A particle moves in a straight line with velocity t-2-25 ft/s. Find the total displacement and total distance traveled over the time interval [3, 6]. Displacement: Distance: ft. ft.

Q: Find the domain and range of the function. (Enter your answers using interval notation.) f(x) = 3x²…

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Q: 1. Find feit dt.

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Q: Find the indefinite integral. 8 [x³ dx + C W

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Q: Use the sum and difference identities to rewrite the following expression as a trigonometric…

A: cos2π5cosπ3+sin2π5sinπ3

Q: A population of insects increases at a rate of 210 + 14t + 1.2t² insects per day. Find the insect…

A: dP/dt = 210+14t+1.2t2

Q: 2) Describe the 3D surfaces in words and draw a graph by hand. Your description should include the…

A: a) y=x

Q: A bacteria culture starts with 620 bacteria and grows at a rate proportional to its size. After 6…

A: A bacteria culture starts with 620 bacteria and grows at a rate proportional  to its size. After 6…

Q: Find the radius of convergence and the interval of convergence of the power n n+1 X series Σ…

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Q: Evaluate the definite integral. 5 [³9. √/7² dx

A: The given integral is ∫059.x23dx To evaluate the integral.

Q: The function f(x) = 3x + 7x¹ has one local minimum and one local maximum. This function has a local…

A: We have given a function fx=3x+7x-1, and we need to find the maximum and minimum values of the…

Q: Consider the given vector field. F(x, y, z) = x²yz i + xy²z j + xyz² k (a) Find the curl of the…

A: The expression of the curl of the vector field F=F1i+F2j+F3k is: curl F=∇×F=ijk∂∂x∂∂y∂∂zF1F2F3 The…

Q: To find local extrema (maximums and minumums), the first step is to find critical points. Critical…

A: (i) To find local extrema (maximums and minimums), the first step is to find critical points. To…

Q: (+ z≥ 0. unts) Set up the triple integral to calculate the volume of the region inside the sphere p…

A: Given,  Density = ρ = 8 z ≥ 0 Volume, V =? Let the spherical region is represented by 'D'. General…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [8 8y³…

A: Green's theorem is given as  ∫( F1dx + F2dy ) = ∬( ∂F2∂x - ∂F1∂y )dxdy

Q: Consider the curve y = √4x + 8. Find the point on this curve which is closest to the point P(2,0).…

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Q: Write an iterated triple integral in the order dz dy dx for the volume of the region in the first…

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Q: Use derivative to determine whether the sequence {7-3/)} is monotonic increasing, monotonic…

A: an=7-4n

Q: (y secx + secatanx) dx + (tanx +2y) dy =1

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Q: Evaluate the definite integral. (Give an exact answer. Do not round.) 6 [e e8x dx

A: We have to evaluate the given integral.

Q: Find the average value of the function f (x) = x x on the interval [0, 2]

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Q: Evaluate the integral. [ y⁹ In(x) X dx, y > 0

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Q: PROBLEM NUMBER 19 Determine h (t) given that h" (t) = 24t² - 48t+2, h (1) = -9 and h (-2) = -4.

A: (19)  h''(t)=24t2-48t+2given h(1)=-9  and  h(-2)=-4

Q: Find the volume of the region bounded above by the paraboloid z = 2x² + 4y² and below by the square…

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Q: Write the equations (a) (b) in cylindrical coordinates. 6x² − 8x + 6y² + z² = 9 z = 4x² - 4y² 128π

A: a) 6x2-8x+6y2+z2=9 b) z=4x2-4y2

Q: a. Use limits to find the derivative function f' for the function f. b. Evaluate f'(a) for the given…

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Q: Find the divergence of the vector field F¹ = div F =

A: we have given vector field F→=yx6, xz5, zy2

Q: The series Σk-o_gk 100 (-1) k is convergent. How many terms do we need to add in order 11 to find…

A: We have to find the number of terms required to get sum correct to 3 decimal places.

Q: Dave borrowed $6300 from his uncle with simple interest of 9% and eventually repaid $8568 (principal…

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Q: A window has the shape of a rectangle surmounted by a semi-circle. Find the dimensions that provide…

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Q: ind Suppose the particle's initial position is P(2,1,-1). Find the particle's position vector r(t).

A: The velocity vector v→t=sinti+t3j+etk

Q: How many 7-card hands are possible with a 21-card deck? The number of 7-card hands possible is

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Q: Solve given Linear Differential Equation Q4.5

A: To solve the following

Q: Evaluate the triple iterated integral. TT/2 /2/5 [³¹²³²² Jo r cos 8 dr de dz

A: I=∫-17∫0π/2∫05rcosθdrdθdz

Q: Evaluate the iterated integral 02 SS -3-2 (17x+10y + 14)dx dy.

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Q: Use the graph to evaluate the limit. lim f(x) -6-5 k 2 3 4 5 6 x

A: The existence of limit at x=a⇒limx→a-fx=limx→a+fx=limx→afx

Q: if a population doubles every 7 years, assuming a continuous exponential growth model, determine the…

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Q: 67cos(x) is incorrect

A: It is not 67cos(x). It is 6zcos(x).

Q: 7. Find real numbers a, b, and c so that the graph of the function yax2+bx+c contains the points…

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Q: A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f…

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Q: Evaluate the integral f x3_5x−1 X dx

A: ∫x3−5x−1xdx Expand: =∫(x2−1x−5)dx

Q: Find the volume of the solid generated by revolving the region bounded by y=4x-x² and y=x about the…

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Q: Find the area of the region that lies inside the first curve and outside the second. r=…

A: The given curves are: r=7-7 sinθ      and       r=7

Q: Find general solution y B) +y = ex

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Q: 16.3 #8

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Q: f(x) = sin(x² + 3)

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: f(x)=sqrt(7x+1)

Q: The function f(x)=1200x-100x represents the rate of flow of money in dollars per year. Assume a…

A: f(x) = 1200x -100x2 r = 4%

Q: PROBLEM NUMBER 17 ●fe-et- Evaluate e-t 4 dt..

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Q: Find f such that f'(x)=x²-3 and f(0) = 7.

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Q: What is the integral of (3t-1) dt? A.(3-1) +C 8.(3-4)*+C C. (3-1)*+C D. (3t-1)³ +C B. Evaluate the…

A: Given that ∫ 3t-13 dt