Hours (x) Bacteria (y) 0 1853 1 2221 2 2714 3 3056 4 4078

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) f(t)…

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Q: 5. The moon is 3476 km in diameter. What radius of curvature should a concave mirror have if it is…

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Q: Fill in the blank. (Enter your answer in terms of t.) {{ D 1 (s-7)³)

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Q: The inverse forms of the results in Problem 49 in Exercises 7.1 are 2² (6-³) and s-a y(t) (sa)² +…

A: Given :y'+y=e-6tcos5ty0=0L-1s-as-a2+b2=eatcosbt and L-1bs-a2+b2=eatsinbt

Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices:…

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Q: = " Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded…

A: By using cylindrical shells to find the volume of the solid obtained by rotating the region bounded…

Q: Find the nth Taylor polynomial for the function, centered at c. P4(x) = f(x) = 1 +2, n = 4, c = 5

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Q: Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile…

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Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = ex from…

A: Topic- Area using definite integral

Q: A first order differential equation involving current i in a series R-L circuit is given by: di/dt…

A: Laplace transform

Q: 15. Find the volume of the solid enclosed by the surfaces 2 = 0 and 2-16-2-², whose projection onto…

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Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

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Q: Find the inverse Laplace transform 01 2 Ou44(1-4) usinh(t — 4) O sinh4(1-4) 0 1 u4cosh4(1-4) 01 4…

A: Given problem:- Find L-1e-4ss2-16

Q: The second derivative has been found and already factored to be f(x) = (3-x)(x+6). interval testing…

A: NOTE: Refresh your page if you can't see any equations. . the second derivative is given by

Q: Question Define as the region bounded by the functions u(y) = y² + 1 and v(y) = y between y = 1 and…

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Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Describe the surface with equation The surface is a sphere with center { i x² + y² +2²³ + 10x + 6y +…

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Q: Determine if the following improper integral converges or diverges. If it converges, find its value.…

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Q: Both x and y denote functions of t that are related by the given equation. Use this equation and the…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → 00. lim n→∞ n i = 1…

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Q: A particle moves along a line with a velocity v(t) = -t² + 3t - 7, measured in meters per second.…

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Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Leta and b denote two sides of a triangle and let 8 denote the included angle. Suppose that a, b,…

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Q: Consider the following graph. -10/ -S 7.5 -7.5 X 1) Determine the intervals on which the function is…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Given figure:-

Q: Use Theorem 7.1.1 to find (ft)). (Write your answer as a function of s.) f(t) = (et-e-t)² L{F(t))

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Q: Find the area shared by the circle r=1 and r=2cos(theta)

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Q: Use the Second Fundamental Theorem of Calculus to find F"(x). F(x)= •Live+sa F(x)= x

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Q: Question Given f(x) = lim h→0 1 x +4' write a limit representing the derivative of f(x) at x = −3.…

A: To write the limit representing  the derivative of f(x) at x=-3.

Q: The critical numbers z = 1 and x = -2 are found from a continuous function f' (z). Given that the…

A: The Solution is given below

Q: Fill in the blank. (Enter your answer in terms of t.) S s² - 65 S 2 6s + 13

A: Laplace transform

Q: Use summation notation to write the sum. 12 - 3 + 3 4 3 256

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Q: Price ($/gal) Demand (million of gal.) 1 790 1.2 700 1.4 640 1.6 580 1.95 497 2.2 450 2.4 430 2.6…

A: NOTE: Refresh your page if you can't see any equations. . you have already found the supply function…

Q: The second derivative has been found and already factored to be f"(x) = (3x) (x + 6). Use interval…

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Q: Identify the surface by completing the squares. A hyperboloid of one sheet. O An elliptic cone. O A…

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Q: Write the first five terms of the arithmetic sequence defined recu = 2.5, a 0+1=3 +0.75 (0 82 N 33…

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Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: b\ State and prove the theorem of these questions below, for each given functions find the value of…

A: answer is in next step.   as per guideline i can answer only one question .

Q: Two cars are moving towards an intersection. One car is 150 meters north of the intersection and…

A: This is a problem related to distance and velocity. Please find the procedure given below.

Q: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and…

A: Let's find amount of accumulated FV.

Q: 2. Evaluate. z²-2i z²-2z+2 lim 1-i 1 + i 1 i as z approaches (1 + i)

A: Solution : Given that     It can be written as

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: We know that for a position vector  rt = xt, yt, zt, velocity  vt = r't = x't, y't, z't speed  st =…

Q: II) Solve the following equations. 3) cot ¹(1-2)-tan-¹(x)= TT

A: Given data÷   cot-11-x-tan-1x=π4   Useful formula   cot-1x=π2-tan-1x So, cot-11-x=π2-tan-11-x

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 Inches above the…

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Q: Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2π). (Enter your…

A: The general solution of cos θ = cos x  is : θ = 2nπ ± x , where n ∈ Z.

Q: A graphing calculator is recommended. Find the area bounded by the pair of curves. (Hint: Use a…

A: NOTE: Refresh your page if you can't see any equations. . using the graphing calculator, we need…

Q: Question 11 For f(x, y) = sin(9xy). evaluate f at the point (2, ○ fx (2. =) = 0 (2²)-18 © ƒ, (2. )…

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Q: 14. Determine the line integral of a scalar function z = x cos y + In(xy) where x(t) = t² and y(t) =…

A: Given: scalar function z=x cosy + ln(xy)     where x(t)=t2 and y(t)=3+t   bounded by the region at…

Q: Evaluate (2x² - 4x + 1)² dx. √

A: Given data:- ∫x32x3-4x+12dx

Q: a definite integral to find the area under the curve between the given x-values. 1 VX f(x) = from x…

A: Please refer to the image below