It is found that 0.5% of radium disappears in 12 years, a.) What percent will disappear in 100 years. b.) What is the half-life of the radium?

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A: Differentiation application

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A: Given query is to find indicated vector.

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A: The Volume of a Parallelepiped Formula  =|(a×b)⋅c|

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2, 6) V = O parallel O…

A: The given vectors,    u=2, 6, v=32,-12

Q: B5: a) (10] Given the complex numbers z = 1- 21, zz = -1+ 31, 23 = 2+ i, z4 = -2 – 31. ) Plot all…

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Q: Find the derivative of the trigonometric function. y = cos(7x)

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Q: Let fand g be the functions in the table below. f(x) g(x) f '(x) g'(x) 1 2. 4 2 3 7 3 1. 7 9 (a) If…

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Q: For the length of the polar curve: r = 2cos(theta) ; 0 < theta < (3pi/2)

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: 2. ts): Find the absolute maximum / minimum values of the function f(x) = x(6-x) over the interval…

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Q: Use logarithmic differentiation to find the derivative of the function. y = (x3 + 2)2(x4 + 4)4

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: To find the sets of parametric equations  and symmetric equations of the line that passes through…

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Q: The marginal cost of a product is modeled by dC 16 dx 16x + 7 where x is the number of units. When x…

A: Given query is to find the cost function.

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Q: Q11. Obtain the general equation of the curve whose slope at any point is equal to y - 2x.

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Q: Determine the value of C in on the antiderivative of F(x) = sin (x)cos (x) for x = 0.784 and y =…

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Q: For a given function f, what does f' represent? Choose the correct answer below. A. f' is the…

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Q: Differentiate the function In x f(x) = In 2x+3 x>0

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Q: y = cosx sinx

A: Given query is to the derivative of the expression.

Q: 4. Determine whether each of the following series is convergent. 2 2 3.4 3.6 24 (1) 3 + +

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Q: -4 -2

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Q: ential equation of the family of curves y B are arbitrary constants

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Q: u = -6i – 2j – 4k, v = 2j + 2k (a) Find the projection of u onto v. (b) Find the vector component of…

A: We have to find projection

Q: 3. Find the first 4 terms of the Maclaurin series expansion for each of the functions below. sin 2r…

A: We have to find the maclaurian series expansion.

Q: Find an equation of the tangent line to the curve at the given point. y = In(x² – 6x + 1), (6, 0) y…

A: As per guidelines we have to solve one question Please repost other questions again

Q: The integral expression J xcos-(2x)dx can be evaluated using integration by parts of the form Judv=…

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Q: Question 1 Determine whether each of the following is a power series. For any that are, state where…

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Q: (a) f(x) = x² – 2x , [0, 5] (b) f(x) = x³ – }z² , [–1, 2]

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Q: Verify that the Mean Value Theorem (MVT) applies to the function f(x) = sin? x – cos x on the…

A: Mean Value theorem states that: f'(c)=f(b)-f(a)b-awhere f(x) is differentiable in (a,b).

Q: The integral expression J xcos²(2x)dx can be evaluated using integration by parts of the form Judv=…

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Q: The fox population in a certain region has a continuous growth rate of 5 percent per year. It is…

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Q: Assume that the linear cost model applies. If the total cost of producing 1600 items at $15 each is…

A: here we want linear relation  for 1600 item cost for each is $15 1600*15 = $24000 so extra is 24410…

Q: Find the points on the surface y? = 36 + xz that are closest to the origin. smaller y-value (х, у,…

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Q: Given f - and 6 = - 4, 5 > , find 5ƒ + 66. 5f + 66 - <

A: Make a component wise addition and multiplication.

Q: x + 4 -dx - 4x .3

A: Here we have to integrate the integral.

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.