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- By using the calculus of variations, prove that the shortest distance between two points in the y z plane is a straight line10. Which equation represents the parabola that has been vertically stretched by a factor of 5, translated 6 units left and 2 units up. A) y = 5(x + 6)² + 2 B) y = 5(x + 2)?+ 6 C) y = 5(x – 6)² + 2 D) y =(x – 6)? + 2Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the other two on the positive y-axis and the negative x-axis where the diagonal has length L = 3, occurs when the angles at both (other) vertices are π/4. Include a sketch.
- Find the point on the parabola x = −t, y = -t², -∞Assume that the water coming from the end of a horizontal pipe 25 ft above the ground is parabolic in shape and the vertex of such parabola is at the end of the pipe. If at a point 8 ft below the line of the pipe, the flow of water has curved outward 10ft beyond a vertical line through the end of the pipe, how far beyond this vertical line will the water strike the ground?Ind the midpoint of the segment with endpoints (3, 6) and (5, -2). 13. Find all exact solutions to the equation x²+ 3x + 5 = 0 using the quadratic formul 14. Let f(x) = Y + ? aly) =16. please solve it on paperSuppose a parabola has symmetry with respect to the line x = 3. If (8, 19) is a point of the graph, what is another point of the graph? Work:Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle x\power{2}+y\power{2}-x-y-6=0 made by the chordwhose rquation is x+y-2=0.Evaluate | a ds, where C is the parabola 7 = (3t, 3t?), for –16. Show that if m is any real number, then there are exactly two lines of slope m that are tangent to the ellipse + = 1 and find their equations in terms of m, a and b.Can you please answer this question and show all of the steps and say the correct letterSEE MORE QUESTIONSRecommended textbooks for youAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill EducationAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education