Determine the slope of the line tangent to y = √² - 3 at x = 2 In case you need help inputting your answer: √2-1.414, √3=1.732, √5 = 2.236, 6 = 2.449

Q: A fence is to be built to enclose a rectangular area of 800 square feet. The fence along three sides…

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Q: On a hot summer afternoon, a city's electricity consumption is -3t² + 12t + 10 units per hour, where…

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Q: Verify the identity. (Simplify at each step.) 5/2 sin 1/2 1/2 sin X COS X - X COS X - sin 5/2 sin X…

A: Here we have to verify the identity.

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: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt…

A: We are asked to find the  number A(t)  of pounds of salt in the tank at a time t

Q: Write an expression for the nth term of the geometric sequence. Then find the indicated term. a₁ =…

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Q: sider the critical value = 3 obtained from a completely continuous function. We find that 0) = -1…

A: Topic:- function

Q: Find the standard form of the equation of the ellipse with the given characteristics. Center: (1,…

A: This question can be solved using the concept of standard form of  equation of ellipse.

Q: 5. Use Newton's method to find all four solutions of 4z cos(2r) - (r-2)2 = 0 in [0, 8 accurate to…

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Q: Find the Laplace transform of the function: O O O : ²2² (2²/1 + ² ) L(s) = e²s 2 0-²₁ (²/17 - 1²/7)…

A: To find the Laplace transform of the function: ft=0,      t<2t2-4t+6,     t≥2

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: Use the table defining f and g to solve: NOTE: Write Does not exist if the value does not exist. a)…

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Q: press -2√3-2i in the form ree with 0 ≤ 0 < 2T. 4e 3 4e 6 4e 2 i -2 4e +i 4e Fi

A: Given the query is express the complex number in the Indicated form.

Q: Use sigma notation to write the sum. 1 7 (2) + 7 (3) j = 1 1 7(1) + 1 7(10)

A: The given sum 171+172+173+.....+1710

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: Complete the table for each radioactive isotope. See Example 1. (Enter all amounts in grams. Round…

A: Please refer to the image below

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: If sin z 8 , x in quadrant I, then find (without finding x) 9 sin(2x) = cos(2x) = tan (2x) =

A: NOTE: Refresh your page if you can't see any equations. . . use the formula

Q: Find the third, fourth, and fifth partial sums of the series. Σ(3) j = 1 (a) third partial sum (b)…

A: The given series is ∑i=1∞12i

Q: 1) Solve for the (veneral or particular Solution of the following 0 (x+4) ydx Differential Equation…

A: Let's solve given diffrential equation.

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &amp;…

Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

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Q: Use logarithmic properties to expand the following logarithm as much as possible into a sum and/or…

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Q: Given the ellipse 9x² + 16y²-144 = 0 a) determine the length of arc in the first quadrant.  b)…

A: Given region in the first octant bounded by  xy=1 , xy=3 , y=2x and bounded below z= 4 i.e z=0 to z=…

Q: (1) Consider the following integral 1-y² LI /2-x²-y2 1 x²+y² x² + y² + 2² (a) Convert the integral…

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = xªcos x, n = 2, C = T

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Q: Examine the function f(x, y) = −3x² - 4y² + 15x - 8y + 5 for relative extrema.

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Q: HOW YOUR CALCULATIONS 2. Do the following directions lie parallel to the plann? [211] ||(111)

A: Do the following direction lie parallel to the plane? [2 -1 -1]||(1 1 1)

Q: A dead body was found within a closed room of a house where the temperature was a constant 65° F. At…

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Q: Find the exact value of the trigonometric function given that sin u = - 8 17 sin(u + v) Need Help?…

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

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Q: Consider the function 2yx+3x T²+3y² 0 Determine whether this function is continuous at (0,0). F(x,…

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Q: n (² f(x) dx Jo Given f(x) dx = 11 and "f'rx (a) f(x) dx. (b) Irox f(x) dx. (c) for f(x) dx. (d) f³…

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Q: A car rental agency rents 210 cars per day at a rate of $30 per day. For each $1 increase in rate, 5…

A: Topic- Application of derivatives

Q: Parametric Equations X = 3t², y = 3√t 54m 12 Jse a graphing utility to approximate the integral.…

A: The solution is given below

Q: lim, 0 6 tan² (5x) 15x²

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Q: d the following for the given equation. r(t) = (et, 6t², 8 tan(t)) (a) r(t) = (b) r"(t) = (c) Find…

A: Topic:- application of derivatives

Q: Find the Laplace transform of coshbt. Recall that coshbt = OL{coshbt} OL{coshbt} O L {coshbt} O = =…

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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: If 2x² + 2x + xy = 5 and y(5) 11, find y' (5) by implicit differentiation.

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Q: Exercise 2. Plot the graph of the function given in polar coordinates tanh 0-1 r = 2 Write analysis…

A: Given: r=2tanθθ-1since θ&gt;1(radians)

Q: A solid is generated by revolving the region bounded by the following about the y-axis. y = y = 8 A…

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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: Find the inverse Laplace transform of the given function. 7! (s — 5)8 NOTE: Express your answer in…

A: The give Laplace transform is Fs=7!s-58

Q: Evaluate foxy dx dy. Round your answer to two decimal places. O 12.64 29.50 O 105.35 O 26.34 O88.49

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Q: At the beginning of every three months, a college student deposits P3,000 in a fund that gives 2%…

A: Given:      Principal =$3000     Quarterly Interest rate =2%=2%4=0.5%=0.005     number of times n=3…

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 appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find the specified term of the geometric sequence. 8 27 (10 81 = a₁: a₂ = 8, a5 =

A: To find the first term a1 of the geometric series.a1:a2=8, a5=827

Q: Find the differential of the function f(x,y)=−x2+3xy−8y2f(x,y)=-x2+3xy-8y2 at the point (3,−2)(3,-2)…

A: Given.