6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed space needs to be a rectangle with an area of 4000 square meters. One side of the enclosed space will be next to the house, so they only need fencing along three sides of the rectangle. How much fencing will they need to buy to minimize the perimeter of the enclosed space?

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Graph a vector, opposite to the given vector, that has an initial point at the origin.

A: In order to graph the opposite vector we need have one more point along with the origin.

Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

A:

Q: Questions 1-4: The graph of a function y = f(x) on the interval [-3, ∞) is shown below. Use the…

A: Given.

Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A:

Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: reply as soon as posible.

A: To find out the conservative.

Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

Q: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: The production output of a certain factory is N(t) = √² + 10t + 8 where N(t) is the output in…

A:

Q: It is projected that the population of a certain town will be P(t) = 2t+4t³/2 + 5000 where P(t) is…

A:

Q: The height of a projectile launched into the air is given by f(t)= - 16t² + 220t + 10, where t is…

A:

Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

A:

Q: 1-) x ² ( xdx tydy) = (x² + y²) dx ; x =1 when y=2

A:

Q: Find the length of the shortest ladder that can extend from a vertical wall, over a fence 2 m high…

A:

Q: Convert the Cartesian coordinate (-1,-4) to polar coordinates, 0≤ 0 0 Enter exact value. 0-

A: Given, (x,y)=(-1,-4)

Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: I have appended the formula used in the solution part of the question.

Q: tanx - x x-0 x - sinx 1. lim

A:

Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: Find the area contained between the two curves y = 3x - x² and y = x + x². 1/3 sq. units 1/4 sq.…

A: Let's find area between two given curves.

Q: Find the derivative of each of the following functions. -6 8. f(x) = x +4x¹ 9. f(x) = 4x² +5x²³ 10.…

A:

Q: Match each of the following vectors with its magnitude. t=(-7, 1) a. 5√2 u = -21-8j b. 2√√5 a vector…

A:

Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

A:

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A:

Q: A particle moves in a straight line from the origin (at t= 0) with given initial velocity u, and…

A:

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A: Given  Population in 2000 = 45,000  Population in 2010 = 65148

Q: B. Determine whether each of the following functions is (a) continuous (b) differentiable. 12.…

A: Please follow the the explanation.

Q: cos sin-cos -d0

A:

Q: (-2,5,7) + t(-3, 1,-4) and that the point Given a line defined by the equation T = P(x, y, 15) lies…

A:

Q: 3. Find f'(x) if f(x)= 3 2x + sin r

A:

Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

A:

Q: 2. If g(x)=√√3-x and f(x) = x³ +1 evaluate the following: gof(-1) b. (g-f)(2)

A: Given, g(x)=3-xf(x)=x3+1

Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

A:

Q: Find dy/dx by implicit differentiation. (cos X + sin #Y)5 = 49

A: The given equation is;  (cos pi x +sin pi y) 5=49.

Q: Given Cost and Price (demand) functions C(q) = 110q+45000 and p(q) = -2.7q+800, what profit can be…

A: Given cost and price (demand ) function C(q) = 110q+45000 and P(q)= -2.7q+800q, what profit can be…

Q: Use the chain rule to find, where First the pieces: End result (in terms of just t): dz = dt 江 西 | z…

A:

Q: 5. Find the Maclaurin Series for f(x) = e²^²+ex 2

A:

Q: 2. You wish to construct a topless crate with a surface area of 230in² and the base with one side…

A:

Q: 1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

A:

Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

A:

Q: Compute the effective rate of interest corresponding to a nominal rate of 4.8% compounded…

A: We need to use effective interest formula.

Q: Use implicit differentiation to determine the derivative of: tan² (xy² + y) = 2x.

A:

Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

A:

Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

A:

Q: A) Suppose that f(5)=-8, g(5)= 2, f^’(5)=10 and g^’(5)=-4, find h^’(5)=, if h(x)=[f(x)+2g(x)]^4 B)…

A: Suppose that f(5)=-8, g(5)=2, f'(5)=10, g'(5)=-4

Q: Problem #1: Using lim 0 6x³ 8x 2 at x = -2, f(x+h)-f(x) h Find the slope of the tangent line y =

A: Let's find slope of the tangent line by using limit definition.

Q: For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√92¹-1…

A: Topic = Derivative

Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

A:

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: topic- quadratic equations and derivatives