A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is pumped out at a rate of 6 gals/min. Find the number A(t) of pounds of salt in the tank at time t. A(t) = lb How long (in minutes) will it take for the tank to be empty after this process has started? min

Q: Explain why the integral is improper. 49 1 1²0 √/x dx 1.6 1.4 1.2- 1 0.8 0.6 0.4- 0.2 10 20 30 X O…

A: An integral will be improper if at least one of its limit is infinite or function of integral is not…

Q: Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt…

A: Since there is no image for flow in the tanks, i use only the given equation with initial values.

Q: (b) Find the differentiation of tan 4√√x 1-4x

A:

Q: 03 // A)) Find the volume of solid below? =Y+X x² + 3² AC D4

A: Given solid is

Q: 12 or younger 13 or older Total Signed waiver 10 8 18 Did not sign waiver 20 12 32 Total 30 20 50

A: Let A and B are two events, then;  P(A∪B)=P(A)+P(B)-P(A∩B)

Q: 1. Let S be a nonempty set. (a) Give the definition for: "a is not an upper bound of S." (b) Give…

A: As per our guidelines only first three subquestions are solved. For remaining question kindly…

Q: Use transformations to sketch the function y=-3log10 (x-1) + 2 y = -310g 10 (x - 1) + 2 Parent…

A:

Q: Find a general solution of the linear system below. x"=-8x + 2y, y"=2x-5y Solve for x(t). Choose the…

A: Given system is x''=-8x+2y,   y''=2x-5y   To Find: x(t) and then y(t) so that x(t) and y(t) are a…

Q: Consider the differential equation dy (yt)¹/5 (y>0, t≥ 0) = dt (a) State the form of the…

A:

Q: 1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T<x< T.

A: f(x) is periodic with period 2π  f(x) is continuous except at the end poits (where f is not defined)…

Q: 8. What rule should be used in deriving f(x) = x³? A. Constant rule B. Sum rule 9. Find dy/dx y=e³x…

A:

Q: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

A: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

Q: (1) Construct an example for three distinguish points A, B and C in a 3- space for validating the…

A: For every three-dimensional vector a→=ai^+bj^+ck^, the corresponding point has the coordinate a,b,c.…

Q: -labelled diagram and calculate the Fill in the blanks below after you ha

A: Given the air speed of the plane is 655 km/h at a bearing of 15°.  The wind speed is 45 km/h at a…

Q: s ago, he has not finished his thesis yet. nce between the brackets, correct? If

A: To explain the true or false as,

Q: 7: 1 The norm of the matrix A = [is is equal 4. 1 3. O True O False

A:

Q: Evaluate the z transform Evaluate the z transform of x(n) = a^(-n) u(n). of x(n) = c^n u(n).

A:

Q: -1 -4 -3 4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁ and…

A: We have to find the distance of the vector y from the subspace spanned by the vectors v1 and v2…

Q: 1- "Dermatology". Add the proper suffix to recognize the more involving person in this field. 2-…

A: As per the company rule, we are supposed to solve the first three sub-parts of a problem. Therefore…

Q: Let u(x,y,t)=(1/t)exp[-(x²+y²)/4t] where exp denotes e to a function. Show that u(x,y,t) satisfies…

A:

Q: 8. Which line does not lie on the plane r = (1,5,0) + s(2,-3,1)+t(1,−1,4), s,t € R? a. V = (1,5,0) +…

A: To Find: Which of the given lines does not lie on the plane r = (1,5,0)+s(2,-3,1)+t(1,-1,4) where…

Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: Q2 Solve the ODE y' = 3 x³ – 4y Using Runge- - Kutta 2nd order Method for xo= 0, yo=1, Xn=2 x₂=2 ,…

A: We have to use the second order Runge Kutta method to find the value of y at x=2. It is given that…

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x&gt;0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A:

Q: PAPER 1 N2010 5 Solve the equation 3x³ +7x²-22x-8 = 0. 5. FACTORS OF POLYNOMIALS

A:

Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

A:

Q: Q3/Solve the non-homogenous equation 3x³ + 1 = cos(2x-1)

A:

Q: Hand written plz In each of Problem, find a fundamental matrix for the system with the given…

A: The solution of the system of differential equations X'=AX is the fundamental matrix.

Q: 4. At x = 4, the function f(x) = (x², x ≤ 4 (4x, x>4 A. continuous but not differentiable B.…

A:

Q: 2 The function f(x) = ax³ + 4x² + bx-2, where a and b are constants, is such that 2x - 1 is a…

A:

Q: 7: The point X = [0 0] for the function f(x) = 2x1 + x2 + 2 represents a A: Saddle Point for f(X) C:…

A:

Q: 8. Let f(x) = √25 - x² and g(x) = sinx. a) Graph f(x) and describe its shape. Is this function even,…

A: Given functions are f(x)=25-x2, g(x)=sin(x) Solution a: Since f(x)=25-x2 and f(-x)=25-(-x)2=25-x2 So…

Q: Max (Z) = 3 X + 5Y Constraints: 2X +3Y≤ 30 5X +4Y≤60 By Condition X, Y20

A: Given LPP is max z=3x+5ysubject to2x+3y≤305x+4y≤60x,y≥0   So, graph of  function

Q: Express the polynomial f(x) = 2x² + 3x³x²+x-2 in the form f(x)=b₁(x - 5)¹. i=0

A:

Q: QUESTION 9 A group of 12 students have to decide among three types of pizza: sausage (S), mushroom…

A: We need to compare them pairwise and if one beats all other options in pairwise comparison then by…

Q: -1 The point A has coordinates (4, 1), AB = 9 5 BC= . Find the coordinates of B and -4 the column…

A: Let B=a,b Now,  A=4,1AB→=-19 So,  AB→=-1 , 9⇒B-A=-1 , 9⇒a,b-4,1=-1 , 9⇒a-4,b-1=-1 , 9⇒a-4=-1…

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

A:

Q: 1 2 If R = 3 1 that R² = 2R + cS. and S= 1 1 0 0 1 find a number c such

A: Solving matrices question by finding square of R matrix

Q: ne blanks and b = -2x+9y, write

A: Given: a⇀=3x⇀-5y⇀ and b⇀=-2x⇀+9y⇀ We should write the given vector5a⇀-8b⇀in terms of x⇀ and y⇀

Q: (30) Prove the following inequalities: log x 1 (a) Vr € R \{1}, X - 1 - √x (b) Vn € N, e- e − ( 1 +…

A: Given,a) log xx-1&lt;1x , ∀x∈R*+\ 1b) e-1+1nn≤ e2n+1 , ∀n∈NWe will use Mathematical Induction…

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional the amount present at time t…

A:

Q: 9 * Q3 B: Determine the - distance (S) to which the 90 kg painter can climb without causing the 4 m…

A:

Q: 2. Solve 2x² x² d² - 2 dx 2 X dy dx - (x + 1)y = 0, by the method of power series.

A: Since you have posted a multiple question according to guildlines I will solve first(Q2)   question…

Q: Which type of speech parts, the below words belong to? Show the part of speech with more details,…

A:

Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 22. Represent the graph of the following functions using a sine and cosine function. 323 124 10 8 m…

A: The general form of the function is f(x) = Asinkx+M or f(x) = Acoskx-π2+M Where M is the midline, A…

Q: Let f be differentiable on the interval (a, b) and f'(x) < 4 for all x € (a, b). Then prove that f…

A:

Q: 6 + 7 dx 1.6 1.4 1.2 Y 0.8 0.6 0.4 0.2 10 20 30 40 X At least one of the limits of integration is…

A:

Q: A waiting-line system that meets the assumptions of M/M/1 has A-1,-4. For this system, what is the…

A: