Find the centroid of the region bounded by the graphs of the functions y = 3x², y = x² +5 The centroid is at (a, y) where

Q: Use Green's Theorem to evaluate [F F. dr, where F = C consists of the arc of the curve y = 4x - x²…

A: Using the green theorem :-F=<√x+4y,3x+√y>

Q: Evaluate the definite integral. 10 [." t t¹ In (5t)dt

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Q: If z = -1e²+3y, find the differential dz. et² + dz= on below +2y (2x dx + 3 dy) Submit Question

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Q: Find the surface area of the helicoid (spiral ramp) with vector eq r(u, v) = (u cos v, u sin v, v),…

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Q: Find the distance fro (3, 5, 7) to each of the following. (a) the xy-plane (b) the yz-plane (c) the…

A: According to bartleby guidelines we supposed to do the first three sub parts of multiple sub parts…

Q: Compute the flux of the vector field (x4, - xy²), out of the rectangle with vertices (0,0), (6,0),…

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Q: Compute and simplify the difference quotient: f(x +h)-f(x) h 15x 7h + 14 - h = 0. 10x² + 5h+ 7x 10x…

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Q: Find the general solution of the differential equation (4)-40y (3) -40y +400y"=0

A: Given differential equation y( 4 ) - 40y( 3 ) + 400y'' = 0Let d be the differential operator

Q: .) Find the derivative of y = x(2x - 1)³

A: y=x2x-13

Q: y lim f(x) = -∞ X-a- (B) a -X lim f(x) = +00 X-a+

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Q: Textbook Consider the function f(t) = 3 sec²(t) — 3t³. Let F(t) be the antiderivative of f(t) with…

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Q: Consider the vector field F = π 1.² F. dr along the curve C: F(t) = 3 cos(t)i + 3 sin(t)j, 0≤ t ≤ C…

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Q: Given f(x, y) = cos(5x + 2y), find faz(x, y) = -25 cos (5x + 2y) fay(x, y) = -cos (5x + 2y) fyy(x,…

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Q: J & W 6n-S nzl

A: Let 0≤an≤bn for all nif∑n=1∞ bn  converges then ∑n=1∞ an convergesif∑n=1∞ bn  diverges then ∑n=1∞ an…

Q: Question 8 (Biological Elimination of Chemical Substances). The way in which the human body breaks…

A: Given: Tylenol has a biological half life of around 2.5 hours. The amount of Tylenol can be modelled…

Q: A ball is shot from the ground straight up into the air with initial velocity of 46 ft/sec. Assuming…

A: A ball is shot from the ground straight up into the air with initial velocity  of 46 ft/sec.…

Q: A company manufactures and sells DVD's. Here are the equations they use in connection with their…

A: Given: Number of DVD's sold each day: n(x)=xSelling price for each DVD: p(x)=12.5-0.07xDaily fixed…

Q: The graph of a function fis given. Determine whether f is continuous on its domain. O continuous O…

A: A graph of the function is given. We have to determine whether the function is continuous or not in…

Q: . Without graphing or solving for the inverse equation, list the transformations of the inverse of y…

A: y = -sin(x+1)+3

Q: Evaluate [yds, C: x = t², y = t₁ - 2≤t≤2

A: To evaluate ∫C y ds, C: x=t2, y=t, -2≤t≤2.

Q: Given f(x)=-25sin (Sx) and f₁0) = -5 and f(0) = 4 Find F(1) 2

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Q: Evaluate the indefinite integral sin³r cos² rdr = + C

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Q: Find the general solution of the following differential equations: (a) y? Ax=(xy-x)dy

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Q: Sketch the conic. Include the directrix that corresponds to the focus at the origin. Label the…

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Q: Use the integral test to see if it converges or diverges

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Q: Evaluate y ds, C: x = t², y=t, −2≤t≤8

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Q: 2. (a) Calculate the exact length of the curve r = 1 - sin for 0 ≤ 0 ≤ 2T. (b) Justify why the area…

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Q: Find average rate of change for the function over the given interval. 5x³5x²-7between x = -9 and x =…

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Q: f(x) = = [x² +6² bx+2b for x < 2 for x ≥ 2 Let f be the function defined above, where b is a…

A: The given function is fx=x2+b2for x&lt;2bx+2bfor x≥2Then values of b, if f is continous at x=2

Q: Evaluate the improper integral if it is convergen Loxe xe8x dx

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Q: If z = -4x² + 2y² + 5y, find the differential dz. You should have variables dx, dy, y, and x in your…

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Q: COS √√2 2

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Q: 3. fx³ (x - 1)20 dx

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Q: Differentiate the function. 2 (5s7 + 4)8 f'(s) = f(s)

A: To solve the following

Q: Use the information to evaluate and compare Ay and dy. (Round your answers to four decir y = x4 + 1…

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Q: A A function f is even if f(-x)=f(x) for all x in the domain off. If f is even, with lim f(x)= -1…

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Q: Find the curl of the vector field F = (5y cos(x), 6x sin(y)) curl F =

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Q: Determine if the function is continuos. If the function is not continuous, find the x-axis location…

A: fx=-x2+3xx

Q: Suppose that f(x, y) = √√3² - ² - y² at which {(x, y) | x² + y² ≤ 3²}. +y=3 Then the double integral…

A: f(x,y)=32-x2-y2 at which {(x,y) | x2+y2≤32}

Q: 1 1. y=2-x, y=0, x= 1, Axis of revolution: x-axis Show Transcribed Text x = 2; Find the volume using…

A: Here, representing the solid's volume as an integral with respect to x or y in order to employ the…

Q: Find the divergence of the vector field F = div F Calculator Check Answer

A: We have to find the divergence of the given vector field.

Q: Find the local maximum of f(x,y) = 6xy - 4x - 9y - 4x²-4y2 Find the critical point(s) and check the…

A: Find the local maximum of  f(x, y )= 6xy-4x-9y-4x2-4y2 Find critical points and check the value of…

Q: Given f"(x) = 3x+4 and f(0) = -1 and f(0) = -6. Find f'(x) and find f(3) = [ Question Help: Video…

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Q: 9+13+17+ 21+000 + 65 = Σ B₁ where n=1 A= B =

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Q: Determine the five-point summary for the function f(x) = cos(2x + 3) +5 using algebraic methods.…

A: Determine the  five-point summary for the function f(x)= cos2x+3π2 +5 using algebraic methods.

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Q: 5. The graph of f(x) is shown below. What does the graph of 3f(x) look like? m/2 0 11/2 31/2 51/2…

A: we have given function of f(x)

Q: Find ford xdy + ydx, where C is the arc of the curve y = e for 0 ≤ x ≤ 6

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Q: 8. Find and classify the equilibrium points of the following equations: i = (9+x-3y)x (-8 + 4x - y)y…

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Q: Find an equation of the set of all points equidistant from the points A(-3, 4, 2) and B(6, 1, -2).…

A: To solve the following