Find the domain of the vector-valued function. (Enter your answer using interval notatio r(t) = V 25 - t2 i + t'j – 3tk

Q: 21 j=3

A: Use the formula for the sum of n natural numbers.

Q: Write an equation for the parabola with a vertex at the origin and directrix y = - 24 An equation…

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Q: Find the values of a, b, c, and d in the matrix equation below. [:] 10 -5 -8 -1 b. + 2 -8 -10 7 a =…

A: We will find the value of a,b,c and d of the given matrix in the following step.

Q: Find all values of x in the interval [0, 27] that satisfy the equation. (Enter your answers as a…

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Q: V4 - x 8. g(x) = at x = 0 %3D

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Q: Vx 3 1- evNīdy dx - 3 y3 e*y dx dy

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Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: Determine if the following statements are true or false. (a) A square matrix has an inverse if the…

A: We have to determine if the given statements are true or false.

Q: Identify the equation as a parabola, circle, ellipse, or hyperbola. (x - 7)2 = 9 – y2 O A. Hyperbola…

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Q: A small hula-hoop was rolled on the ground.  After rolling exactly 6 times, it went 37.7 feet.…

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Q: 74. Aerobic Exercise A woman keeps fit by bicycling and running every day. On Monday she spends h at…

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Q: O f (x) = -6 sin(3x + 1) cos(3x + 1)ecos"(3+1)

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Q: In how many ways can 2 letters be chosen from the set (A, B, C, D, E, F} if order is important and…

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Q: d d. dx tan(t)dt -4

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Q: 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that…

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Q: Find an equation of a plane containing the three points (-5, -4, -3). (-10, -3, -1), (-10, -2, 1) in…

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and 10г — 5у — 52 — 36 — 0. NOTE:…

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Q: A follasng vector fiebdo are conserva hal function. c)

A: We have to find the potential function if the given vectors are conservative vector field

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y – T = 2 and I = 4. In…

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Q: vith nonzero terms and let m Which is valid An converges absolutely. an converges absolutely an…

A: Series

Q: Evaluate the limit x +y lim (x,y)→(0,0) sin y O None of these O The limit does not exis O-3 O3

A: Given problem:-

Q: (-1)" Given: In(1 + x) = En=0' tu+1 if |x| < 1. n+1 1. Find the Maclaurin series for f(x) =…

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Q: ·4 2. 3 a) Find lim g(x), lim g(x) and lim g(x) X+1 -2 x→1+ b) Find f(1). c) Is g continuous at x =…

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Q: What is the area of triangle ABC if a = 5 ft, b = 6 ft, and c = 7 ft?

A: Follow the procedure given below.

Q: d,e,f

A: We will solve the limits.

Q: Consider the function f(x)=4x^2−10x^7 Let F(x) be the antiderivative of f(x) with F(1)=0 Then F(x)=

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Q: Question 2 Given: y = (sin x) , determine y'/y. O a (sin a)" [cot a+ (1+ ln x) (In sin æ)] (E) None…

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Q: dx COsxtanx

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Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: Let B and F be the following matrices. 7 -10 -3 6 -5 4 B= - 10 8 4 -1 -1 6 7 -3 F = -2 -10 -9 6 7 10…

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Q: diverges: 3n/22n-4=27/4+81/16+243/64+729/156

A: Given query is to find series converges or diverges.

Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Speedometer readings for a vehicle (in motion) at 11-second intervals are given in the table.…

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Q: Find (3a+6x*) da

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Q: Integrate x sqrt of (x+4) dx using algebraic substitution

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Q: (y?ty)dx - (x² x ) dy = o

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Q: Use the Substitution Method to evaluate the following indefinite integral. (Don't forget your…

A: Consider  ∫x(x2+1)9dx

Q: Convert the equation r = 4 csc (0) from polar coordinates to rectangular coordinates. (Express…

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Q: 3. (Section 4.1) Evaluate each indefinite integral. (a) /202 (b) /(3e* + 2)dr 4x (c) / (182² + 6x +…

A: We have to solve in image

Q: (y n?(1 + 3*) dy 1+ y? 2.

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Q: Suppose that f has zeros at 1 and 3. Show that there are two distinct real numbers x1 and x2 such…

A: answer is in next step

Q: Solve for ∂w/∂y and ∂w/∂x w=(1-2y)(x2-xy)

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Q: Find the area represented by the definite int 8. x-2 dx

A: ∫08x-2dx=∫01-(x-2)dx+∫18x-2dx

Q: 4. f (x) %3D (5х — 3)2 5. у %3D cos (5х) 6. f(z) — е5z?+72-13 7. у %3 4x2 + сot (3x) 8. f(x) —D (6х?…

A: Given problems:- 5.    y=cos(5x)  6.    f(z) = e5z^2+7z-13 7.   y=4x2+cot(3x)  To find:- Derivative…

Q: Calculate -3 + li. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 27. a = b =

A: This question is based on conversion of rectangular form to exponential to polar form of complex…

Q: Fill in the Venn Diagram below by dragging the appropriate entry to the correct location given that:…

A: Given  n(A∩B∩C)=3n(A∩C)-B=18-3=15n(A∩B)-C=14-3=11n(B∩C)-A=13-3=10only A = 36-15-11-3=7only B = 30…

Q: y = x°, y = 256 , y axis , revolved at y axis 3.

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Q: The area of a soccer field is represented by a? 12a + 32 square metres. - Find a simplified…

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Q: Find the equation of the curve that passes through the point (5,4) if its slope is given by…

A: dydx=5x-2dy=5x-2dxIntegrate on both sides

Q: Mw.3 Find Ihe arca region for me fallowwig H.w.3 Regian bawndedby. nddy=x+2 Region b.audad.by X-5nd…

A: Area Bounded by the curves : If f(x) and g(x) be two continuous function and f(x)≥ g(x) on a≤x≤b ,…