Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle 0 above the horizontal at which it is thrown. SPEED v (ft/s) 80 85 90 95 35 188 212 238 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278 Use the accompanying table and the equations below to estimate the stated partial derivatives. f(xo + Ax, yo) – f(xo. Yo). lim f(xo, Yo + 4y) – f(xo, Yo) f (xo, Yo) f, (xo, Yo) lim Ay-0 %3D Ax→0 Δχ Ду Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer. ANGLE O (degrees)

Q: A function of the form y ax + bx + c, a + 0, is called a/an function.

A: The given function is, y=ax2+bx+c, a≠0 For the given function, the degree of the function is 2.

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: An airline's revenue, R, is a function of the number of full-price tickets,.X, and the number of…

A: Given information: The airline's revenue R is a function of : x = number of full-price tickets sold…

Q: Suppose that f is a linear function such that f(5) = 10 and f(9) = 3. Find the equation for f. (Use…

A: Given f is linear function such that f(5) = 10 and f(9) = 3we find f(x)

Q: Find an equation for f(x) using the tangent function. f(x) = f(x) 12- 10 8. 6. 4 2 X 3 2 6. 6 3 6 -8…

A: The given graph is:   To find the equation for f(x).

Q: Let f : A → B be a function. If Y ⊆ B, then f(f-1(Y )) ⊆ Y .

A:

Q: Which type of discontinuity does the function exhibit at x = 3? %3D (-x2 + 1, -1 sx<0 2х, f(x) =…

A:

Q: The volume V and surface area of a sphere [Figure 6(A)] are expressed in terms of radius r by V(r) =…

A: GivenVolume , V = 11πr3Surface Area , S = 41πr2As V = 11πr3r3 = V11π⇒r = V11π13 = r(V)Now, Surface ,…

Q: Consider the function f (z) = e²z.

A:

Q: Find the function f given that the slope of the tangent line at any point (x,f(x)) is f '(x) and…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: ------------------------------------------------------------------  r = rv,θRight hand estimate∂r∂v…

Q: A jogger ran 4 miles and then walked 2 miles. The average velocity running was 3 miles per hour…

A: Given  A jogger ran 4 miles and then walked 2 miles. Total time is T  The average velocity of…

Q: The height, h, in meters, above the ground on a Ferriss wheel can be modelled by the function h(x)=…

A:

Q: The number N of cars produced at a certain factory in 1 day after t hours of operation is given by…

A: Given problem:- The number N of cars produced at a certain factory in 1 day after t hours of…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: Find the partial derivatives.

Q: The wind-chill index is modeled by the function W = 13.12 +0.6215T – 11.37v0.16 + 0.3965TV0.16 ,…

A: When partial differentiation is done with respect to a variable, then other variables are treated as…

Q: evaluate the function at the specified points. f (x, y) = x + yx3, (2, 2), (−1, 4)

A: Given function is fx,y=x+yx3

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: Given : v = 85 ft/s and angle is 45°

Q: Find the equation of the tangent to the graph of f(x) = (x² + 28)*/5 at x = 2. 8 96 (A y= 및 + 5 8 (B…

A: givenf(x)=(x2+28)45 at x=2f(2)=(22+28)45=16therfore co-ordinates will be (2,16)slope of…

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Given: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be…

Q: Suppose utility function takes the following form: uz = u(c¿, m,, l;) = (c;m¿)'l&.

A:

Q: Find the derivative of the function at the given point in the direction of A. f(xу,2) - 4x - 5у -…

A: Use the formula of the directional derivative and solve accordingly.

Q: Two ships leave port at the same time. One sails south at 9 mi/h, and the otiyer sails east at 12…

A:

Q: Two ships leave port at the same time. One sails south at 18 mi/h, and the other sails east at 24…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Let a + 0 be a constant. Give an example of a function y = f(x) for which ay – y' = 0 and g?y – y" =…

A:

Q: Suppose that w and t vary inversely and that t = when w = 3. Write a function that models the…

A: The variables w and t vary inversely implies that as the value of w increases, the value of the t…

Q: An open box is to be constructed from a piece of cardboard 20cm by 40cm by cutting squares of side…

A: a Let length=l , breadth= b and height=h   So , l=40-2xcm         b= 20-2xcm        h= x cmThus ,…

Q: If an object moves along a line so that it is at y = f(x) = 9x² – 7x at time x (in seconds), find…

A: Given : fx = 9x2-7x

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Suppose that f is a linear function such that f(3) = 6 and f(7) = 3. Find the equation for f. (Use x…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: The baseball leaves Nolan's hand at the same height at which it is caught by Ryan. To Find: Estimate…

Q: Find the equation of the tangent to the graph of f(x) =(x²+28)*/5 at x =2. 4 64 A y= 3**5 8 64 y=x+5…

A: To find the tangent to the graph of f(x)=x2+2845 at x=2. Here, the equation of the tangent at x=2…

Q: Find the direction in which the function is most repidly at the point P0

A:

Q: Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the…

A: Given: Let the ball is rolling down a ramp. The distance travelled by the ball is given bythe…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: TO FIND: Partial derivative

Q: Find domain and range of the function f(x, y) = In[ e – x² – y°]

A:

Q: The position of a mysterious object in space is represented by the given function f(x, y) = 2x² +…

A: differentiate the given function with respect to x and y partially ∂f∂x=4x+2y+0+2 =0 ∂f∂y=0+2x+2y+0…

Q: The velocity of Engr. Garcia in meters/sec when he jumped out of the plane given is given by the…

A:

Q: Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

A: Given: y'''-16y''+63y'=144ex y0=12 y'0=21 y''0=18 To find: Solution to the given differential…

Q: Use a formula to express y as a function of t if  y = 3x2 + 9x and x = t − 1.   y =

A: First of all, both equations i.e. y in terms of x and x in terms of t.

Q: Find y as a function of a if y(0) = 7, y'(0) = 10, "(0) = 36, "(0) = 0. y(x) = 0 y(4) 12y" +36y" =…

A:

Q: If an object moves along a line so that it is at y = f(x) = 9x-2x at time x (in seconds), find the…

A: Given query is to find the instantaneous velocity of the object using derivative.

Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

A:

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A:

Q: Consider the following.       Function                 Line f(x) = x2 − 6              2x+y=0   a.)…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Find a function in the form of w= zo+ z1 r + z2 e² that best fits the following points: (-1, 2), (1,…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: