Let C be the positively oriented square with vertices (0, 0), (1, 0), (1, 1), (0, 1). Use Green's Theorem to evaluate the line integral fly²x dx + 3x²y dy.

Q: For the following matrix, det(A)= -57, find the value of a: -1 2 01 A = 5 -2 3 4 -3 0 1 7-N 1 2 ONEL…

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Q: Find the total area between the region and the x-axis. a. y = -x²2x, -3 ≤x≤2 b. y = 3x²-3,-2 ≤x≤2

A: Given that the region bounded by  and the x-axis.and the x-axis.

Q: The displacement (in meters) of a particle moving in a straight line is given by the equation of…

A: The objective of this question is to find the velocity of a particle at different points in time…

Q: Compute for the interval [4, 6], where y = 5x − 6. Ay Ax What is the slope of the tangent line at x…

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Q: Find the limit. 4 lim x3 3x + 7 X

A: Check at which value you need to find limit.

Q: The height of a ball t seconds after it is thrown upward from a height of 4 feet and with an initial…

A: The objective of the question is to verify the height of the ball at two different times and then…

Q: Find the volume of the solid generated by revolving the region bounded by the given curve and lines…

A: The Formula for the volume of solid generated about y axis is given as follows Given data are as…

Q: Given the points A(1, 0, 0), B(0, 1, 0), and C(0,0,1), find projc AB State the EXACT answer only. NO…

A: The given points

Q: For each expression below, solve for the second derivative of y with respect to time using only x…

A: For each of the expression below, to solve for the second derivative of  with respect to time by…

Q: Does Not Exist 0 -0.63 3. Consider the function (x)=(x+3). Find lim x) by making a chart with values…

A: f(x)=-(x+3)1/(2-5x)

Q: -example 1- Evaluate each sum. a. b. Σ2 i=1 n=1 (−1)"tn n+1 c. Σ(k+1)x* k=0

A: To evaluate each of the following sum.

Q: Use the two given functions to write y as a function of x. x+3 6 y=6m-3, m= y= (Simplify your…

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Q: solve: 4x+6(4-x) = 5

A: Consider the equation

Q: ow did the integr

A: There is not only  but also an  which multiplied to get .

Q: 10 (1) If f(x) = x¹0, then f'(x) = (2) If g(x) = -8x², then g'(x) = 1 (3) If h(x) = −3 then h'(x) =

A: The objective of these questions is to find the derivative of the given functions. The derivative of…

Q: Find the inverse, if it exists, of the matrix A: 0 A = 1 -1 -2-3 3 3 -2 -2

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Q: Use the given acceleration function and initial conditions to find the velocity vector v(t) and…

A: The objective of this question is to find the velocity vector v(t) and position vector r(t) using…

Q: The beaker shown has a radius of 4 cm. To the nearest tenth of a centimetre, what is the distance…

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Q: Given f(x), tell how it has been transformed to g(x). Draw both graphs labeling at least 2 pts on…

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Q: The table below gives the annual sales (in millions) of a product. 1998 1999 2000 2001 2002 2003…

A: The objective of this question is to calculate the average rate of change of annual sales between…

Q: Graph the line that goes through the point (-6, -4) with slope of 1. 10+ 8 6 4 2 10 -8 -6 -4 -2 -2…

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Q: The path of a projectile launched at an angle is r(t) = (vo cos())ti + + (vo sin())-gti where vo is…

A: Note: According to our guidelines, we can answer only the first question or the first three…

Q: he number of daily sales of a product was found to be given by S = 700xe−x2 + 700 x days after the…

A: Given that the number of daily sales of a product was found to be given by  ,x days after the start…

Q: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and…

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Q: y = 4. of 'T', p (x, y, z) = y, where T is region bound by y = x² + z² and

A: The density function isT is region bounded by curves,

Q: Consider the equation: y² - 3xy + x 5 = 1 a) Calculate dy using implicit differentiation. dx b) Find…

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Q: ii) Given sec 0 = 5 and 3πT 2 <0<27 Find cos 0, sin 0, tan 0, csc 0, and cot 0.

A: Given .To find .Note: Since, the student has posted multiple questions and has not mentioned to…

Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-4, -2)…

A: The objective of this question is to compute the line integral of the given function over the curve…

Q: Given, f(x), tell how it has been transformed to g(x), then analyze g(x). Draw both graphs labeling…

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Q: 3. +y =p³x dy dx

A: According to the condition we can solve only one question.

Q: (2) f cos³xsinxdx

A: To integrate the expression  you can use a substitution. Let u=cos(x), then du=−sin(x)dx.

Q: The half life of polonium is 139 days, but your sample will not be useful to you after 93% of the…

A: The formula for amount of polonium-210 in the sample after t days Decay rate Initial amountAmount of…

Q: 5. Given the vector = (-8,5), find the magnitude and angle in which the vector points (measured…

A: The objective of the question is to find the magnitude and direction of the given vector (-8,5). The…

Q: Convert the point from cylindrical coordinates to rectangular coordinates. (x, y, z) = 7, 3π 2 -1 6

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Q: 1. Two cars start moving from the same point. One travels south at 30 km/h and the other travels…

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis.

A: Given that, the function is .

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: Problem 3. ( ) Suppose that f(x, y) is a function defined by f(x, y) = x4 - 4xy + y¹. Suppose f has…

A: Suppose that  is a function defined by Suppose  has critical points at .By using the second…

Q: Create a table of values for the function f(x) lim X-0 4 -0.1 -0.01 -0.001 Use the result to explain…

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Q: 2. In the following exercises express the integrand as a sum of partial fractions and evaluate the…

A: To express the integrand as a sum of partial fractions and to evaluate the integral.

Q: 3) y = sin(x-7) Period: Amplitude: Reflection: Phase Shift: Vertical Shift: Transformations: + H|H…

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Q: Solve the following problems and show your complete solutions. Explain your answers for better…

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Q: 2. Find the total area between the region and the x-axis. a. y = -x²2x, -3 ≤x≤ 2 b. y = 3x²3,-2 ≤ x…

A: To find the area between the region and the -axis.

Q: Suppose that f has a domain of [5, 13] and a range of [6, 16]. (a) What are the domain and range of…

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Q: Solve the differential equation. dy = 1, dx 5√xy y = x, y> 0

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Q: 2. In the following exercises express the integrand as a sum of partial fractions and evaluate the…

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

Q: Find the length of the following curve. If you have a grapher, you may want to graph the curve to…

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Q: The pH scale measures the acidity or the alkalinity of a solution. A difference of one unit of pH…

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Q: Ten percent of a radio-active substance decays in 4 days, what is the half-life of the substance?…

A: 10% of radioactive substance decays in 4 days.

Q: Find the limits. f(x) = x + 5 g(x) = x² (a) (b) (c) lim_f(x) = = x → 5 lim_g(x) X→ 4 = lim_g(f(x))…

A: The objective of this question is to find the limits of the given functions as x approaches certain…