Please solve question no 96 SolutionI In Problems 90–93, check that the point (2, 3) lies on the curve. Then, viewing the curve as a contour off(x, y), use grad f(2, 3) to find a vector normal to the curve at (2, 3) and an equation for the tangent line tothe curve at (2, 3).90. x² + y² = 1391. ху %3D6Answer92. y = x2 – 193. (у — х)2 + 2 %3 ху — 3Answer Solution94. The temperature H in °Fahrenheit y miles north of the Canadian border t hours after midnight is givenby H = 30 – 0.05y – 5t. A moose runs north at a speed of 20 mph. At what rate does the moose perceivethe temperature to be changing?95. At a certain point on a heated plate, the greatest rate of temperature increase, 5°C per meter, is towardthe northeast. If an object at this point moves directly north, at what rate is the temperature increasing?O Answer96. An ant is at the point (1, 1, 3) on the surface of a bowl with equation z = x² + 2y², where x and y are incm. In what two horizontal directions can the ant move away from the point (1, 1, 3) so that its initial rateof ascent is 2 vertical cm for each horizontal cm moved? Give your answers as vectors in the plane.97. Let T = f(x, y) = 100e-(="/2)–v represent the temperature, in °C, at the point (x, y) with x and yin meters.(a) Describe the contours of f, and explain their meaning in the context of this problem.(b) Find the rate at which the temperature changes as you move away from the point (1, 1) toward thepoint (2, 3). Give units in your answer.(c) In what direction would you move away from (1, 1) for the temperature to increase as fast aspossible? AnswerSolution98. You are climbing a mountain by the steepest route at a slope of 20° when you come upon a trailbranching off at a 30° angle from yours. What is the angle of ascent of the branch trail?99. You are standing at the point (1, 1, 3) on the hill whose equation is given by z = 5y – x² - y².(a) If you choose to climb in the direction of steepest ascent, what is your inisi-the horizontal distance?-nta af naeant relat146 / 237(b) If you decide to go straight northwest, will you be ascending or descen(c) If you decide to maintain your altitude, in what directions can you go?( AnswerStrengthen Your Understanding1 In Problems 100–102, explain what is wrong with the statement.100. A function f has a directional derivative given by f:(0,0) = 31 +43.101. A function f has gradient grad f(0, 0) = 7.Answer Solution102. The gradient vector grad f(x, y) is perpendicular to the contours of f, and the closer together thecontours for equally spaced values of f, the shorter the gradient vector.1 In Problems 103–104, give an example of:103. A unit vector i such that fa(0,0) Answer104. A contour diagram of a function with two points in the domain where the gradients are parallel butdifferent lengths.I Are the statements in Problems 105–116 true or false? Give reasons for your answer.105. If the point (a, b) is on the contour f(x, y) = k, then the slope of the line tangent to this contour at (a,:::

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Please solve question no  96 SolutionI In Problems 90–93, check that the point (2, 3) lies on the curve. Then, viewing the curve as a contour off(x, y), use grad f(2, 3) to find a vector normal to the curve at (2, 3) and an equation for the tangent line tothe curve at (2, 3).90. x² + y² = 1391. ху %3D6Answer92. y = x2 – 193. (у — х)2 + 2 %3 ху — 3>Answer> Solution94. The temperature H in °Fahrenheit y miles north of the Canadian border t hours after midnight is givenby H = 30 – 0.05y – 5t. A moose runs north at a speed of 20 mph. At what rate does the moose perceivethe temperature to be changing?95. At a certain point on a heated plate, the greatest rate of temperature increase, 5°C per meter, is towardthe northeast. If an object at this point moves directly north, at what rate is the temperature increasing?O Answer96. An ant is at the point (1, 1, 3) on the surface of a bowl with equation z = x² + 2y², where x and y are incm. In what two horizontal directions can the ant move away from the point (1, 1, 3) so that its initial rateof ascent is 2 vertical cm for each horizontal cm moved? Give your answers as vectors in the plane.97. Let T = f(x, y) = 100e-(=&#34;/2)–v represent the temperature, in °C, at the point (x, y) with x and yin meters.(a) Describe the contours of f, and explain their meaning in the context of this problem.(b) Find the rate at which the temperature changes as you move away from the point (1, 1) toward thepoint (2, 3). Give units in your answer.(c) In what direction would you move away from (1, 1) for the temperature to increase as fast aspossible?> Answer>Solution98. You are climbing a mountain by the steepest route at a slope of 20° when you come upon a trailbranching off at a 30° angle from yours. What is the angle of ascent of the branch trail?99. You are standing at the point (1, 1, 3) on the hill whose equation is given by z = 5y – x² - y².(a) If you choose to climb in the direction of steepest ascent, what is your inisi-the horizontal distance?-nta af naeant relat146 / 237(b) If you decide to go straight northwest, will you be ascending or descen(c) If you decide to maintain your altitude, in what directions can you go?(> AnswerStrengthen Your Understanding1 In Problems 100–102, explain what is wrong with the statement.100. A function f has a directional derivative given by f:(0,0) = 31 +43.101. A function f has gradient grad f(0, 0) = 7.Answer> Solution102. The gradient vector grad f(x, y) is perpendicular to the contours of f, and the closer together thecontours for equally spaced values of f, the shorter the gradient vector.1 In Problems 103–104, give an example of:103. A unit vector i such that fa(0,0) < 0, given that f,(0, 0) = 2 and f,(0, 0) = 3.> Answer104. A contour diagram of a function with two points in the domain where the gradients are parallel butdifferent lengths.I Are the statements in Problems 105–116 true or false? Give reasons for your answer.105. If the point (a, b) is on the contour f(x, y) = k, then the slope of the line tangent to this contour at (a,:::

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