The boundary of a lamina consists of the semicircles y = V1 - x? and y = V9 - x² together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin. ã, 5) = ( | 0,

Q: [xsechtx'dx

A: Topic:- integration 

Q: Find csc (-270°). Select the correct choice below and, if necessary, fill in the answer box to compl...

A:

Q: 1. Use the graph of the function below to answer the following: -6 -5 -4/-3 -2 1 2 /3 4 $ 6

A: According to grapha. f1 =2b. limx→2+fx=-3c. f2=1d. limx→0fx=-4e. f3=12f. limx→-1.5fx=0g. f4=2h. limx...

Q: Consider the function f(æ) = x²e3". For this function there are three important intervals: (- 0, A],...

A: The given function is  f(x)= x2e3x  Find critical point and interval of increasing and decreasing. 

Q: An object is dropped from a tower, 256 ft above the ground. The object's height above ground x secon...

A:

Q: Given the general solution to a differential equation and its initial conditions y (x) = C, e-3* + C...

A:

Q: Find dy/dx by implicit differentiation. 7e^x^2*y = x+y

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 4 6 8 7 7 2 7 9 (a) If h...

A:

Q: Find the the arc length of y = 4x? – 2 from = 0 to x = 2 No decimal entries. Find the exact value. L

A:

Q: Given the general solution to a differential equation and its initial conditions y(t) = C,14 + C,-2 ...

A:

Q: Q12. The amount of infected people S in thousands by a new flu variant depends on the time t in days...

A:

Q: Find the derivative as indicated: 1) y = 3 cos x +2 sin x; find y' 2) f (t)-t sin t find f' ()

A:

Q: 1 (x-4)°(x² +9)²

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the ...

A: Given:    x = 8     dx/dt = 1.3  Ladder length = 10

Q: u du Formula Answer dx 6. S x In x+x

A: ∫1xlnx+xdx

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 81 xp

A: Let,I=∫x2-81x3dxI=∫x2-81.1x3dxI=x2-81∫1x3dx-∫∫1x3dxddxx2-81dxI=x2-81∫x-3dx-∫∫x-3dxddxx2-81dxI=x2-81x...

Q: Find the slope and equation of the tangent line to the graph of the equation at a given point. 1. y ...

A: Given y = 2x² + 4x.     Point ( -2 , 0 ) To find slope & equation of tangent line.

Q: Find the radius of a cylindrical can (with a lid) to contain 1728 cm³ of water, using the minimum am...

A: This is a problem of mensuration. Based on the general formula of volume of cylinder we will calcula...

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequence x2 + 1 n An ...

A: Topic  - function and derivative 

Q: uppose that you have deposited a certain amount of money in a bank that pays an terest rate of 2.5%,...

A: Topic:- algebra

Q: 11. f(x, y) = x' + 2y – xy – 7x

A:

Q: Find the extrema of the given function f(x, y) = 6 cos(x² - y²) subject to x² + y? = 1. (Use symboli...

A:

Q: Given the combined differential operators for a given differential equation (D² + 16) D² (D + 10) De...

A: We have to find the general solution to the given differential equation.

Q: 6y°dx-x(2x° + Y)dy -0 : y(1)=1 2.

A:

Q: Solve the equation In(x – 11) – In(x – 6) = In(x + 1). %3D

A: Here have to solve the given equation,  ln(x-11)-ln(x-6)=ln(x+1)  

Q: Solve the initial value problem: a" - 2x' = 12e2 – 8e-2", x(0) = -2, r'(0) = 12 %3D

A:

Q: First make a substitution and then use integration by parts to evaluate the integral 7x°e" dx Note: ...

A:

Q: Write the first five terms of the sequence, give the exact answer: +oo n n + 19 n=1 Determine whethe...

A: We have to find first 5 term of sequence and we have to check weather it is convergent and divergent...

Q: Given the differential equation y" - 4y' + 5y = 0 Determine the General Solution for the differentia...

A: See the details solution in below

Q: 32. (a) For a = 1, 2, and 3, draw position vectors for (1) ð = a²7 + 63 (ii) = 57 – a²3 (b) Explain ...

A:

Q: Find the minimum and maximum values of the function f(x, y, z) = 5x + 6y + 4z subject to the constra...

A: Here we have f(x,y,z)=5x+6y+4z subject to the constraint x2+6y2+6z2=1 Let g(x,y,z)=x2+6y2+6z2-1

Q: Write out the First three terms of the following infinite series (-1)" Sin nt n=1

A:

Q: 2 у + y 2xy=X+Y!

A: Given  equation y2+2xy=x+y

Q: Find a simplified expression for (3). (-1)" 4 · 7· 10 • .*• (A) . (Зп - 4) (-1)" -1 3 - 6 · 9 . (В) ...

A: Let's find. 

Q: Given the differential equation y" + 5y' + 6y = &x² e=7x Determine the General Solution for the diff...

A:

Q: Solve the following differential equation using appropriate method. 3. (r+ sine - cose) dr + r(sine+...

A: r+sinθ-cosθdr+rsinθ+cosθdθ=0

Q: -Зx2-2х+1 5. S ***) dx х+2

A: We have to solve given integration

Q: Given the differential equation y" - 4y' + 13y = 8 e2* cos(3x) Determine the General Particular Solu...

A: Given differential equation, y''-4y'+13y=8e2xcos(3x)  

Q: 3x²-2x+1) **1) dx x+2

A: Topic:- integration

Q: The profit (in dollars) from the sale of x lawn mowers is P(x) = 20x-0.02x – 550. (A) Find the avera...

A:

Q: Given the differential equation y" - 16y = 5 x2 Determine the General Particular Solution for the di...

A:

Q: Evaluate the following indefinite integral. Use C for any constant of integration. 56 dx x2 – 49

A:

Q: What are the quartiles of a distribution? O A. The quartiles consist of the lowest value, the median...

A:

Q: Find the equation of the tangent line to the graph of f(x)= (x/x+3)^3 at x= -2

A:

Q: 19. Supposethat the normalunit vector N of a surface S at z = f(x,y) is determined, how does the den...

A: As per company guidelines we can solve first question. I hope that the given solution will help you....

Q: Given the differential equation у" + 5y' — 14у %3D 7х2 езx sin(&x) Determine the differential operat...

A:

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: Please refer to the image below

Q: Evaluate the integral dx et – e-x Note: Use an upper-case "C" for the constant of integration.

A:

Q: 4. y = sin(cos 3x) – sin x cos 3x |

A:

Q: Given the differential equation, its particular solution, and its wronskian y" + 1ly' + 18y = 14 e* ...

A: