= a tank contain 100 gallons of the pure water, a Brine solution w/ 41b/gall OF salt enters at 4 gal I min and leaves at 3 gall m Find the time at w/c the brine leaving will contain 60lb/gal of salt. .

Q: A solid is contructed so that one side is the region between the lines x = a, x = b, the graph of y…

A: The given data is:   y=fxx=ax=b

Q: 2 Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and x = 3,…

A: we have to find the volume abouts y-axis

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 25 - x². What…

A:

Q: T 2 2. S 8xdx 4 2 0x -8x +32

A:

Q: At which points on the curve y = 1 + 40x³ - 3x5 does the tangent line have the largest slope? (x, y)…

A: we need to find out the points on the given curve where the tangent line has largest slope.

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=x² + xy + 2x + 5y…

A: Given function:- fx,y=x2+xy+2x+5y-3

Q: 2 Functions f and g are defined by f(x)=2(3+1)₁³ ,x+0 and 1 g(x)==-=-3₁ X≠3 respectively. (a) Find f…

A: The given functions are:f(x)=23+1x ;    x≠0       and        g(x)=1x-3 ;     x≠3

Q: [4-R] [CLO 15] Let f : R → Rx ↦ x2. That is,  is defined by the formula f (x) =x2. Give a formula…

A: The given function is: fx=x2

Q: 3 Find the values of constants a, b, and c so that the graph of y = ax³ + bx² + cx has a local…

A: The equation of curve is:y=ax3+bx2+cx   Local maximum and local minimum of the curve y=f(x) are the…

Q: Assume that w=fl Əw Ət Əw əs 11 aw at =f(s³ +1²) and f'(x) = ex. Find and ?w ds

A:

Q: 3, 3, 1 > and b Let a = . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A:

Q: 4 16 16-y -!!!- Here is the region of integration of the integral a. dy dz dx b. dy dx dz c. dx dy…

A:

Q: Consider the curve r(t) = (6 cos(t), 6 sin(t), e), 0 ≤ t ≤ π. Find r'(t). r'(t) = Consider the plane…

A: Given curve:- rt=6cost,6sint,et

Q: [1-R] [CLO 12] What is the slope of the line f⊥, where f⊥ is a line perpendicular to the line f,…

A: The given line is: 4y-3x=5

Q: The weight of a fish varies jointly as its girth and the square of its length. One fish weighed in…

A:

Q: Find the average value of F(x,y,z)=x² + y² + z² over the rectangular solid in the first octant…

A:

Q: a) Suppose that lim n-00 ∞ The series Enan n=1 an+1 an 1 == 2 converges ✓ by the ratio test <

A:

Q: Find the derivative of the function. In(e²x + 3) y =

A: y=lne2x+3d dx(lnx)=1xd dx(ex)=ex

Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

A:

Q: 6. Use the Mean Value Theorem to find all values of c in (6, 14) such that f(b)-f(a) f'(c) = for…

A:

Q: We can represent planes using either vector equations or scalar equations. Which form do you think…

A: We have to answer which form of plane is better Either vector or scalar

Q: Determine if Rolle's Theorem can be ap plied to r²+3r-18 x+9 f(x) = on the interval [-6, 3), and if…

A:

Q: Given c = - 2 + 10j and u = -107 + 3j, find |e+u and le| + |ú. Give EXACT answers. You do NOT have…

A: I have solved step by step in detail....go through the solution

Q: Use calculus to find the area A of the triangle with the given vertices. (0,0) , (4,3) , (1,8)

A:

Q: The safe load, Z, of a wooden beam supported at both ends varies jointly as the width, w, and the…

A: Terminology Load = L width = w length = l depth = d

Q: Learning Target INTI: I can correctly antidifferentiate basic functions and identify…

A: To find the general antiderivative of the given functions . The general antiderivative, also known…

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

A:

Q: Using the equation y= x^3/ x^2 - 4 Determination of equations of horizontal asymptotes (if they…

A:

Q: Given the graph of y = f(x) below, at which of the marked x-values can the following statements be…

A: Given: Graph of y = fx To find: The value of x for which the given statements are true.

Q: fx cos(3x) dx

A: M=∫xcos(3x)dx∫cosxdx=sinx+c∫sinxdx=-cosx+c∫(a.b)dx=a∫bdx-∫(dadx.∫bdx)dx

Q: (a) Find the derivative of r(t) = (4 + t)i + tej + sin(5t) k. (b) Find the unit tangent vector at…

A:

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? *x+9² [1,…

A:

Q: Assume that x=​x(t) and y​=y(t). Find dx/dt, using the following information. x^2+y^2=0.73: dy/dx=-2…

A: x2+y2=0.73given dydt=-2x=-0.3y=0.8d dx(xn)=nxn-1

Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: Find the distance from the point (-6,3,1) to the plane: x-2y-4z = 8.

A:

Q: Find ax dy II of of ax dy f(x,y)=√√x² + 4y² || and (Type an exact answer, using radicals as needed.)…

A: f(x,y)=x2+4y2∂ ∂x(x)=12x∂ ∂x(xn)=nxn-1

Q: Find the mass of the solid bounded by the planes x+z=1, x-z = -1, y = 0, and the surface y=√z. The…

A:

Q: Evaluate the limit tan 7x lim x 0 sin 4x

A:

Q: Solve the given differential equation. 3ydx - 3xdy + xdx = 2dx

A: 3ydx-3xdy+x9dx=2dxwe know ∫xndx=xn+1n+1+cd dx(yx)=xdy-ydxx2

Q: Answer the following True or False. If f(x) is a positive 1-1 function, then 2πT cb a xf(x)dx = 2π…

A:

Q: Ĉ the given curve is rotated around the y-axis Find the area of the resulting surface y = I 9 2 "² I…

A: The given curve is:y=14x2-12ln x ;           4≤x≤5

Q: The perimeter of a rhombus is 68 inches and one of its diagonals measures 30 inches. Find the area…

A: Topic = Geometry

Q: [2-R] [CLO 13] On the Cartesian plane, sketch the solutions to 2x + 4y ≥ 8.

A:

Q: Consider the following vector function. Find each of the following. r'(t) = = r'(0) r(t) = cos(t) i…

A:

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

A: The given region is: D= x,y | 0≤y≤sinπxL, 0≤x≤L  ρ(x,y)=13y

Q: Q17 Given P(q) = -2q² + 30q-25 (a) Find the profit from selling the 2nd unit. (b) Use marginal…

A: Given:- Pq=-2q2+30q-25

Q: The position of an object with respect to time is given by the following function: d(t) = t³ + 2t² -…

A: Derivative

Q: Obtain the general solution of the following differential equations. 8. (ysin x+xy cos x) dx +…

A:

Q: You are designing a 1152 cm³ right circular cylindrical can whose manufacture will take waste into…

A: We use the differentiation method to find the required ratio