Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: 4t² = [x(t) = ly(t) = −10+ 2t The resulting equation can be written as x =

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Q: Evaluate the integral: O x = (A) Which trig substitution is correct for this integral? 7 X = x = x =…

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Q: 2 Find the volume of the region bounded below by z= x² + y², laterally by the cylinder x² + y² = 1,…

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Q: Differentiate implicitly to find dx x²y-2x²-4-0: (2.5) 2-0 The slope of the curve at (2,5) is Then…

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Q: Evaluate (x² + y²) d.S, where S' is the surface z = 4 - æ, 0 ≤ x ≤ 2, 0 ≤ y ≤ 2. S (036² + y²) ds =…

A: To find:-  Where S is the surface

Q: A car travels down a highway at 25 m/s. An observer stands 250 m from the highway. (a) How fast…

A: Given that,speed of car = 25 m/sand observer distance = 250m

Q: Qestion 2 a). Use vector projection to explain the distance in part (iii) equation b). find the…

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Q: You did not answer the domain. Please see  b) what is the interval of your interest (domain) for…

A: The objective function is

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Q: Let f(a, b) = a/ (b − 1)^2 . a. Describe the domain of f. b. Sketch the level curves of f…

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Q: If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

A: The objective of this question is to find the remainder when the square of a prime number greater…

Q: Differentiate the following function. √√/2²2² +4√√/13³ u u'(t) = || X

A: u=5) +4 sqrt(t3)

Q: Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and…

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Q: a. Determine, without graphing, whether the function has a minimum value or a maximum val b. Find…

A: f(x)=3x2-30x-3

Q: 4. I-¹ 2 s² 4 (s + 1)ª

A: Since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: g(b) Use the Substitution Formula, f(g(x)) • g'(x)dx= f(u) du where g(x) = u, to evaluate the…

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Q: 2. Determine whether each of the following matrices are in row-echelon form, Reduced row-echelon…

A: A matrix is row echelon matrix if (i) The first non zero element in each non zero row is unity which…

Q: Construct a polynomial function with the following properties: fifth degree, 2 is a zero of…

A: Degree = 5 2 is a zero of multiplicity 3−2 is the only other zeroleading coefficient is 3.

Q: 23. Copy and complete the following table of function values. If the function is undefine at a given…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: The surface of an island is defined by the following function over the region on which the function…

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Q: Find dx al dx y=3 log ₂x (Simplify your answer.)

A: Giveny = 3 loga x

Q: Let T be a linear transformation induced by the matrix A = Find the matrix of T-¹.

A: The given matrix is,A=(4−32−2)Find the determinant of the matrix…

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 1400 yd…

A: A lifeguard needs to rope off a swimming area in front of Long Lake Beach, using 1400 yd of rope and…

Q: A(x) = f(t) d t where f is the function given by the graph f₁ Let below. 4+ 3 2 1 -1 -2 -3- graph of…

A: For a function f( x ) Area under the curve f( x ) from a to b Given Function

Q: Find the derivative of the function. f(x) = (2x3)4(x² + x + 1)5 :- 3) ³ ( x² + x +: f'(x) = (2x-…

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Q: Assume the point (5,7) is on the graph of y=f(x). Determine the value of n in the following…

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Q: 20. Use the graph of y² = 9x + 9 to determine what type of symmetry the graph displays. 3r

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Q: 5. Use the method of linear system (the Gaussian-elimination method) to determine whether the…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Evaluate the integral 3 √9-x² √9-x² 0 3 √9-x² √9-x² 0 dz dy dx. dz dy dx = (Type an exact answer.)

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Q: Sketch the given region of integration R and evaluate the integral over R using polar coordinates.…

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Q: on f(x) = −3x² − 5x + 2 ir

A: given quadratic function

Q: Suppose you are given a triangle with Then a = degrees, and C = degrees. Enter your answers with two…

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Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: Consider the function

Q: Graph the polynomial P(x) = x³ + x² - 5x + 3 using calculus by showing the given steps: (d)…

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Q: If k is a positive integer, what is the remainder when (k+ 2)(k³ - k) is divided by 6? aburitowd ned…

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Q: A rectangular closed box is to be built at minimum cost to hold 343 cubic inches. Since the cost…

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Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. Then use the second…

A: To find all points (x, y) where f(x, y) has a possible relative maximum or minimum.Then, by using…

Q: If the quotient is positive, which of the following must be true? (A) a>0 (B) b>0 (C) ab>0 (D) a-b>0…

A: The objective of the question is to determine which of the given conditions must be true if the…

Q: Graph the polynomial P(r) = ³ + ² -5r +3 using calculus by showing the given steps: (a) Find the r-…

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Q: Where should the point P be chosen on line segment AB so as to maximize the angle 8? (Assume a = 3…

A: The value of lengths a,b and c are

Q: Evaluate the iterated Integral [.. Answer: ry da dy.

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Q: 4. Solve the following linear systems. 21 + 2x2 2x1 + x1 (a). - 22 x2 x3 3 + 24 = 4 x4 1 + x3 +

A: The system Ax=b is,The augmented matrix is,The reduced system is,The general solution is,

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim 848 3…

A: L=limx→∞e3x−13xUsing the expansionex=1+x+x22!+x33!+⋯⋅

Q: Find the total differential U=-2t tan(7st)

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Q: 364. lim x²/x 20+0

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Q: 6) X1 -6 -5 -4 X3 -3 -2 -1 6 5- 4 3 2 2+ 1+ 0 -1 -2+ -3+ -4+ -5 6 2 X₂ 3 4 10 6 -X Examine the…

A: The graph of the coordinate points are given.The aim is to examine the points of their coordinates.

Q: Activity 10.6.5. Consider the function f defined by f(x,y) = =−x + 2xy − y. a. Find the gradient ▼…

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Q: A sphere, centered at the origin, has radius 3. Find integrals that compute its volume, using…

A: We find the integral that compute the  volume of the sphere, centered at the origin, has radius 3 in…