3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at the rate of 4 liters per minute and the solution well mixed is pumped out at the same rate. Find the amount of salt in the tank after 5 minutes? O 41.86 g 46.18 g 61.84 g 68.41 g

Q: Describe the graph of the equation. r = 7 sin 8t i – 7 cos 8t j It is a circle of radius 7 in the…

A: Explanation of the answer is as follows

Q: 1. S sin x cos 3x dx.

A:

Q: #3 Evaluate F. dr. F(x, y) = 3xi + 8yj C: r(t) = ti + V4 - t²j, -2 st< 2

A: Given problem:-

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: Use the formula r(t) - – P) x r"(0)|| to find giớ). ||P() × to find x(t). r(t) = e!l"i + e tj 156…

A: Given problem:- Find k(t) of r(t) =e12t i +e-t j

Q: y" - 2у/ + у 3 tet + 4, y(0) — 1, у (0) — 1 || %3D

A:

Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: 1) Find and of the following equation then simplify whenever possible. dx dx² x = 2u* – u³ + u – 11…

A:

Q: 21. Solve the equation y' = (x²+ 7) / 9 (2x / 9) + c b. y = (x / 18) + c 22. Solve the equation y' =…

A:

Q: I. Evaluate the following Definite Integral. 1.) L,9 6x3+4x2-8x dx 2.) x²(2x³ + 1) dx 2x 3.) sž…

A: Integration

Q: (d) r'(t) x r"(t)

A:

Q: Q-What is the volume of the solid obtained by rotating the region bounded by the graphs of y = vx, y…

A: Volume of solid of revolution

Q: (x – y²)dx + 2xydy = 0

A: We have to find integrating factor of given differential equation.

Q: In series RL circuit, L=4 henry, R=100 ohms and E =200 volts, find the value of current when t =2…

A: Given ; L= 4 henry , R=100 ohms and E=200 volts , t= 2 sec

Q: Find V (V x F), if F(z, y, =) = 3e""i+7ze'j – 3e"k. V. (V x F) =

A:

Q: e2y dy Solve using algebraic substitution Tey-i

A:

Q: Use the formula «(t) ||r'(t) × r"(t)|| to find «(t). r(t) = e12i + e-j K(t) = %3D

A:

Q: Find curl (5z i+ 6x j+ 8y k). curl (5z i+ 6x j+ 8y k) = ( )i + (i Oj + ( i Ok

A: Given that,    curl5z i+6x j+8y k

Q: Find div F and curl F if F(x, y, z) = 13y°z³i – 9x*z³j – 4ry°k. div F= curl F=

A:

Q: The temperature T in a metal ball is inversely proportional to the distance from the center of the…

A:

Q: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

Q: Repeated Imaginary Roots of Auxiliary Equations Solve the equations: 4) (D3 + 36D)²y = 0 5) (D3 +…

A: The given differential equation,4. D3+36D2y=05. D3+1002y=0

Q: Find div F and curl F if F(x, y, z) = 14y°z°i – 10x°z°j – 5xy°k. 35: 6.8 - div F= curl F=

A: We have to find div F and curl F.

Q: Using appropriate substitution 1 dx V9x² – 36x + 37 Is equal to

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 6…

A:

Q: 6. lim (sinx)* X0+

A:

Q: d 10.(4* tan x) dx

A: Find the derivative

Q: Evaluate xe-X dx, if it exists. O 1) 1/2 2) 1 3) 1-e 4) It does not exist.

A: We have to evaluate given integral

Q: Find div F and curl F if F (x, y, z) = 10e*V i – cos yj+ 3 sin zk. %3D div F= curl F=

A: div F=∂Fx∂x+∂Fy∂y+∂Fz∂z∂Fx∂x =ddx(10exy)=10y exy∂Fy∂y =ddy(-cos y)=sin y∂Fz∂z=ddz(3 sin2z)=3(2sinz…

Q: 3. Evaluate the integral 7/4 1 + cos²0 do cos²0

A:

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

A:

Q: Of the Sollds gene by Volving the regions Doundeu by graphs of equation given iines. y = 3x2 y = 0 X…

A:

Q: 5. Find the integral | 2(x* - x°) (x5 – 1)®dx x In(x + 2) dx а. d. | In x? dx | 2xe** dx b. е. 1 2x…

A:

Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos (0) sin(0) de

A: Given query is to find integral of the expression.

Q: Using appropriate substitution 3. tan’x dx sec5x is equal to -cos°x + cos"x + C tan*x + 6 sec°x + C…

A:

Q: Find curl (5z i + 6x j + 8y k). curl (5z i+ 6x j + 8y k) )i + ( i )j + ( i i )k

A:

Q: Differentiate the following functions: 1) f (x) = 5 2) f (x) = -2x 3) ƒ (x) = -2x + 2 -2r +2 %D

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use Green's Theorem to evaluate the line integral. | y? dx + xy dy C: boundary of the region lying…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: Given: x=4y, x=-4y, y=1   From the given curves the bounded region is as shown below;

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A:

Q: lim,0+ ((sinx)tan

A:

Q: 'ind V · (V × F) if F(x, y, z) = 9 sin ci + 5 cos(9x – 10y)j + 2zk. - V · (V × F) =

A: To find div (curl F).

Q: 2. Determine the area of the region bounded by the curve y = x³ – x² – 2x, and а. the x-axis b. the…

A: This is a problem related to area calculation using integration. Please find the procedure given…

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A:

Q: Solve the equUations: 1) (D² + 9)²y = 0 2) (D2 + 49)²y = 0 3) (D2 + 36)²y = 0

A: As per our guideline we are supposed to be answer only first three parts of question you can repost…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

A:

Q: Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.

A:

Q: Need

A: