1. equation for relation (x2 + 4) y? = 8 %3D { (x^2 + 4) y^2...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. equation for relation (x2 + 4) y? = 8 %3D { (x^2 + 4) y^2 = 8 } a) Differentiate implicitly to find (dy/dx). Evaluate at the point (2,1). b) Give the relation for the corresponding inverse { x<->y } Then differentiatie implicitly to find the derivative of this inverse. Also evaluate at the corresponding point (2,1) {smmetric about y=x). c) Also observe the relation between these derivatives QUESTION 3 10 points Save Related Rates (Speed of Plane) An airplane is tlying at an altitude of 6 miles and passes directly over a radar antenna (based on same figure used in class, and also found in the textbook). When the plane is 10 miles away, the radar detects the distance s is changing at a rate of 520 mph. How fast is the plane actually travelling at that point in time? (Find dx/dt.) QUESTION 4 10 points Save Answer Related rates (angle and trigonometry) Observers of rocket An observer is watching the launching of a rocket at a location 200 ft form the base of the rocket. The angle A. (th), for the observer represents the angle of elevation from the ground level to the height of the rocket. a) Write an equation relating the variable h, the height of the rocket to this angle of elevation 0. b) Take the derivative and apply the methods from related rates to find the rate of change of the angel of elevation, de /dt, in terms of the speed of the rocket dh/dt. c) Evaluate this rate of change de/ dt,if the rocket is at a height of h = 200 ft and moving at a rate of dh/dt = 450 mph Also evaluate when the height is h = 1000 and the speed is dh/dt = 650 mph 1. equation for relation (x2 + 4) y? = 8 %3D { (x^2 + 4) y^2 = 8 } a) Differentiate implicitly to find (dy/dx). Evaluate at the point (2,1). b) Give the relation for the corresponding inverse { x<->y } Then differentiatie implicitly to find the derivative of this inverse. Also evaluate at the corresponding point (2,1) {smmetric about y=x). c) Also observe the relation between these derivatives QUESTION 2 Derivative for inverse function Apply the following formula for the derivative of an inverse function to compute the given deriative at the given point. Also illustrate the relation graphically. Y (b) = 1/f(a) { [FM(-1)I'(b) = 1/f(a) where ( f(a) = b; f^(-1) (b) = a a) Apply this formula to compute -1r (b) = 1/f(a) for the following function f(x) f(x) = x-3 + 4 where b = 6. [f^(-1)]' (6) } where { f(x) = sqrt(x - 3) + 4 b) Sketch the gaphs of both f(x) and f^M-1) (x) and describe the relation between them. Also include the tangent lines to each (corresponding to part a)) and give the relations between these. (How is this relation used in the formula above?) QUESTION 4 10 points Save Answer Related rates (angle and trigonometry) Observers of rocket An observer is watching the launching of a rocket at a location 200 ft form the base of the rocket. The angle A. (th), for the observer represents the angle of elevation from the ground level to the height of the rocket. a) Write an equation relating the variable h, the height of the rocket to this angle of elevation 0. b) Take the derivative and apply the methods from related rates to find the rate of change of the angel of elevation, de /dt, in terms of the speed of the rocket dh/dt. c) Evaluate this rate of change de/ dt,if the rocket is at a height of h = 200 ft and moving at a rate of dh/dt = 450 mph Also evaluate when the height is h = 1000 and the speed is dh/dt = 650 mph 1. equation for relation (x2 + 4) y? = 8 %3D { (x^2 + 4) y^2 = 8 } a) Differentiate implicitly to find (dy/dx). Evaluate at the point (2,1). b) Give the relation for the corresponding inverse { x<->y } Then differentiatie implicitly to find the derivative of this inverse. Also evaluate at the corresponding point (2,1) {smmetric about y=x). c) Also observe the relation between these derivatives QUESTION 3 10 points Save Related Rates (Speed of Plane) An airplane is tlying at an altitude of 6 miles and passes directly over a radar antenna (based on same figure used in class, and also found in the textbook). When the plane is 10 miles away, the radar detects the distance s is changing at a rate of 520 mph. How fast is the plane actually travelling at that point in time? (Find dx/dt.) QUESTION 4 10 points Save Answer Related rates (angle and trigonometry) Observers of rocket An observer is watching the launching of a rocket at a location 200 ft form the base of the rocket. The angle A. (th), for the observer represents the angle of elevation from the ground level to the height of the rocket. a) Write an equation relating the variable h, the height of the rocket to this angle of elevation 0. b) Take the derivative and apply the methods from related rates to find the rate of change of the angel of elevation, de /dt, in terms of the speed of the rocket dh/dt. c) Evaluate this rate of change de/ dt,if the rocket is at a height of h = 200 ft and moving at a rate of dh/dt = 450 mph Also evaluate when the height is h = 1000 and the speed is dh/dt = 650 mph 1. equation for relation (x2 + 4) y? = 8 %3D { (x^2 + 4) y^2 = 8 } a) Differentiate implicitly to find (dy/dx). Evaluate at the point (2,1). b) Give the relation for the corresponding inverse { x<->y } Then differentiatie implicitly to find the derivative of this inverse. Also evaluate at the corresponding point (2,1) {smmetric about y=x). c) Also observe the relation between these derivatives QUESTION 2 Derivative for inverse function Apply the following formula for the derivative of an inverse function to compute the given deriative at the given point. Also illustrate the relation graphically. Y (b) = 1/f(a) { [FM(-1)I'(b) = 1/f(a) where ( f(a) = b; f^(-1) (b) = a a) Apply this formula to compute -1r (b) = 1/f(a) for the following function f(x) f(x) = x-3 + 4 where b = 6. [f^(-1)]' (6) } where { f(x) = sqrt(x - 3) + 4 b) Sketch the gaphs of both f(x) and f^M-1) (x) and describe the relation between them. Also include the tangent lines to each (corresponding to part a)) and give the relations between these. (How is this relation used in the formula above?) QUESTION 4 10 points Save Answer Related rates (angle and trigonometry) Observers of rocket An observer is watching the launching of a rocket at a location 200 ft form the base of the rocket. The angle A. (th), for the observer represents the angle of elevation from the ground level to the height of the rocket. a) Write an equation relating the variable h, the height of the rocket to this angle of elevation 0. b) Take the derivative and apply the methods from related rates to find the rate of change of the angel of elevation, de /dt, in terms of the speed of the rocket dh/dt. c) Evaluate this rate of change de/ dt,if the rocket is at a height of h = 200 ft and moving at a rate of dh/dt = 450 mph Also evaluate when the height is h = 1000 and the speed is dh/dt = 650 mph
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Given vectors A = x2 y3 z, B = x2 y z3, and C = x4 y2 z2, show that C is perpendicular to both A and B.
-
Given vectors A = x + y2 _ z3, B = x2 _ y4, and C = y2 _z4, find (a) A and a, (b) The component of B along C, (c) AC, (d) A x C, (e) A. (B ^ C), (f) A x (B x C), (g) x x B, and (h) (A x y) z.
-
Find a function whose derivative is (a) 2x (b) sin x (c) x2 + x + 1
-
The last two decades have taught us that when it comes to financial deregulation, it is possible to have too much of a good thing too quickly. Financial deregulation has often taken place...
-
Answer the below questions. (a) What factor can be used as a proxy for cash-out refinancing incentives? (b) Why are prepayments attributable to cash-out refinancing likely to be insensitive to...
-
A headline in the Wall Street Journal stated, Firms Increasingly Tap Their Pension Funds to Use Excess Assets. What is the accounting issue related to the use of these excess assets by companies?
-
Liberty's inventory turnover during 2007 was a. 6 times b. 7 times c. 8 times d. Not determinable from the data given
-
Jefferson Products, Inc., is considering purchasing a new automatic press brake, which costs $300,000 including installation and shipping. The machine is expected to generate net cash inflows of...
-
Based on what he has heard regarding the profitability of such items, Fred Goldstein is considering adding a fresh shellfish case in his grocery store. Fred knows very little about this product or...
-
Prepare Trial Balance? Angela Mosely owns Innovative Designs. The Accounts and their balances for the Trial Balance of the first for January 31, 20X1, the first month of operation, are shown below....
-
A company can produce a small batch of products the first time at a cost of $3,000. If their 65 percent learning curve allows them to reduce their costs on each batch, what is the cost of producing...
-
3. A firm has decided to donate $3 million to its local school district to purchase computers for the school's students. The expected benefits from tax savings, reputation, etc... are likely to be $1...
-
The following is an interesting interview with Ray Kurzweil that explains what the "Singularity" is. It is only two months ago, before the explosion Chat GPT....
-
1. A flywheel rotates at 5.0 revolutions per second when it is brought uniformly to rest in 20 seconds. What is the magnitude of the angular acceleration of the flywheel during this time?
-
Use the two force relationships you just derived with Newton's 2nd law to write an algebraic expression for the coefficient of kinetic friction (u) that depends only on 0.
-
A company has the choice of either selling 1 , 0 0 0 unfinished units as is or completing them. The company could sell the unfinished units as is for $ 4 , 0 0 0 . Alternatively, it could complete...
-
Identify the four key financial statements in australian accounting that allow interested parties to evaluate the profitability and solvency of an organisation and briefly explain how each financial...
-
The column shown in the figure is fixed at the base and free at the upper end. A compressive load P acts at the top of the column with an eccentricity e from the axis of the column. Beginning with...
-
Using the proof of Theorem 7.58, prove that (20) holds if r/2 replaces r. Use part a) to estimate the difference |4 - |, where x0 = 3, f(x) = sin x, and xn is defined by (19). Evaluate x4 directly,...
-
Let f : R R be periodic and a > 0. Suppose that f is Lipschitz of order a; that is, there is a constant M > 0 such that for all x, h R. a) Prove that holds for each h R. b) If h = Ï/2n+l, prove...
-
If a, b R and b - a > 1, then there is at least one k Z such that a < k < b.
-
Name four disruptive business models and describe what they offer to their customers.
-
How is IT contributing to the success of the on-demand and shared economies?
-
What are the key strategic and tactical questions that determine an organizations profitability and management performance?
Study smarter with the SolutionInn App