) Rectangular bathtub has a fixed height of 10ft. The length of the bathtub is increasing at a rate of 2ft/sec, and the width is increasing at a rate of 1.5ft/sec. How fast is the volume increasing at the moment when length is 30ft and width is 12ft?

Q: 6. Suppose f f(x) dx = -5, and fg g(x) dx = 1. Evaluate the following integrals using the properties…

A: To find values of given definite integrals.

Q: Let f be the function defined as f(x) = { 1 3x-4 for x <3 for x ≥3 Which of the following statements…

A:

Q: Determine which test can be used to show that the series (a) Geometric Series Test (b) p-Series Test…

A:

Q: Express the vector P₁ P₂ in the form v=v₁l+V₂j+V3k if P, is the point (0,5,0) and P₂ is the point…

A: given  and

Q: Let u = (5,-4) and v= (-4,7). Find the (a) component form and (b) magnitude (length) of the vector.…

A: The vectors are given by(a) The component form of the vector  can be obtained as follows:

Q: Calculate af Әх af ду af ?х af ду af af af ах ду' Әх -f (1, f(x, y) = ex + y (1, -1) (1, -1) = = = =…

A:

Q: find the intervals where the graph of fis concave upward, the intervals where the graph of fis…

A: Firstly find inflection point (f"(x)=0).Concave upward: f"(x)&gt;0.Concave downward: f"(x)&lt;0.

Q: Find a parametric representation for the lower half of the ellipsoid 2x2 + 6y2 + z² = 1. (Enter your…

A:

Q: 1. Given the following graph and A(x)=f(t) dt, f , find: -2 -1 4 -3- --2- 1- 0 -1 --2- -3 1 2 3 5 6…

A: Given: To Find: To find .

Q: Question Given f (x) below, find f'(x). Do not include "f'(x) =" in your answer. Provide your answer…

A:

Q: Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² +…

A:

Q: Find a parametrization of the line in which the planes x+2y+4z=-4 and 2x+3y+6z= -7 intersect. Find…

A:

Q: The graphs of y=-e following. y=esin 4x and y-e are shown. Use them to graph the For one period of y…

A: Draw the graph of the given function

Q: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

A: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

Q: 29. a(t) = -32; v(0) = 70; s(0) = 10 30. a(t) = -32; v(0) = 50; s(0) = 0 31. a(t) = -9.8; v(0)=20;…

A: 29) a(t)=-32, v(0)=70, s(0)=1031) a(t)=-9.8, v(0)=20, s(0)=0

Q: The total profit from selling x units of cookbooks is P(x) = (2x-2)(4x-9). Find the marginal average…

A:

Q: If f'(x) = x, what is f(x)? (Remember the constant of integration.) 2 f(x) =

A:

Q: Region R is bounded by the graphs of y=e2x + 1, y = 0, x = 0, andx = 2

A: Region R is bounded by the graphs of y=e2x+1,y=0,x=0, and x=2

Q: Graph the following function: y = -2 sin 2x - 37) 2 T 2

A:

Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

A:

Q: 7. Determine critical points for each of the following functions. b. f(x) = x(4- x)³

A: To determine the critical points of the following function.

Q: Find the area under the given curve over the indicated interval. X5 y = 6x + 2x+5e; x = 1 to x = 3

A:

Q: Question Suppose K(x) = f(g(h(x))). Given the table of values below, determine k'(0). x f(x) g(x)…

A:

Q: T In the closed interval 0≤x≤3, if h(x) = k·cos -x, for what value of k does the region bounded by…

A: Region bounded by h(x)=k⋅cos⁡(π6x),y=0 on 0≤x≤3

Q: b(x) = √√√x Answer O 21 2√2|x| t(x) = 2x

A:

Q: Using n = 2 equal-width subintervals, approximate the area of the region bounded by the graph of,…

A:

Q: Find the point on the line 3x + 7y+ 6 = 0 which is closest to the point (-4,-3). )

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 4t, where 0 ≤ t ≤ 2.5…

A:

Q: If s(-2) = 1 and s'(x) < −3 on [-2,9],

A: s(−2)=1 and s′(x)&lt;−3 on [−2,9], Using the mean value Theoremf′(c)=f(b)−f(a)b−a

Q: Draw the region whose area is given by the definite integral. (6-2 (6 - 2x)dx

A:

Q: 6 Use efºxc x² dx = 72 to evaluate each definite integral without using the Fundamental Theorem of…

A: Since you have posted a question with multiple sub parts. As per guidelines we are supposed to…

Q: Which of the following expressions represents the volume of the solid generated when the region…

A: Region is bounded by y=x2−5x+9 and y=4+6x−x2Rotating the region about line y=−5Using the washer…

Q: Consider the marginal cost function C'(x) = 0.12x² - 2x + 140. a. Find the additional cost incurred…

A: Consider the marginal cost function .(a) To find the additional cost incurred in dollars when…

Q: 1. Show that y PRACTICE EXERCISES FOR $9.1, 89.5, X is a solution of the differential equation that…

A:

Q: a) Find a potential function for the vector field, i.e., find a function ƒ so that F =Vƒ. b) Use the…

A:

Q: The hull speed (in knotts) of any watercraft is given by V = 1.34-L¹/2 where L is the length of the…

A:

Q: Find ♬ as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. -["sin e de Ꮎ F(x) F(0)…

A:

Q: Consider moving a particle along a path given by r(t) = (e³¹, e¹, e³¹) with 0 ≤ t ≤ 1 subject to a…

A: Given that a particle moving along a path  with  subjected to force

Q: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

A: Find the distance (m) traveled by a particle in the x-y plane with position (x, y) for the time…

Q: Evaluate the line integral e F. dr where F H ScF. dr = (5 sin x, 5 cos y, 5xz) and C is the path…

A:

Q: 3. g(x) x² +5

A:

Q: For Questions 1 and 2, region R is bounded by f(y) = y²- 14 and g (y) = 2y +1. Which of the…

A:

Q: For f(x) = (a) fog 7 x-3 2 =, find the following composite functions and state the domain of each. X…

A:

Q: 1. [xds, where C is the curve y=x², z = 0 from (0, 0, 0) tom (1, 1,0)

A: 1.∫Cxds,where C is the curve y=x2,z=0 from (0,0,0) to (1,1,0)y=x2 from (0,0) to (1,1)Let…

Q: Calculate af ax af af ax af Əy (1, -1) af af af af ax' ay ax (1, -1) ay (1,-1) f(x, y) = 7,000 - 65x…

A:

Q: (ii) Given f(x) = ¹ and the interval [1, 3]. Find the average value of f on the given interval. Find…

A: The given function is

Q: Use the zero, 5+ i, to write P(x) as a product of linear and irreducible quadratic factors.…

A: we need to write P(x) as a product of linear and irreducible quadratic factors

Q: Use Stokes's Theorem to evaluate b F dr. In this case, C is oriented counterclockwise as viewed from…

A:

Q: Question Which of the functions shown below is differentiable at x = -1? Select the correct answer…

A: We have to find a graph that is differentiable at x= -1.First, let's define differentiability at a…

Q: A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees…

A: Given that a patient has an illness that typically lasts about 24 hours. The temperature, T, in…