The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate to the amount present at time t. How long will it take for 90 percent of lead to decay if 1 gram of the isotope is present at the start?

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A: Please see the below picture for detailed solution. 

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A: This is a series problem

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A: topic - integration 

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Q: Let f(x) = 6/x + 1. a. What is the average rate of change of f over the interval from x = 3 to x = 4...

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Q: The "vertex" of the graph of a quadratic function is the point that corresponds to the minimum (or m...

A: a) f(x)=11x-63x-8b) gx=x2-92c) hx=3x2+12x+5

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A: We will use properties of pdf( Probability density function) to find value of A.

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Q: Consider the following function. (x) = 3x3 + 9x2 – 27x (a) Find the critical numbers of f. (Enter yo...

A: Consider the function f(x)=3x3+9x2-27x, then we have to answer the following... Solution (a): To fin...

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A: Given query is to find solu of the differential equation.

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Q: Question d²y Find if-x2 + 3y² = 4. dx2 Provide your answer below:

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Q: Given f(x) = 4x+9x-16x-21, answer the following. Part: 0/2 Part 1 of 2 Factor f (x), given that -1 i...

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Q: 2y 4. у'+ х+1 = (x + 1} %3D

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A: topic- differential equations

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Q: 6-x Problem 3. Solve the rational inequality x s 2x-5 Leave your answer in interval notation.

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Q: 1-2n The sum of the series 1 is: A) 1. B) 2. C) D) E) Diverges.

A: The given series is: ∑n=1∞121-2n which can be rewritten as: ∑n=1∞1212-2n=12∑n=1∞2-1-2n=12∑n=1∞22n=12...

Q: Use the following graph and write the shaded area as integrals. A(-1,3) D(2,1) B(0,0) y= h(z) y = S(...

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Q: The concentration C of a chemical in the bloodstream t hours after injection Into muscle tissues is ...

A: Here, the given function is: C(t)=8t27+t3, t≥0 is the contraction function with t in hours.

Q: Find f'(-3) if f(x) = - 7x. f'(-3) = (Simplify your answer. Type an integer or a fraction.)

A: topic - derivative of a function

Q: A differentiable function f has one critical number at x = 8. Identify the relative extrema of fat t...

A: We have to choose correct option

Q: The position of a car traveling along a highway is given by the function s(t) = 21² – 2t where t is ...

A: Position function iss(t)=2t2-2tThen acceleration is given  bya(t)=s''(t)

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Q: Given the the parametric curve | x(t) = t3 – 13 |y(t) = t³ – 7t dy (a) Find an expression for dæ dy ...

A: we are allowed to solve only 3 subparts of a question. Here are the solution of part 

Q: Show that the sequence 5n n=1 is eventually strictly increasing or eventually strictly decreasing. A...

A: Given is the question of sequence and series.

Q: Evaluate the (-5z"+6z°–18 dr -3z2 O a. 글2-2z +21nr-을 +2 In |z-3| +c O b. + 2z + 2lnz -2In a 3 + e O ...

A: we have to solve the integral.

Q: Convert the parametric equations of a curve into rectangular form. No sketch is necessary. x = Vt, y...

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Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series s-(.) S = п+1 n + 2 n=3 wh...

A: Given telescoping series∑n=3∞ 11+n-12+n