(5) Find the center of mass of the region bounded by y = sin x between x = 0 and x = 7 above the x-axis.

Q: Consider the following curve. y = √√√2+x²³ Find y'(x). y'(x) = Find an equation of the tangent line…

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Q: Which of the equations below is a second order nonlinear differential equation? O A. 2 ¯\x²y - (1 -…

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Q: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

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Q: Authorities conducted an investigation and found that the chemical Trioxin was illegally dumped into…

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Q: Question 9 Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y +…

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Q: . If (OM-ON) / - - - O A. B. O E. "Q y5 -5 then what is the integrating factor? None of the Choices

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Q: Use the Gauss-Jordan method to solve the following system of equations. 3x + 8y4z = 0 5x - y + 5z =…

A: NOTE: Refresh your page if you can't see any equations. . the system Ax=b is  augmented matrix is

Q: Solve for the value of C in the equation: (3xy2 + 2y)dx + (2x²y + x)dy: = 0 when y(1) = 2

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Q: In order to expand (x3 - y4)5, I find it helpful to rewrite the expression inside the parentheses as…

A: Given data:- The given expression is, x3-y45

Q: Which of the following equations is NOT an exact equation? OA. (2x sin y + y)dx + (x² cos y + x)dy =…

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Q: Give the implicit solution of y'my-x³-2 Oe-2x = y²(x²+c) Oe²-y²-c 2x Oe² = x²(x²-c) 0²¹-y²(x²-c)

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Q: Evaluate the following integrals: 2 5cos x - 3tan x COS X S- -dx

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Q: (a) lim 2 – 52+6 H-2 4-x² pts

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Question 1. Find the solution of the following differential equations (i) cos²x sin x + (cos³x)y = 1

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Q: Which of the following is a non-homogeneous function?

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Q: Given the vectors à = (2, -1,3), b = PQ where P(1, 1, 1) and Q (5, 1, −1) and Ĉ=i+j+ 3k. Find a)…

A: Given the vectors a→=2, -1, 3, b→=PQ→ where P1, 1, 1 and Q5, 1, -1and c→=i→+j→+3k→.To find 7b→-3c→

Q: Which of the following is NOT true about the linearity of differential equations? A. Which of the…

A: Degree of the differential equation is always 1 because if degree is more then 1 then we get product…

Q: Obtain the differential equation whose general solution is y = ₁ + ₂³x A. B. |y" - 3y' = 0 D. E. 3y"…

A: Differentiate both side with respect to x

Q: Eliminate the arbitrary constants of y=c₁e*+cx*— sin3x

A: We use differentiation to Eliminate the arbitrary constant, we differentiate the given equation as…

Q: The degree of homogeneity of the function ƒ (x, y) = (x² − 4y²)−¹/² A. 1 B.-1 C. -1/2 D. None of the…

A: The given function is fx,y=x2-4y2-12 We have to find the degree of the homogeneity.

Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

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Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

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Q: Let g(x,y,z)=x^3 y^2 z sqrt(14−x−y−z)   1. Evaluate g(1,2,3).g(1,2,3). Answer:…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x + y = 4 2√2 sin…

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Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: Which of the following statement is TRUE? O A. An ordinary differential equation (ODE) contains…

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Q: 5 5 3 Suppose ff(x) dx = 25, f f(x) dx = 10, f g(x)dx = 10 and h(x) = = 3 0 0 the following: 0 b.…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

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Q: The domain of the piecewise function is (-∞0,00). a. Graph the function. b. Use your graph to…

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy² + 2y)dx + (2y³ + 2x²y +…

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Q: Which of the following equations OA. (2x sin y + y)dx + (x² cos y + x)dy = 0 OB. 1 dx-dy-0 y O E.…

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Q: 11. Define what it means to say that lim g(x) = k. the motion y X-0 Choose the true statement below.…

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Q: Which of the following equations is NOT a variable separable differential equation? O A. 2xydx + (x²…

A: Option D is not a variable  separable  differential  equation .

Q: what is rational function ?

A: Relational number Our connection is number three. As you'll see that number is specific to our…

Q: dy What is the IF for solving the linear equation: x + = C0SX,x >0 dx 2 O O O O A. B. D. E. MIN 3x 2…

A: To find IF

Q: What is the value of k so that the differential equation (y³ + kxy4 − 2x)dx + (3xy² + 20x²y³)dy = 0…

A: We need to find out the value of k that makes the given differential equation exact.

Q: Question Use the formula to evaluate 4e4x 16+e4x dx. Include +C in your answer. Provide your answer…

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Q: Show that:

A: Given, nr+nr+1=n+1r+1

Q: (a) If y=f(x) = 7e²+3x² - 20x-5, find the derivative f '(x).

A: given that,   y=f(x)=7ex+3x4-20x-5,   find the derivative of f(x)? formula:   ddx(xn)=nxn-1

Q: Which of the function is not an exact equation of the first order?

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Q: Which of the following equations can be made into a linear differential equation? O A. (x² + xy)dy -…

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Q: Find the equation of the tangent line to the curve y = 8 sin æ at the point (7,4). The equation of…

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Q: find the average rate of change of the function over the given interval or intervals. 1. f(x) = x³ +…

A: Given expression, fx=x3+1 a) 2,3 b) -1,1

Q: dy Solve for the value of C in the equation: + ycotx dx O A.-5 OB. 5 OC.-4 O D. 4 O E. None of the…

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Q: SIT lim t-0 CATA 3+t-√3-t t anot

A: To find the limit.

Q: Another model for a growth function for a limited population is given by the Gompertz function,…

A: The givne growth function for the limited population is dpdt=clnkpp…

Q: If (OM-ON) 1/12 - - 5, = ?х M y OA. e5 O B. OC. y5 O D. e-5 O E. -5 then what is the integrating…

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Q: -3 Σ Σ 4 Τ 1 Σ k=i (k + 2)(k + 3) IME 1 4*+2 7K-1

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: what is decreasing function?

A: What is decreasing function?

Q: dy Solve for the value of C in the equation: + ycotx = 5ecosx when y() = 1 dx OA.-5 OB. 5 OC.-4 OD.4…

A: It is a linear differential equation of first order so find first integrating factor