Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = cos(t)i + 8tj + 2 sin(3t)k, t = 0 T(0) = X

Q: Use Ayf '(x)Ax to find a decimal approximation of the radical expression. √29

A: By using ∆y≈f'x∆x to find a decimal approximation of the following  radical expression. 29

Q: Obtain the general solution of the following differential equations 7. (cos x + x cos t)dt + (sint —…

A: Differential equation

Q: Find the volume of the solid obtained by rotating the region bounded by Y = 8x², x = :1, and y 0,…

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Q: The region R is bounded by the curves y = √√x and y and y = x³

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: Find r(t) if r(t) = + i + e¹j + 2te²² k and r(0) = i +j+ k. r(t) =

A: integral

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: Question 19 ( ) Let f(r) Inz for all z>0. Determine all intervals on which is decreasing.

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Q: A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 90 ft high. a) How…

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Q: Find an equation for the plane through the point (6,7,5) and perpendicular to the line X=1-8t,…

A: Given equation of line:- x=1-8t,y=1+7t,z=4t+2

Q: Find the volume of the solid obtained by 8x², rotating the region bounded by y = x = 1, x 2, and y =…

A: The given data is: y=8x2x=1x=2y=0

Q: Find the volume of the solid formed by rotating the region enclosed by y = e²x + 5, y = 2x + 5, y =…

A: The given data is: y=e2x+5y=0x=0x=0.7

Q: Given (y)-16-²-², use the total differential to approximate or at (4.1) towards (24,1.05). Round…

A: △x=2.4-4=-1.6△y=1.05-1=0.05

Q: Let a = - 4i +3j - 5k and b = 5i +2jk. Find - 2a - 36. V

A: a→=-4i+3j-5kb→=5i+2j-kC=-2a→-3b→

Q: Given c = - 2 + 10j and u = -107 + 3j, find |e+u and le| + |ú. Give EXACT answers. You do NOT have…

A: I have solved step by step in detail....go through the solution

Q: Let f(x, y) = √/175-4x² − 3y² - Evaluate f(1, 3) Question Help: Video Calculator Submit Question

A: The given equation is;  f(x,y)=sqrt(175-4x2-3y2) .

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Q: If   C(t)=55te−0.1t measures the​ concentration, in ngml​, of a drug in a​ person's system t hours…

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Q: A baseball team plays in a stadium that holds 53,000 spectators. With ticket prices at $10, the…

A: Given attendance denoted by = x there are two points ( 38000 , 10 ) & ( 42000 , 8 )

Q: If is differentiable, then the function. e + f(x) √√3 is differentiable.

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Q: Use the theorem given below to find the curvature of r(t) = √62²i + 2tj + 2t³ k. k(t) = Theorem: The…

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Q: The masses m; are located at the points P₁. Find the moments Mr and My and center of mass of the…

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Q: Solve the problem. 2) Given the total-revenue function R(x) = 7600x, and the total-cost function…

A: Given:- Revenue function Rx=7600xCost function Cx=x3-2x2+5x+100

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. y" + gy…

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Q: a tank contains 1000L of brine with 15kg of dissolved salt. pure water enters the tank at a rate of…

A: The answer is in step 2.

Q: h(x)=5.5x-3.42 The leading coefficient of the polynomial ​

A: We know that the leading term of polynomial is term that contain the highest power of variable.

Q: Solve the given differential equation. 5ydx-5xdy + xdx=9dx

A: 5ydx-5xdy+x7dx=9dxwe know  d(yx)=xdy-ydxx2∫xndx=xn+1n+1+c

Q: A hemispherical tank has a radius of 5 ft. Given that the water weighs is 62.5lb/ft³, find the work…

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Q: J xlnxdx X X

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Q: Find the surface area of revolution about the 2x + 2 over the interval x-axis of y 1 < x < 4.

A: y=2x+2, 1≤x≤4 Differentiating with respect to x, we get dydx=21+0=2

Q: Obtain the particular solution satisfying the initial conditions indicated. 2. (t² − x)dt - tdx = 0;…

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Q: Write an iterated integral for and x = 243 using a. vertical cross-sections, b. horizontal…

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Q: nf is shown. f'(x) 6 X nter your answer using interval notation.) Enter your answer using interval…

A: We have to find the intervals such that function is increasing and decreasing according to the given…

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

A: The given region is: D= x,y | 0≤y≤sinπxL, 0≤x≤L  ρ(x,y)=13y

Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

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Q: Consider the curve r(t) = (6 cos(t), 6 sin(t), e), 0 ≤ t ≤ π. Find r'(t). r'(t) = Consider the plane…

A: Given curve:- rt=6cost,6sint,et

Q: If f is decreasing and its graph is concave up on (0, 1), which of the following could be the graph…

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Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: Let f(x) = 4x² - 2x4. Find the open intervals on which f is increasing (decreasing). Then determine…

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Q: Q14 Find the equation of the tangent line to the curve f(x) = 2x²(x − 3) at x = 1.

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=x² + xy + 2x + 5y…

A: Given function:- fx,y=x2+xy+2x+5y-3

Q: The graph of a twice-differentiable function is shown in Which one of the following sets of…

A: Please see the below picture for detailed solution.

Q: 19. What is the general-term equation, an, for the arithmetic sequence below and what is the 27th…

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. ³ (3x²y − x²)dx + ex³…

A: The given differential equation:ex33x2y-x2dx+ex3dy=0

Q: ← aw Əw For the functions w = xy + yz + xz, x= 2u+ 3v, y = 2u - 3v, and z= uv, express and du Əv…

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Q: Docking a Boat A boat is pulled toward a dock by means of a rope wound on a drum that is located 5…

A: let distance between boat and dock is x ftlet rope length is y ft

Q: 5 The curve y = -5 x³ + x² + x + 1 "Trident of Newton". y 7 1 X 1 y= is known as the x³ + x² + x + 1…

A: To find the coordinates of the point where tangent to curve is parallel to y=2x.