How much money must be invested now at 10% interest compounded continuously so that $120, 000 will be available in 5 years? Round to the nearest cent.

Q: Find the minimum value of f (x,y,z) = 2x² + y² + 3z² subject to the constraint 2x - 3y - 4z = 49

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Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

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Q: What two nonnegative real numbers with a sum of 66 have the largest possible product? The numbers…

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Q: Of all rectangles with a perimeter of 10, which one has the maximum area? (Give the dimensions.)

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Q: St-1.0t vemos anoitasu) InemzeozeA B C E M N K JH G Identify each of the following in the figure…

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Q: B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a 0, then f has a…

A: Topic:- calculus

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

A: We have to convert the given equation.

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: This question can be solved using the concept of tangent and normal under application of…

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Problem 2. Do both parts. 8 Part (a) Find the sum: 12 4 + +· 3 9 27 81 Part (b) Solve the equation…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t2…

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Q: x² + 4xy + y² = 13, (2, 1)

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Q: ·SS v₂ Vx (2yi) •n do where S is the hemisphere x² + y² + z² = 9, z≥ 0. Use the normal vectors…

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Q: Let z = g (x, y) = x³ + xy³ + y4 - 6x - 2y + 4, where x = r cos (0) and y дz Use the chain rule to…

A: We will use chain rule to find the derivative

Q: Find and classify the critical points of f(z) = 82°(8 - z)7 as local maxima and minima. %3D Critical…

A: Critical points are the points of a function where the derivative does not exist. local maxima: the…

Q: Weather condition Sunny Cloudy Rainy Snowy Percentage of days 42% 31% 18% 9% A) 1240 B) 3300 C) 2100…

A: Number of days in 2008 = 366 ( leap year ) Number of sunny days  =42%*366=0.42*366 Number of people…

Q: Use the formula к(t): k(t) ||r' (t) x r"(t)|| 3 ||r' (t)||³ r(t) = esti + e¯tj = to find (t). #1

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Q: For the function, find the relative maxima, relative minima, and horizontal points of inflection.…

A: The given function,  y=13x3+x2-8x+15

Q: The minimum hourly wage in a particular country has grown over the years, as shown in the table. a)…

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Q: Solve the integral below using integration by part. [(2x - 3) 3) e* dx

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Q: Find all solutions in [0, 2π): 2 sin (x) - sin (2x) = 0: 4.8 00, π R/+ 4

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Q: Find the differential dy of the function y = Provide your answer below: dy = dx 5x4 + 4 4x + 3

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Q: gra Ốf j at point (b) Find the directional derivative of f at the point (0,–2) in the direction of…

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Q: Find the number of distinguishable permutations of the letters in each word below. (a) tilted (b)…

A: This is a problem related to permutation and combination. Based on the general formula we will…

Q: Use the simplex method to maximize the following: Maximize f=6x1+4x2+10x3f=6x1+4x2+10x3 subject to…

A: We need to use simplex method.

Q: Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the…

A: According to the guidelines, we are instructed to answer 1 question or 3 sub question,the others can…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. So f(x) dx…

A: Let's find.

Q: For what values of x does the series converge conditionally? Σ (-1)^(4x+7)" n=0 OA. x = -2 3 OB. X=…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: PART I: Write an expression that is complex enough to be differentiated using the: Product Rule…

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Q: The graph of a function f is given. Use the graph to estimate the following. y 5 (a) All the local…

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Q: ∞ -1. Σ(-1)" n=1 n! 2"

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Q: Let f(x) = x². a) Find the tangent line to the graph of the function at x = 9. y = b) Find the…

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Q: Write down the matrix A that represents the linear transformation ƒ : R² - (a) R² (i.e. so that f(x)…

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Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

Q: Solve the triangle with the given information. a= 8.3, c= 2.8, p= 19.4° b 5.7 (Type an integer or a…

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Q: Hamzah who is 5 feet tall is walking away from a lamp post at the rate of 30 feet per minute. When…

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Q: Figure (a) shows a vacant lot with an 80 ft frontage in a development. To estimate its area, we…

A: It is midpoint Riemann sum      here length of interval  △x=20

Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: TC=575+2Q

A: ANSWER Is in next step

Q: Determine if the following series converges. If the series converges, determine if it converges…

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Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: Determine the maximum value of f(x)=-x²+2x²+2 on -2 ≤x≤ 3. a) 3.185 b) -7 Od 2 d) 18 2

A: To find the maximum value of the function.

Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

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Q: i-2yj + (z+3)k and suppose the outward flux of F through Side A is 1 and through Side B is -3. Can…

A: answer is in next step

Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given

Q: Use the method Laplace transform to solve the following. (a) 2r' + 7r=3e-t, x(0) = 4. (b) 2r' +…

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Q: ³√xy = 2x²y-8x

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