Use differentials to approximate the change in revenue (in dollars) corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in revenue. Function x-Value x = 60 R = 90x0.65x² dR = AR = X dollars dollars

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: To find the volume of the solid generated by revolving the region bounded by the below equations…

Q: Calculate (ri(t) r₂(t)] and [ri(t) x r₂(t)] first by differentiating the product directly and then…

A: In the three dimensional space, a vector A→ has three components, namely the x-component written as…

Q: - 1 10 1 - 4 01 Select the correct choice below and, if necessary, fill in the answer box to…

A: We want to find product of matrices -7-11-41000

Q: Show that if m and b are fixed (but unspecified) real numbers then the function f(x) = mx + b is…

A: A function f(x) is said to be continuous at a point x=a, in its domain if the following three…

Q: High school swimming state averages are as follows: Freestyle: mean time 72.39 seconds, standard…

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Q: QUESTION 5 a) Show that S5 is a non-Abelian group. b) Give an example of a non-trivial Abelian…

A: (a) To show that S5 is non abelian group.

Q: H.W solve by picard method (up to third approtination) c =X+y² y (0)=0 Find y (0-1)? dx aus/ "Y3…

A: Picard Iteration method :  yn(x)=y0+∫0xf[t,yn−1(t)]dt here we have f[x, y]=x+y2

Q: What is the equation of the graph shown? 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 0 2 -8 -10 -12 -14 -16…

A: We will start with a basic graph and then transform that to the graph given , Correspondingly…

Q: Use the Green's Theorem area formula, shown below, to find the area of the region enclosed by the…

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Q: 1 ²+1 (a) Find the inner product (f. 9) = (b) Verify the Cauchy-Schwarz Inequality. 2. Let f(x)= x…

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Q: Compute ffs FdS for F = where S surface of the olid region bounded on the "side" by the cylinder x²…

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Q: b) A cargo plane is flying west at 600 km/h. A fighter jet on an aircraft carrier 400 km due south…

A: To determine the optimization function and boundary interval.

Q: Calculate 1₁ ₁² ² a feas = e¯² ds for the piece of the cylinder x² + y² = 16 for 0 ≤ z ≤ 7.

A: we have to find the ∬Se-zdS for the piece of the cylinder x2+y2=16 for 0≤z≤7

Q: B. Find the area of the region bounded by the following: 18. common to r = 3 cos 0 and 1=1+cos (

A: We have to find the area of the region bounded by r=cosθ and r=1+cosθ

Q: 4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is…

A: To use the divergence theorem to calculate ∫∫SF⋅dS.

Q: Calculate the consumers' surplus (in dollars) at the indicated unit price p for the demand equation.…

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Q: Plot the polar function r=3+6cos. Then find the area of the inner loop.

A: To find the area of the inner loop of the polar function.

Q: Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the…

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Q: QUESTION 7 Suppose you deposit $10 every week into an account that eams 4% interest compounded…

A: As per our problem, d = $10 r = 0.04 N = 52 (52 weeks in a year) k = 5 years

Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

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Q: Which of the following expressions correctly sets up the line integral r(t) = (²+2t)i + (t²-2t)j for…

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Q: Provide the contrapositive to the statement below, then use a proof by contrapositive to prove that…

A: Solution

Q: Let {ƒn (x)}~_₁ be a sequence of functions. ptwise Explain very clearly the difference between ƒn…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

Q: QUESTION 9 Use the Fundamental Theorem of Line Integrals (FTLI) to evaluate ending at (1,3) O a.…

A: Evaluation of the line integral over the curve

Q: finition with right endpoints to find an expression for the area under the graph of fas ग f(x) = 5x…

A: In this question, the concept of Riemann Sum is applied. Riemann Sum To estimate ∫abfxdx, Riemann…

Q: $(8y + x -x)dx + (y + 7x)dy = C (Type an exact answer, using as needed.)

A:

Q: Find all the values of 0, if 0 is in the interval [0°, 360°) and has the given function values. 1)…

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Q: QUESTION 7 Find the area of the region that lies inside both curves. = 8 + 2 sin , r = 7

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Q: Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of…

A: We have to Verify Green's Theorem and find value of Flux. We know that  Green Theorem is

Q: Consider the following basis functions: (sin(x), log(x), 11. Using Least Squares on given data set…

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Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. 34 49

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Q: A graph of y=f(x) is shown. In the same coordinate system, sketch a graph of the derivative function…

A: Note: If f(x) is decreasing, then the graph of f'(x) will be below the x-axis. If f(x) is…

Q: Find the amount of money (Future Value) in an account where $1,300 is deposited (Present Value) at…

A: To find the future value of the investment.

Q: Alice received the following ciphertext from Bob, "08 01 08 05". Bob had encrypted it using the RSA…

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Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: Let H = {β ∈ S5 : β(4) = 4}. Prove that H is a subgroup of S5. (Reminder: The group operation of S5…

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Q: 3. Find all Critical points of the given plane autonomous system. 3.1 2 x² = x (1-x²-3y²) y₁ = y (3…

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Q: Alex's Evil Twin wishes to steal 18 piece of candy from the 5 kids in his neighborhood. However,…

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Q: Find a coterminal angle between 0° and 360° or between 0 and 2π radians. 3) -555°

A: Coterminal angles : To find the coterminal angles we may add or subtract 360° of the terminal angles…

Q: Omar has decided to finance a $25,000 car at 8% interest compounded monthly for 10 years.  Determine…

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Q: 6. 2y" y' = 0. Sketch the phase portrait (including equilibria, orientations/directions of arrows),…

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Q: fr (3x - y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² Evaluate…

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Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: 0 N R Consider the graph given above. Give an Euler circuit through the graph by listing the…

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Q: The table contains data on the admission price (in dollars) for one-day tickets to 10 theme parks in…

A: First obtain the five number summary then use the formula for interquartile range (IQR), i.e.,…

Q: For f(x)=12x¹-44x² −8x³ + 2x² −6x² +72x² −24x+8, compute f(2), roots of f(x) and plot for 0≤x≤ 30

A: The function given is as follows: fx=12x10-44x9-8x8+2x7-6x3+72x2-24x+8 We are asked to find the…

Q: B. Find the area of the region bounded by the following: r = 8 sin in ²0 16.

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Q: Ellen is looking to purchase a car.  She determines that she can afford a monthly payment of $325.…

A: To determine the cost of car that Marie can afford.

Q: QUESTION 15 a) How many elements of order 2 are there in S5? b) How many elements of order 2 are…

A: