1. The half-life of a certain radioactive substance is 30 years. Assume we have 10 grams of the substance initially. a) How much will remain after 80 years? b) After how long will only 2 grams remain?

Q: nd the equation of the line / in the figure below. Give exact values using the form y = mx + 7= y…

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Q: Question 6. > Consider the function f(x) = 2x³ - 15x²2 - 36x +8 on the interval [ - 6,7]. The…

A: The given function is; f(x)=2x3-15x2-36x+8, interval [-6,7].

Q: Question 1 - Consider the function f(x) = 4x² + 48x +3 on the interval [ 10, 2]. Evaluate this…

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Q: Evaluate the limit, using L'Hopital's Rule. 3 lim (1+4x) x+0+ =

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Differentiate with respect to T Answer T : T⁹ d = cb-da-db T btd bc-ad 2bd

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Q: If √√3-2x² ≤ f(x) ≤√√3-x² for 1 ≤x≤ 1, find lim f(x). 2 X-0 lim_ f(x) = X→0 (Type an exact answer,…

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Q: onsider the function f(x) = 2x² - 6x on the interval [ - 3,3]. he average rate of change of f(x) on…

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Q: 10 *[." The value of 2x dx is the same as the area of a Select an answer Finding the appropriate…

A: we do the first one of multiple questions , repost for others∫0102xdx

Q: A(4,30°,3) and Given two cylindrical coordinates B(5,135°, −5), find the vector from point B to A…

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Q: Consider the function f(x) = 7 - 2x² on the interval [-3, 6]. Find the average or mean slope of the…

A: Given function, f(x)=7-2x2

Q: 4. Consider the parametric curve given by x(t) = -7t and y(t) = −3t². (a) Sketch this curve on the…

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Q: Find an equation of the tangent plane to the given surface at the specified point. -², (3, -3,1)

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Q: Evaluate the limit using L'Hôpital's rule e + 2x - 1 4x lim x 0

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Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A: Given query is to find average cost and marginal cost function.

Q: The manager of a large apartment complex knows from experience that 80 units will be occupied if the…

A: Let number of apartments = x revenue function = R(x)

Q: The function f(x) 2x³ + 42x² one local minimum and one local maximum. This function has a local…

A: Given f(x) = -2x3 + 42x2 - 270x + 11 Concept first find x for f'(x) = 0 then find f''(x) if f''(x)…

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Q: The owner of a cattle ranch would like to fence in a rectangular area of 2000000 m² and then divide…

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Q: 3x + 5 Consider the function f(x) = 5x +31 and (A, ∞o) where the function is not defined at A. Find…

A: We need to find out the intervals of increase and decrease.

Q: Use L'Hospital's rule to determine the following limit. Use exact values. 1 cos 2x x 0 1 cos 5x lim…

A: Given; Limx-0(1-cos2x)/(1-cos5x).

Q: SOLID OF REVOLUTION Find the volume of the solid of revolution of the section bounded by the line…

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A: 07:130M   3.00 KB/S   vo LTE   41   (94   D   A   rtal A spring mass system consists of a spring…

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Q: Find the particular solution. dy y y dx=2+ 1+ ; when x = 1, y = 8 X X L

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Q: We have the following. f(x, y, z) = 7(x² + y²) 2-2-x²-y² 7²-1 a) Express the triple integral "I'…

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Q: Consider the function f(x) - 2x³ + 30x² 126x + 2.

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Q: For what values of a and b will the function ƒ(x) = ax³ − 2x² + bx + 1 have a local maximum at x =…

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Q: (2) Expand f(x) = cos x into a Taylor series centered at the origin (a = 0).

A: To expand fx=cos x into a Taylor series centered at the origin a=0.

Q: Given: (x is number of items) Demand function: d(x) = = 1600 √T Supply function: s(x) = 4√√x

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Q: Given the following vectors A=-4a +3a-2a B=a + 5a +7a X y 2 X C=-2a-4a +6a y Evaluate AX (BXC)

A: A→=-4ax+3ay-2az B→=ax+5ay+7az C→=-2ax-4ay+6az To evaluate: A→×B→×C→

Q: Find the derivative y = ecotx Ody da Ody dx Ody dx dy -ecotx csc²x = cotx csc²x ecotx csc²x cotx

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Q: Use the power series 1 1 + x (-1)^x, x < 1 n = 0 to find a power series for the function, centered…

A: Here we have to find the power series of the given function f(x) = ln(x8+1) and also determine the…

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

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Q: Question 3.4. Determine the following integrals 13 15x - 2

A: Integration

Q: (c) Σ cos(n) n=1

A: 13(c) The series is given as , ∑n=1∞cosn Find whether the series is absolutely convergent,…

Q: Given the following vectors A=-2a-8a +5a y B=3a +4a-a y X C=5a +4a +6a_ y Evaluate BX(AXC)

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Q: Evaluate the definite integral by interpreting it in terms of areas. 3 ∫6 (2x−8)dx

A: Topic = Integration

Q: Let R be a rector - valued function defined by R(t) = cost + +1,et) if t#0 ¡ J - K if t = 0 a. Find…

A: Aim:  To determine the continuity of R→t at t=0. -------------------------Given: R→t=1-costt, t+1,…

Q: box with an open top has a square base and four sides of equal height. The volume of the box is 98…

A: Given query is to find dimensions of the box.

Q: A certain population is modeled by the differential equation dy = dx 1.075 (y-2) (y – 5) dy (a) For…

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Q: 1. The Laplace transformation of a continuous function f defined on [0,00) is given by F(s) =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the particular solution. 3 x(y²-1)dy + (y³ - 3y)dx = 0; when x = 1, y = 2

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Q: The function f(x) 2x³ local minimum and one local maximum. This function has a local minimum at x =…

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Q: Consider the following equation. f(x, y) = sin(5x + 3y), P(-9, 15), u=¹/(√√3i-i) (a) Find the…

A: The given function: fx,y=sin5x+3y

Q: how many units and in what directions the graphs of the given equations are to be shifted. Give an…

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Q: 10 π/2 9 cos(x) sin(sin(x)) dx

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Q: f(x) = = '(x) = '(4) = 2x + 4 2x + 5 I find:

A: Given query is to find indicated derivative.

Q: Solve the following trigonometric equation on the interval [0, 2π). Choose all correct answers.…

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Q: Partial Fraction decomposition for the rational expression 8 X (1-x)

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