Hello Tutor, I need an urgent help with the Calculus equations in the pictures attached below. Thank You! Full solution not needed, just the answers.

a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to the curve at the given point. 6x2 + 3xy + 2y2 = 20; (1,2) a. How do you know that the point is on the given curve? O A. The point (1,2) is in the domain of the implicit function. B. The value of 6x2 + 3xy + 2y2 is 20 when x is 1 and y is 2. O C. The point (1,2) is in the first quadrant. O D. The value of 6x2 + 3xy + 2yz is less than 20 when x is 1 and y is 2. b. Write the equation for the tangent line in slope-intercept form. y =0 (Use integers or fractions for any numbers in the equation.)An object thrown vertically upward from the surface of a celestial body at a velocity of 36 m/s reaches a height of s = - 0.612 + 36t meters in t seconds. a. Determine the velocity v of the object after t seconds. b. When does the object reach its highest point? c. What is the height of the object at the highest point? d. When does the object strike the ground? e. With what velocity does the object strike the ground? f. On what intervals is the speed increasing? a. The object's velocity after t seconds is v(t) = b. It takes the object to reach its highest point. (Simplify your answer.) C. The object reaches a maximum height of (Simplify your answer.) d. The object strikes the ground after (Simplify your answer.) e. The object strikes the ground with the velocity (Simplify your answer.) f. The speed is increasing on the interval(s). (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)dy For the following composite function, find an inner function u = g(x) and an outer function y = f (u) such that y = f(9(x)). Then calculate dx y = tan (6x2) dy S dxCompute the derivative of the following expression. 3ex+7e -x 32x+ 70-x dx 8For the following composite function, find an inner function u = g() and an outer function y = f (u) such that y = f(g()(). Then calculate dy dx y = sin 18x Select the correct choice below and fill in the answer box to complete your choice. dy d O A. du (418) . d dx dix (sin x) = dy d O B. d dx = du (sin 1su) .. do(X )= dy d O C. d du (4) . dx (sin 18x) = dy d OD. d dx du (sin u) . dy (x19) =dy a. Use implicit differentiation to find the derivative dx b. Find the slope of the curve at the given point. sin (y) = 7x3 - 7; (1,x) dy a. dx b. The slope at (1, x) is (Simplify your answer.)Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(x) = 0.01x# + 0.3x