Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the indicated expression. Complete parts (a) through (f) below. x + y = 160 and the product P=xy as large as possible.

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 4x²-x³, (1, 3) y =…

A: Solution: f(x)=4x2-x3, (1,3)

Q: 2. Find the area of the region between two concentric circles r =7 and r=10

A:

Q: Determine if the limit lim (1+5x) 1+0+ exists, and if it does, find its value.

A: Given: limx→0+1+5x12x

Q: 1 3 I(t) = ²/³ - 5 ² + 3 2 +86 (0 ≤ t ≤ 10)

A: I(t)=13t3-52t2+86for critical numbers put I'(t)=0d dt(tn)=ntn-1d dt(constant)=0

Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

Q: Differentiate the function. h'(x) = h(x) = In(x + √x²-2)

A: Use the derivative of log function.

Q: the

A:

Q: he given curve is rotated about the y-axis. Find the area of the resulting surface. y =  1 3x3/2,…

A: Given

Q: Find equations of the tangent lines to the curve y = at the point (1, 0) int (e, ²) at the point y =…

A:

Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: 3√/t-1 S (³√t=¹) dt = 3 − 2t + c - C

A:

Q: 1. Make a sketch for each parabola a. y² = 4x b. x² =−16y

A: To draw parabolas

Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A: Profit = Revenue - Cost

Q: (b) g(x) = (x + e*)², [0, In 4]

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: 3 x-Vinc dx =

A: Given: ∫3xln(x)dx

Q: Let f(x) = 7x sin(x) cos(x). Evaluate 3TT f'(x) at x = 3³77₁ ƒ' (³)

A: f(x)=7xsinxcosxd dx(sinx)=cosxd dx(cosx)=-sinxd dx(a.b)=adbdx+bdadx

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A:

Q: 4 Function f is defined by f(x)= √√x+1, -1<x<1 x-1, otherwise (a) Find lim f(x), lim f(x), lim f(x)…

A:

Q: . Evaluate the limit for the graph: lim f(x). |y4 4 a. 3 b. 2 2 -4-20 2 -2 -++-% x c. d. 5 does not…

A: We will find the required.

Q: Write an equation of the line containing the given point and parallel to the given line. Express…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A:

Q: If a ball is given a push so that it has an initial velocity of 6 m/s down a certain inclined plane,…

A:

Q: Question 2 Find all critical numbers of the function f(x) = sin²6x + cos 6x, 0<x<3. O T N 2x 36 0 9…

A: We have to slove above question Find the critical number of function

Q: Find the distance between the skew lines: x = 5+7t, y=3+7t, 2=8-9t x = 1-t, y = 6, z = 5+8t NOTE:…

A: The given skew lines: L1:  x=5+7t,  y=3+7t,  z=8-9tL2:  x=1-t,  y=6,  z=5+8t

Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

A:

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: A function y=f(x) is said to be increasing in the interval (a,b) if for every x∈(a,b), f'(x)&gt;0.…

Q: Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this…

A:

Q: Find the equation of the tangent line to the without eliminating the parameter ‚t=-1/1/12 x= 3t,…

A: Given parametric equations:- x=3t, y=8t3 ,t=-12

Q: Consider the function f(x) = 2x³ - 5x on the closed interval [-4, -2]. Find the exact value of the…

A: We have to find the slope and value of c.

Q: Find the derivative of the function. F(t) = e5tsin(2t) F'(t) =

A:

Q: Estimating the Amount of Paint Required A coat of paint of thickness 0.07 cm is to be applied…

A:

Q: 2. Find polar coordinates a. (3-√3.3) b. (0, -2)

A: We need to find the polar coordinates of the given points :

Q: Let f(u) = √u and g(x) = u = 4 + 9x². Find (f o g)'(3). (fog)'(3) = (Type an exact answer.)

A: f(u)=u3g(x)=4+9x2(f∘g)(x)=f(g(x))

Q: Consider the ellipse 9x² + 64y² = 576. Consider the point P(16,3). Find an equation for both lines…

A:

Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: Consider the given function. fx=5excos x

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: To find where the function is increasing or decreasing.

Q: Using substitution differential equations. methods to solve homogeneous Y'= Y+X

A:

Q: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second…

A:

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (4,…

A: To Find : Distance of point (4,6,3) from the plane x-y+2z=10

Q: Solve the equation for x given that 1 ≤ x ≤ 8: ln x = sin x, using 5 iterations of Newton's method.

A: To find the solution of the following equation ln x = sinx by using Newton's method For the…

Q: 7. Solve for x: 16 X 70⁰ 10

A: As we know from the Sine Rule: sinAa=sinBb=sinCc Given:

Q: ts) Let f(x) = 1. f'(x)= 2. f'(4)= 5x² tan(r) sec(x) Find the following:

A:

Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: The data in the table concerns the lactonization of hydroxyvaleric acid at 25°C. They give the…

A:

Q: The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer…

A: We have to find m'(-1) and n'(6) Where m(x)=f(x).g(x)        n(x)=g(x)/h(x)

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: To solve the following problem

Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy = 0 dx

A:

Q: f(x) = 1 X-3

A: f(x)=1x-3if f'(x)&gt;0, than f(x) is increasing if f(x)&lt;0, than f(x) is decreasing d dx(xn)=nxn-1…