4-2x2 dx. Draw the graph of the function y=x4-2x2 as shown below. .

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5", where the value ab is as…

A: We need to find the minimum value of ab So, let fx,y=xy We need to minimize this function and find…

Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

A:

Q: A. Find the shortest distance between the point A (3, 10) and the line y = x +1.

A:

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: The area of the region enclosed by the x axis, the curve y=f(x)>0  for all x ∈ R and the lines x=b2…

A: Given: The area of the region enclosed by the x-axis, the curve y=f(x)&gt;0 for all and the lines…

Q: Given a set of observations [(x,y)], [(1,10), (8,9), (1,5)], what is the slope that minimizes the…

A: Given that              x     y          xy      x2              1    10        10      1…

Q: Find all points on the y-axis that are a distance 6 from P(5, 3).

A: P5, 3 is at a distance of 6 units from the y-axis

Q: The minimum value of Df(z, y) is ||Vf(z, y)||- Select one: O True O False

A:

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find all points on the y-axis that are a distance 6 from P(4, 8).

A: Given: Find all points on the y-axis that are a distance 6 from P(4, 8)

Q: Find the shortest distance from the given point to the line whose equation is given.

A: 6. The shortest distance from the point (0, 10) to the line y=13x is:…

Q: Use Lagrange multipliers to find the point on the circle x2 + y2 = 1 which is (a) closest to and (b)…

A:

Q: The minimum value of Duf(x, y) is ||Vf(x, y)||. Select one: O True False

A: The properties of gradient: If z is a function of two variables x and y then assume  fx and fy  are…

Q: Use the method of Lagrange multipliers to find the points on the circle x2 + y2 = 52 that are…

A:

Q: Aki's Bicycle Designs gas determined that when x hundred bicycles are built, the average cost per…

A: Consider the given average cost per bicycle is  Cx=0.5x2-0.5x+7.024 where C(x) is in hundreds of…

Q: Sketch the region defined by the inequalities -1 < r< 2 and -T/2 < 0s T/2.

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.