b) Let at time t years, an industry consumes fuel at the rate of (2t + 9) million barrels per year. If the total supply of fuel available to the industry now and in the future is 63 million barrels, how many years will the supply last?

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A: We have given differential equation, y'' - 9y' + 18y = 0 Here , f(D) y = 0  where , D = ddx Thus, D2...

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A: We have to find either the given series is convergent or divergent 

Q: QUESTION 4 2 =16 3*+1 = 34 4.1 4.2

A: We, know that  ax=ay⇒axay=1⇒ax-y=a0⇒x-y=0⇒x=y

Q: Problem 3. First verify that y(x) satisfies the given differential equation. Then determine a value ...

A: The solution of the equation is defined as the function that satisfies the differential equation. In...

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A: Given A = 83-2953  and u→ = -3-21  ,  v→ = abc

Q: t-3 The domain of the function f(t) = is (-v2, v2) and [3,0] %3D t2-2

A:

Q: EX show that 2. J능 (x)

A:

Q: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even.

A: Given: Show that if n is a positive integer, then n is even if and only if 7n + 4 is even  

Q: 2. g(x) = 2-v4+3E Values of x from g(x) Values of x from g(x) the right of -1 the left of-1 0.5 -0.5...

A: Given: g(x)=2-4+3xx To evaluate: The given function at indicated points and then find left and righ...

Q: d. Find the multiplicative inverse of 5. e. Explain why division is not well-defined in Z, .

A: We will apply multiplication modulo 12 to find multiplicative inverse of 5.

Q: J why boyther to define the Lebesgue do we integrad, wasn't the Riemann integrd good enough? Explain

A:

Q: Write each of 40–42 as a single summation. т+1 + k+1 k 40. i + (k+1)³ 41. т+2 i=l k=1

A:

Q: The difference between divergence and curl is represent vector field O true O False

A: True

Q: A = -3 4 3 0 -1 1 -3 3 1 4 -3 9 1 3 -1 3

A:

Q: Express the complex number 2 + 2√3 i in polar (trigonometric) form.

A:

Q: Solve the initial value problem by using Laplace transform, y" – 3y' + 2y = 4t-8 y(0) = 2, y'(0) = 7

A: Given initial value problem is: y''-3y'+2y=4t-8,  with y0=2, y'0=7. In Laplace transform method firs...

Q: f the integra n (x –1)

A:

Q: Q1/ Find all the second-order partial derivatives of the functions 1. g(x, y) = xy + cos y + y sin x

A: To find- Find all the second-order partial derivatives of the functions gx, y = x2y + cos y + y sin ...

Q: OLet Faffasb)tairbeR} and + defined on AF as fellows! (asb) +ceod) = (atc,b+d) (arb).ccod)= (ac, bd)...

A:

Q: Con sider X={,2, --., 106? togcther with the largest 8-algebra p(X). capower set of x). Define 1 if ...

A:

Q: For the ODE 4y'' +100y=sin(wt), determine the value of w where this will experience resonance. For t...

A:

Q: 1.88 † If An is a countable set for each n E N, show that A = U An, n=1 is again a countable set. (H...

A:

Q: tet r and m be integer, prove that 17/20+3m iff, 17/9n

A: Solution 

Q: Cost to Rent a Local Moving Truck (in U.S. Dollars) 140 120 100 81 80 72 63 60 54 40 20 10 20 80 40 ...

A: Apparently if we extend the line , we can reach  100miles when the cost is around 135 us dollars.

Q: 1. Without directly using the calculator, compute the zero- through fourth-order approximation of v7...

A:

Q: As part of his summer job at a restaurant, Bren learned to cook up a big pot of soup late at night, ...

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Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: . 

Q: 2. Given the data 0.2 0.4 0.6 f(x) 1.9934 2.1465 2.2129 2.1790 0.8 1.0 1.2 1.4 f(x) 2.0683 1.9448 1....

A: We can solve this by using given data and formula of Central difference

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A:

Q: 5. (a) Ifp is a prime then the group U, has (d) elements of order d for each d dividing p- 1. (b) If...

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Q: Why use the hypothesis of n=m-1 with a step-by-step explanation of the solution and a clear line, pl...

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Q: A market survey was conducted in four cities in Zambia in order to find out the preference for brand...

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Q: lockwise SE

A:

Q: Find the solution of y" – y – 6y = 48 et with y(0) = 7 and y' (0) = 3.

A:

Q: Consider the following recursively defined sequence: 5 an+1 = 2' 1 - (а, + 2), п € N. aj = 1 Prove t...

A: Given sequence is  a1=52,an+1=12(an+2),n∈N To prove  an>12n ∀n∈N

Q: Q of y = e(cosx+4tanx+5t-tx²) dp

A: We have to find derivative of y with respect p.

Q: 6. (a) Write the following in reduced row echelon form.. Determine (b) a basis for and (c) the dimen...

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Q: The most frequently occurring statistic * .measurement is the arithmetic mean True False O O

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Q: Write an inequlity comparing with +4 for n > 1. (Express numbers in exact form. Use symbolic notatio...

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Q: Compute the dissimilarity matrix for the following objects name sex colour character Bella F red tam...

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Q: n of the initi (0) = 2 is

A:

Q: 7. Give an example of (i) a non-planar graph that is not homeomorphic to K5or K3,3 .

A:

Q: Find the differential equation of the given general solution by eliminating the arbitrary constant. ...

A: Given: The differential equation, xsiny+x2y=c   To find: The differential equation of the given gene...

Q: la) show that the necessary & sufficient condition VE constant to be constant gcodesic on EE, +FE, -...

A: Geodesic Curve: Let A and B be two given points on a surfaces. Let these points be joined by curves ...

Q: Disprove the following statements using counterexample. Explain your answers. 4. x >x 5. x Sx?

A:

Q: 5. prove that S"erf cx) dx =0

A:

Q: xy cos.x f(x, y) =+3y²

A:

Q: 3. Consider the vector field shown below. (a) Is ſe F · di positive, negative, or zero? (b) From you...

A:

Q: Solve the initial value problem. y" – 2y' + 2y = e; y(0) = 0, y' (0) = 4

A: Given differential equation is y'' -2y'+2y =e-t;  y0=0, y'0=4 Take "t" as independent variable.

Q: following differential equation: y" + 4y + 4y = e* cos I

A: Introduction: The higher order linear differential equation can be generalized as andnydxn+an-1dn-1y...