Thirty percent of a radioactive substance disappears in 15 years. Find the half – life of the substance.

Q: 4. x³+2x+2 2 x²-1 dx

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Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: Question Find the linear approximation L(x) of the function f(x) = cos(x) at a = - 품. (Enter an…

A: We can find the linear approximation as below.

Q: Find the power series representation of the function f(x) = = x 2x² +1'

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Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (14, 3,…

A: Topic- Equation of line through given points

Q: ล. b. TM8 M8 n=1 n=1 (−1)n-1(x - 1)n n2n n! (x − 3)” 272

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Q: 11) Suppose that f is a solution of the differential equation y' + = 1 with f(1) = 1. Then f(2)= 3.…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Evaluate r2 ff dyda.

A: Given itegration ∫-12∫x2-2x   dy dx

Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: Express the complex number, 1 + ¿, in the form re¹ with 0≤0 < 2π. O √2e O √žeti ○ 2e Ti O eti O 2e7¹…

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Q: Classify the given differential equation according to its type, order, degree, and linearity. (+)*…

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Q: 1. √x+2 dx X+1

A: Hi learner, we can answer the very first question as per the honor policy. Please resubmit other…

Q: (8) A SUPPOSE VECTOR FIELD FY₁Z) =<X₁Y+Z₁ HAS PARAMETERIZATION z(t)=7+4 AND A x) = ²x WHERE CURUE C…

A: A detailed solution is given in steps 2 and 3.

Q: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

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Q: Find the curl of the function G = (xcosy)i + xy² j. (y² + xsiny) k ○ (y² + xsiny) î ○ (y² - xsiny) î…

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Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

A: Here we have to solve the differential equation.

Q: Calculate the vector area of the helicoid parameterised as follows: F(t, s) = (t cos s, t sin s, s)…

A: Please see the below pictures for detailed solution.

Q: Find the derivative of the function at the given point in the direction of A. Options are: 1)…

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Q: . (x + 2y) dx + (2x + y) dy = 0. ANS. x² + 4xy + y² = c.

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Q: Consider the function f(x) = 2x³ 12x² 30x + 7 on the interval [-4, 7]. Find the average or mean…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. 4x -…

A: we use the maclaurin series of sin x to find the maclaurin series of the given function

Q: Find a and b such that ƒ(x) = x² + ax + b 8 17 has an average value of 933 over [0,1] and an average…

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Q: Use integration by parts to evaluate the definite integral fr² ln x dr

A: Topic- integration by parts

Q: If 6√√x + 15√y = 177, find y'(x) by implicit differentiation. y'(x) = Y I Find the exact value for…

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Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: Evaluate the integral and choose the correct answer. Sin In x dx

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Q: Classify the given differential equation according to its type, order, degree, and linearity. J²u 8²…

A: Please see the below picture for detailed solution.

Q: Let P be the point in R^3 with rectangular coordinates (√2, −√2, 2√3). How to find the cylindrical…

A: We have given rectangular coordinates  (x,y,z) = (√2, -√2, 2√3)

Q: Question 3 A dilution tank initially contained 100L of fresh water. Then water which contained…

A: As per our guidelines answer first three subpart of a multipart question. So please resubmit the…

Q: 6) Assume that f(t) is continuous on [a, b] and that u = g(t) is continuously differentiable on [a,…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Determine whether the vector field F(x, y) = conservative. yi + xj 1 + xy is

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Q: Find the total area of the shaded region. 1.5- 1- 0.5- 0 y x=12y³ 6 x=12y² (12,1) 12 18

A: The equation of the curves are: x = 12y3 x = 12y2 The graph of the curves is To evaluate: The area…

Q: 6)    State whether the series converges absolutely, conditionally, or not at all. ∞ n = 1 (−1)n +…

A: The given series is ∑n=1∞(-1)n+1n+9

Q: Which of the following equations is/are exact? □ 3x²y² dx + (2x³y + 4y³) dy = 0 (3x²y-x²) dx + e³ dy…

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Q: 10) Let g(x) = f(t)dt, where y = f(t) is the function whose graph is given below. Find g(2), g(3),…

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Q: 4 In the following differential equations, test for exactness and determine the solution of each: 1.…

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Q: 3. (6x + y²) dx + 2x - 3y) dy = 0. ANS. 3x + xy² ya:

A: Here we have to solve the differential equation.

Q: A manufacturer wants to design a rectangular box with a square base and an open top. (In other…

A: Let  side of square = x  height of box = y    surface area = area of base + 4 * area of side face…

Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: 1. Let S be the triangular region in R3³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: we know that triangular  region is part of plane since all the vertices  ( 2, 0,0)  , ( 0, 6, 0)…

Q: = 4 cost, Use an integral to find the area of the region bounded by the curve x = y=5sint, 0≤t≤2π.

A: SOLUTION-

Q: Show the complete solutions, draw or graph the given for illustration. Find the orthogonal…

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Q: drawing the slope field for the differential equation , I would place slope lines of _________ at…

A: We have to find the required

Q: Bottom of the page is cut off i cannot see the solution.

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Q: Find an appropriate elementary matrix for each of the following transformations: 1 2 1 2 2 4 1 2 •-)…

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Q: Express the equation in logarithmic form: (a) 45 = 1024 is equivalent to log4 A = B. A = and B = (b)…

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Q: 33. Cost A manufacturer has an order for 1000 units of fine paper that can be produced at two…

A: Given data:- Order value of fine paper = 1000 units Produced at two location, x1 &amp; x2 The cost…

Q: ∞ f(x) = L n=1 (7-2x)" Sn

A: