Find the minimum distance from the point to the sun (-2,-2, 0) 2y. (Hint: to simply the computations, of the distance.,

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: Given: R(x)=55x-0.5x2C(x)=6x+20 We are required to find: Rate of change of:a. Total revenueb. Total…

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: y = (2y^4 + 2x)y' How can I solve it?

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Q: 12:33 r = 7 hing fins Tine X Slope of tangent z

A: Slope of tangent line is find by differentiate the function.

Q: Find the absolute minimum and absolute maximum values of f on the given interval. (Enter your…

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Q: A spherical balloon’s radius is denoted by r, and the volume is V. (a) What is the rate of change of…

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Q: ← For a certain product, cost C and revenue R are given as follows, where x is the number of units…

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Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

A: This is an optimization problem l. We will solve this using differentiation.

Q: An ice cube that is 7 cm on each side is melting at a rate of 5 cm per minute. How fast is the…

A: Let the side of the cube is (x) Given an ice cube (x) = 7cm and dv/dt = -5cm3/minute

Q: The graph of a 5th degree polynomial is shown below. Use it to answer the questions. y, -1 Al N (a)…

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Q: ) Find an equation of the tangent plane to the surface at the given point. x² + y² + z² = 26, (1, 3,…

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Q: 17. If f is periodic, then f' is periodic.

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Q: B. Given the system of equations - 1.1x₁ + 10x₂ - 120 -2x₁ + 17.4x₂ = 174 (a) Solve graphically and…

A: Given system of equation-1.1x1+10x2=120-2x1+17.4x2=174we have to solve to system of equation by…

Q: (a) Consider a rectangle of length L inches and width W inches. Find a formula for the perimeter of…

A: Consider a rectangle of length L inches and width W inches Find a formula for the perimeter of the…

Q: ↓ 2 The graph of 5 (x² + y²)² = 169 (x² - y²), shown in the figure, is a lemniscate of Bernoulli.…

A: The given curve is:

Q: Find the directional derivative of f at the point P in the direction of a. a=i-j f(x, y) = 3x³ -…

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Q: Find the absolute maximum and minimum y-values of f(x) = 6x on the interval [-6, 3], as well as the…

A: Application of derivatives.

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Use P(x) = x+++x³ to answer the questions. (a) Find the x- and y-intercepts. (If an answer does not…

A: Functions

Q: The length of time (in years) until a copier feed mechanism needs to be replaced has probability…

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Q: The integral in this exercise converges. Evaluate the integral without using a table. 8 s dx 2 2 x…

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Q: (2) Show that f(x) = e³x cos(2x) is of exponential order.

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Q: 4. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Find the Maclaurin series for the function f(x) = x 3* and choose the correct answer from the…

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Q: If In(a) = 2, ln(b) = 3, and ln(c) = 5, evaluate the follow a² 6³c² (a) In (b) In √b²c5a3 (c) In…

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Q: √ √ √³x - Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0,8] × [0, 2] 3x + 4ydA…

A: We have to use the mid point rule to find the value of integral.

Q: f(x)=21x^4+Ax^3+Bx^2+Cx-9. how would you list potential zeros? (A,B,C are integers)

A: We have to find the potential zeroes of given equation.

Q: Evaluate the function at the given values of the independent variables. z = x³ + 9xy + y²; x = -2, y…

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Q: 31, 32, 33, 34, 35, and 36 Use a linear approximation (or differentials) to estimate the given…

A: The formula for approximating is,

Q: Given that the directional derivative of f at the point (8, –1,7) in the direction of a = 8i - 4jk…

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Q: Decide the following integration formula is correct. O yes O no S x² dx = x5 + c

A: Check Integral is correct

Q: Find Vz. 7xe³y x + 3y NOTE: Give your answer in unit vector notation; that is, in terms of i and j.…

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Q: A hemispherical bowl of radius 11 cm contains water to a depth of h cm as shown below. (a) Find the…

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Q: y₁ y=9x ∞013 8 y = X =3x y=52-x X

A: To find the area of the shaded region in the following figure.

Q: The concentration C(t) of a salt solution is given by the formula to the right, where t is measured…

A: C(t)=20tt2+1

Q: 10. Find the n th root of 1 - i√3; n = 3. Express your answer in rectangular form

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Q: Find the volume of the region under the surface z corners (0, 0, 0), (5, 0, 0) and (5, 5, 0). 8 1+x²…

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Q: 15. If f is increasing and f(x) > 0 on I, then g(x) = 1/f(x) is decreasing on I.

A: If f is increasing and f (x) > 0 on I,  then g(x) = 1/f(x) is decreasing on I.

Q: Sand falls from a hopper at a rate of 0.3 cubic meters per hour and forms a conical pile beneath.…

A: dVdt=0.3 m3/hrr=h2  Where r is the radius of the cone and h is the height of the cone

Q: Find the indicated derivatives. (a) g(x) = mtan(x) g'(x) = (b) h(t) = sin(10t + p).

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Q: QUESTION 6 Determine if the given function y = f(x) is a solution of the accompanying differential…

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Q: K dy Assume x and y are functions of t. Evaluate for 2xy - 4x+6y³ = -42, with the conditions dt dx…

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Q: Use the values in the table below to answer each of the following: f(x) g(x) f'(x) g'(x) 5 1 -1 -3…

A: Table

Q: Calculate dy xy + x = 12; O A. 3 O B. 9 O C. -3 OD. -9 using the given information. dx dt =-3, x=2,…

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Q: Find the directional derivative of f at P in the direction of a. f(x, y, z) = xy + z²; P(-1,-1,-3);…

A: The directional derivative of the function f in the direction of u at a point px,y is:…

Q: The circulation time of a mammal (the average time it takes for all the blood in the body to…

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Q: 27, 28, 29, and 30 Compare the values of Ay and dy if a changes from 1 to 1.05. What if a changes…

A: We have to compare the values of ∆y and dy.

Q: Use elimination to solve the system of equations. Identify the system as consistent or inconsistent.…

A: Given: System of equation is:5x+y=-207x-3y=-50   We are required to find: a. Solution of the system…

Q: (a) Consider a circular oil slick that forms on the surface of a large lake. When the radius of the…

A: Let the radius of circular oil slick=r mArea of circular oil slick =πr2