3. Determine the curvature and radius of curvature of y = 6x-x³ at (1,5). a. 0.18973; 5.2704 b. 0.14256; 7.0145 c. 0.56236; 1.7782 d. 0.29321; 3.4105 c. 3.2 cm² quare has sides 8 cm long. If each side is increased by 0.20 cm, determine the approximate change in its area.

Q: Find y as a function of a if y" - 14y" +48y' = 70e", y(0) = 12, y'(0) = 29, y" (0) = 28. y(x) =…

A: Given: Here, the characteristic equation is     m3-14m2+48m=0. Now,…

Q: Which of the functions are polynomial functions? (Select all that apply.) > > S 13 33 J U C P e 2…

A: To determine the functions that are polynomial functions.

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A:

Q: Sketch the region that corresponds to the given inequalities. 2x + 4y = 4 2x - 4y s 4 20 -10 O -5 y…

A: The given inequalities are:2x+4y≥42x-4y≤4x≥0

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A:

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A: Given height function s = -16t2 + 48t + 36

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A: Given :ft=t2-1t2+1    -2, 2

Q: Let f(x) - 2x² - 6x - 8 = Determine the equation of the tangent line to f at x = 6. Report the…

A: We have given a function  fx=2x2-6x-8 Put x=6 f6=2×36-6×6-8=72-36-8 f6=28 Point : x1,y1=6,28…

Q: 2 Given Cost and Revenue functions C(q) =q³ - 8q² +55q+5000 and R(q) = -3q² +2400q, what costs…

A: Given: Cost function  C(q)=q3-8q2+55q+5000 Revenue function: R(q)=-3q2+2400q To find: The costs…

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A: To determine the intervals where f is increasing The function is increasing when function goes up…

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A: please see the below picture for detailed solution.

Q: 3. Find an equation for the surface obtained by rotating (a) the ellipse x² + 4y² = 4, z = 0, about…

A:

Q: K Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost…

A: △C=C(x+∆x)-C(x)△C=C(90+1)-C(90)△C=C(91)-C(90)   for x = 90 for x = 91 △C=C(91)-C(90)=167.41 -…

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A: The total number of Atlanta Braves shirts a small gift shop has sold  during a calendar year is…

Q: 11. Find the differential equation of the family of lines passing through the origin 12. Solve the…

A:

Q: 5) Evaluate the sum 101 1 143) (i+1 i +3,

A: as per company guidelines we can solve only first question when multiplie question being posted

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A: f’(2) = slop of tangent line at x=2 f’(x) = m = (y2 - y1)/(x2 - x1)

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A:

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A:

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A: let distance between boat and dock is x ftlet rope length is y ft

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A: Please see the below picture for detailed solution.

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A: The given data is: at=10k Initial conditions  v0=1j+5kr0=-4i+5j-3k

Q: Find the investment needed today to make $ 100,000 in 5 years with a simple interest rate of 8% per…

A: Given data÷ A=$100,000 t=5 years r=8% =0.08 per year

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Q: 85,000 is deposited in a saving account with 6.35% annual interest. When will be the initial sum…

A: To solve this problem, we can use the formula for compound interest:

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A: Given: N(t)=7501+14e−0.4t

Q: If   C(t)=49.7te−0.24t measures the​ concentration, in ngml​, of a drug in a​ person's system t…

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Q: Question 7 The direction of maximum increase of f(x,y,z)=x² + y² - 4z at the point (2,-1,1) is O a…

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Q: F. Write an equation for a rational function which would yield the graph depicted below

A: Given graph

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A:

Q: Determine the intersection if any between the line L₁: [x, y, z] = [3, 2, − 5] + r[0, 1, 4] and the…

A:

Q: [cos* xdx

A:

Q: For the following integral.Sed using n=5 subintervals b) Find the Trapezoid Rule Approximation, as…

A: (b) Given that , ∫01e-xdx , n=5 find the Trapezoid Rule Approximation , as well as the error bound.

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A:

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A: To solve the following problem

Q: If   C(t)=71.4te−0.4t measures the​ concentration, in ngml​, of a drug in a​ person's system t hours…

A: The concentration of drug in a person's system is given by the function:C(t)=71.4e-0.4t

Q: construct a function and graph:

A: We need to construct trigonometric graph.

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Q: g'(x) = - g'(x) = g(x) = -4x³ + 14x² + 2x - 63 3

A: To solve the following problem

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Q: Let y = tan(2x + 5). Find the differential dy when x = 4 and dr 0.2 Find the differential dy when I…

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Q: Obtain the general solution of the following differential equations 8. (y sin x + xy cos x) dx + (x…

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution to the…