A 15-kg quantity of a radioactive isotope decays to 7 kg after 11 years. Find the decay constant of the isotope. (Use decimal notation. Give your answer to three decimal places.) k = years-1

Q: A. Evaluate the integral of the follo x+4 1. dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: . Find f 6x5-25x*+8x3 +43x2-8x-12 (3x-11x3+9x2-11x+6)(9x2+12x+16) dx if this can be reduced to…

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Q: H.W: Evaluate the integral 1 1 1. || x²e*ydxdy o y

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Q: 10) Given f'(x) = 3x+ 2x + 1 and f(1) 4, determine ƒ(x). %3D %3D

A: Given f'(x)=3x²+2x+1....(i) and f(1)= 4...(ii)

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A: We have to choose correct option

Q: r(t) = cos(Tt)i – In(t)j+ vt – 16k; to = 17 %3D Choose one▼

A: Given

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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Q: 1. Describe the graph of the equation: x2 – 5y2 – 4x – 10y – 46 = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from x = 0 to x = 6

A: ∫c(2x-y)dx+(x+7y)dy x axis means y=0 dy=0 limit of x from x=0 to x=6

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We can solve as follows

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the Cartesian coordinates of the given point. (8, 0) 1) (0, 8) 2) (-8, 0) 3) (8, 0) 4) (0, -8)

A: Given problem:- Find the Cartesian coordinates of the given point.   (8,0)

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A: Find out the maxima and minima.

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Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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A: Integral

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Q: Yz01003 b00 Cos07+3 2. 7) 300 Sing Y=0.002 Ysine dr do dø

A: A detailed solution is given below

Q: Charlie is driving when her vehicle detects an obstacle in the road 300 ft ahead. The vehicle's…

A: Given that: Charlie is driving when her vehicle detects an obstacle in the road 300 ft ahead. The…

Q: dx 4 XVx - 4

A: We need to find the solution for the given  integral by trigonometric substitution.

Q: The solution to the indefinite integral 3. + 7x 1)dx is given by which of the following? Note: C is…

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Q: Let f (x) = x(8+6x). Evaluate the definite integral 1 rOF So f (x) dz. (F(1)]* Enter the value of…

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Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

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Q: b) Find the inflection points. 4. For the given function find the local extrema using the Second…

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Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: Find the area, A, of the region enclosed by the cardioid ... r = 8+8 cos 0. A 96 a (B) 48 A 100 A 52…

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Q: Evaluate the definite integral. i+ej+tk)dt O es - 1 -- (-~" - 1) + 5 O es i- e- 5 O es i + (e- - 1)…

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Q: Graph the function Ax) = 4x-1, if x <-1 Determine if the function is continuous x-3, if x2-1…

A: The given function is  f(x) = 4x-1x-3if x&lt;-1ifx≥-1 A function is said to be continuous at a point…

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A: First we will draw graph for function.

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Q: A. (2x +x+3 dx

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Q: Nx+ 10 - 100 Rationalize the numerator of

A: Solution of given question is written in below steps.

Q: An employee invests £1000 at the end of each month into her Pension Fund for 30 years. What is the…

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Q: 1. For which function below does lim f(x) = -∞? X-2+ 1 f(x) = - x-2 1 f(x) = - (2 – x) x² - 4 a. с.…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…