A farmer has 1,520 feet of fencing available to enclose a rectangular area bordering a river. No fencing is required along the river. Let x represent the length of the side of the rectangular enclosure that is perpendicular to the river. Complete parts a. through c. A(x) = 1520x-2x² (Simplify your answer.) b. Find the dimensions of the fence that will maximize the area. X a. Create a function, A(x), that describes the total area of the rectangular enclosure as a function of x, where x is the length of the rectangular enclosure that is perpendicular to the river. The length of the side of the rectangle perpendicular to the river is rectangle parallel to the river is River and the length of the side of the

Q: A baseball diamond is 90 ft in a side (it's Matthew runs from the first base to th base at the rate…

A:

Q: What percentage grade should a road have if the angle of elevation of the road is 2 degrees? (The…

A: Angle of elevation is 2°Horizontal distance is 100 foot

Q: On the interval [0, 9] the polar curve r = 80² has arc length units.

A:

Q: A toy rocket is shot vertically into the air from a 8-foot-tall launching pad with an initial…

A:

Q: Find the unit tangent vector to the curve defined by r(t) = (5 cos(t), 5 sin(t), 2 sin²(t)) at t= 3m…

A: The unit tangent vector,

Q: √2-x x-2- x+5x Problem 1. Compute lim Show all work.

A:

Q: A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end…

A:

Q: Find the derivative of hyperbolic function f(x)= sinhx+2coshx

A:

Q: Suppose that f(x + h) − f(x) = −6hx² +7hx + 2h²x - 1h² +7h³. - Find: ƒf'(x)= =

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: The profit function is

Q: Find the general (analytical) solution of the following equation. day dx4 2a² + a¹y = 0 d²y dx² |

A:

Q: (√x+x-1) +x-1)dx= ?

A:

Q: A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the…

A: A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the per…

Q: For the function f(x) shown in the graph below, sketch a graph of the derivative. You will then be…

A: The graph of the function f(x) is shown as,

Q: U(x,y)=(x+2)^2(y+3)^3 Find the partial derivative of x and y

A: U(x,y)= (x+2)2(y+3)3We have to find partial derivative of x and y

Q: Compute the arc length function s(t) = f ||r' (u)|| du for r(t) = (6√/2+¹/2, In(t), 9t) a = 1 (Use…

A:

Q: Find a plane containing the point (2,5,3) and the line (t) = +t

A:

Q: lim X-800 in (1-1) X In

A: Given Limit

Q: An object is thrown vertically upward whose height is given by the function s(t) = - 16t² +50 where…

A:

Q: Find all intervals on which the function is positive and all intervals on which the function is…

A:

Q: 16x² 77.9 45 (45)² horizontal distance of the golf ball from the point of impact. What is the…

A:

Q: 7x²-7 x3 Sketch the function y=. i. Domain ii. Intercepts iii. Symmetry using the following steps.

A:

Q: The helix of radius R, height h, and N complete turns has the parametrization 2πΝt r(t) = (Rcos…

A:

Q: The plane with normal vector (6,-5, 1) containing the point (0,-2,3) has equation Ax+By+Cz = D. If…

A:

Q: What is F(x) = Sdx? O F(x) = 4ln |x|| O F(x) = 4ln |x|+C O F(x) = 4lnx + C O F(x) = 4ln x

A:

Q: 2. Follow the steps to determine the centroid of the area shown. a. Estimate the coordinates of the…

A:

Q: 2. Find the limit. sin (2x) x-0 sin (7x) (a) lim sin (2x) x-1/4 sin (TX) (b) lim

A:

Q: Find the equation of the parabola with the given properties Focus (3,0), directrix x = -3. = x

A:

Q: Question 3 Let s(t) = 3t² - 3t - 2 be a position function. Find the velocity and acceleration…

A:

Q: If f(x) f'(x) f"(x) = f""(x) = 3x -, compute the first, second, and third derivative of f(x). 4x +…

A:

Q: 3. The motion of a particle is defined by the function s(t), where s is the displacement from the…

A: (a) S(t) is displacement and t is Time in second. S'(2) = 0 It mean that t = 2 is critical point.…

Q: Find the total area enclosed by the limacon r = 3 - cos 0. Answer:

A:

Q: Evaluate ſƒƒ£y² dV, where E is the solid hemisphere x² + y² + z² ≤ 9, y ≥ 0.

A:

Q: Find the speed over the path r(t) over the path r(t) = (2t + 4, 8t + 2, 3t - 7) at t = 8. (Use…

A: r(t)=<2t+4, 8t+2,3t-7>We have to find speed,v(8)

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

A:

Q: Based on the given table of data, compute each of the following derivatives. X 1 3 5 7 f(x) 6 7 3 -4…

A:

Q: Use the Algebra to evaluate the limit. Use the Algebra to evaluate the limit. Lim h-0 (2+h)2-4/h…

A:

Q: lim [tan 3x]2x X-> 0¹

A: Since , then    Simplify:       Move the limit under the exponential:

Q: Find the equation of the hyperbola with the given properties Vertices (0,6), (0, 5) and foci (0,…

A: Vertices of hyperbola: Foci of hyperbola: To find: Equation of HyperbolaSince, vertices and foci…

Q: Determine the degree 4 Taylor polynomial for ln(x) centered at c = 1.

A:

Q: Evaluate the triple integral. JIL (x - y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1…

A:

Q: Calculate the Taylor polynomials T₂(x) and T3(x) centered at x = for f(x)=tan(x). a. T₂(x) = b.…

A:

Q: A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find…

A:

Q: 1) Given the curve y = x² over the interval [1,3], (a) Find the exact value for the area under the…

A: The curve is given as ,

Q: Find the linearization of the function f(x, y, z) = Sqrt(x^2+y^2+z^2) at (3, 2, 6) and use it to…

A:

Q: Consider the following differential equation (tan y − 2)dx + (x sec²y + dy = 0, y> 0

A:

Q: The graph of f(x) = 2x³ + 12x² - 72x+5 has two horizontal tangents. 3 What is the negative value of…

A:

Q: Write an iterated integral for da over the region R bounded by R y = 5√√x, y = 0, and x = 32 using…

A: we can see from the figureThe bounded grey region represents the region R.

Q: The proportion of items in a population that possess a specific attribute is known to be 0.30. a. If…

A: Sample size = 100Sample proportion = 0.35Population proportion= 0.30Sampling error = sample…

Q: Integrate: [2 200e0.02z dz + C

A: