Find the missing value for the radioactive isotope. (Round your answer to two decimal places.) Half-life Initial Amount After Isotope (years) Quantity 1000 Years 239pu 24,100 g 1.4 g

Q: Q1\ Differentiate the following 1)2xsin-13x x+1 2)y = In Vx-2 1 3)y = sin-1 2x

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Q: Find the curvature of r(t) = (9t, t2, t) at the point (9, 1, 1). Need Help? Read It Watch It

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Q: d d Calculate ri(t) r2(t)] and r:(t) x r2(t)] first by differentiating dt the product directly and…

A: Given; r1(t)=4ti+4t^2j+4t^3k , r2(t)=t^4k

Q: A rectangular garden is to be fenced in next to a garage so that fencing is needed on three sides…

A: Let the dimension of the rectangular garden be:                             Length=L and Width=W…

Q: x* (x – 1)? (x + 2) (x² + 1)* Calculate the derivative by logarithmic differentiation: g(x)

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Q: 12 (2). Here is an Ry region, in the XY plane: Consider the change of variable u = xy and v = 3y +…

A: Here we have to write the integral by using change of variable.

Q: Find the inflection points of f(x) = 2x* + 11x³ – 9x² + 12.

A: For inflection points , f''(x) =0 .

Q: Find the partial sum for the firs 4, 10, 16, 22, ... い +6 +6

A: Sequence

Q: Given f(z, y, z) = V31 – 4y + 6z, find fz(x, y, 2) = fy(x, y, z) = f:(1, y, z) = %3D

A: Given :f(x,y,x)=3x-4y+6z

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +7 1 lim t+ 6t2 + 7' 5t (?, ?)

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Q: Note: Enter 'DNE' if the limit does not exist or is not defined. a) lim F(x) = 3 lim F(x) = 3 X--1*…

A: Solve the following

Q: Evaluate f x3 using substitution (3–2x)5

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Q: Find the radian measure of the central angle of a circle of radius 3 meters that intercepts an arc…

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Q: Find the slope of the tangent line to the curve - l2? – 2æy – 2y³ = 19 at the point (3, - 2).

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Q: Use the properties of logarithms to rewrite and simplify the logarithmic expression. In In 5 In 3 In…

A: We will use logarithmic properties.

Q: dx x² – 2x + 2 = dy

A: Given:      dxdy=x2-2x+2⇒dy=dx x2-2x+2Integrating both sides,⇒∫dy=∫dx x2-2x+2⇒y=∫1x-12+1dxLet u=x-1.…

Q: Q2\Find the point at which the tangent to the curve y = v4x2 +1-2 has its slop 2

A: Tangent to curve

Q: 4. For each series determine if it is convergent or divergent. Give reasons for your answers. (-3)*…

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Q: (a) dz (2z4 + 1)3

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Q: Given the vector-valued function R(t) = -6cos(1-2t) i+8t j+6 sin(1 2t) k. Find: (a) the length of…

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Q: x3 Evaluate J 3-2x) using substitution

A: Given ∫x3(3-2x)5dx To find integration

Q: Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon…

A: Given; A=Ao e^(-0.0001213)

Q: Evaluate the function at the indicated value of x= 3. f(x)=log243* -5 5

A: To find the value of given function at x=3.

Q: Which of the following are equivalent to log, (4)? Choose all that apply. 1 log, (16) log, + log,…

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Q: Find the first 4 terms, a10, and a,5 of the sequeñce with the following nth term. a = |(Simplify…

A: The sequence                        an=nn-3, n≥4 then we have to find the first 4 terms and a10 and…

Q: Question * Suppose X, Y are two discrete random variables with probability function given by: Y \ X…

A: Given

Q: Complete the table for a savings account in which interest is compounded continuously. (Round any…

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Q: Given the functions f(x) = . x + 2 and g(x) = x², determine all values of x for which Ag(x)) =…

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Q: Differentiate the following (choose two only )( 5 .. ) 1)2xsin-13x x+1 2)y = In Vx-2

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

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Q: Describe the graph of the equation. r= 18 cos ti - 9 sin tj - O tis an ellipse in thez = 1 plane,…

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Q: 12. The function f(x) and its first and second derivatives are as given below. f(z) - 2 6- 2z g"(z)…

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Q: Sketch the region from the first quadrant, bounded by y = 2x2, x = 0, and x- 2y + 3 = 0, and find…

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A: Use rate of change concept

Q: Jse a graphing calculator to construct a table of values and a graph for the first 10 terms of the…

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Q: 5. Evaluate each of the following integrals. (a) dr. (b) Vr2 +9 dx

A: LetI=∫x32x4+13dxPut 2x4+1=udifferentiate  on both side8x3dx=dux3dx=du8ThereforeI=∫1(u)3du8Take the…

Q: (a) Evaluate the double integral. бу 4x5 + 1 dA, D = {(x, y) |0sys 1, vỹ s xs 1} (b) Evaluate the…

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Q: The buyer for a retail store located in a shopping mall has convinced himself that if he prices…

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Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: find the laplace transform L{cosh3tsin3t}

A: Solved below.

Q: Find the slope of the tangent line to the curve 3x? – 3xy – 2y = - 92 at the point (- 2, 4).

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Q: Find the derivative y = 2 Arcsin 2 -2 a. y' = b. y' = c. y' = d. y' = V2x-x² V2x-x2 V2x-x? 2x-x²

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Q: Let g(x) = (t)dt, where f is the function whose graph %3D AY 21 1.5 1 0.5 0,5 1 -0.5 -1 a. At what…

A: Graph of function

Q: ( 2x + 6 x -2 Enter DNE if the limit does not exist. a) lim g(x) = X--2 b) lim g(x) = X--2* c) lim…

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Q: Find the slope of the tangent line to the curve - 42? – zy + y - 4 at the point (– 2, 2).

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Q: Let g(x) be a differentiable function for which g'(x) > 0 and g"(x)< 0 for all values of x. It is…

A: Given query is to find the possible value for g(7).

Q: Graph the function. f(x) = 3*

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Q: 5. (r' -12r +43r? - 41r +5)÷(r –5)

A: Given query is to perform long division.

Q: Find the limit. Enter DNE if the limit does not exist. 15zy lim (2,9) → (0,0) 22+ y?

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Q: b) Calculate the integral: - .- (x+ 2y) dædy where the region R is defined as: R= {(x,y) E R² : 0 <…

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