Given the following functions: f(u)=u^5/2 and g(x)=x^6+1. Find f(g(x))= f′(u)= f′(g(x))= g′(x)= (f∘g)′(x)=

Q: This problem tests calculating new functions from old ones: From the table below calculate the…

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Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

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Q: If you roll a 1-m-diameter wheel forward 30 cm over levelground, through what angle will the wheel…

A: Given data:- The given you roll a 1-m-diameter wheel forward 30 cm over level ground. Formula used,…

Q: 38. Critical Thinking How many students receive each grade? Each student receives a grade of A, B,…

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Q: Which of the equations below is a second order nonlinear differential equation? A. "x²y-(1-2)² = ²x…

A: (A) Here by the square of the term (1-dy/dx)² we get the term (dy/dx)² which makes this differential…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x A. sin2x B. cot2x C. Lnsin2x D.csc2x None…

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

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Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

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Q: Uranium-238 (0-23 has a hall-me of 4. and determine that 67% of the original U-238 remains; the…

A: We will find the age of rock.

Q: Determine the solution of the differential equation: (3tanx-2cosy)sec²x dx + tan x siny dy = 0

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Perform the indicated matrix operation, if possible. - 2x+2y -5x + y - 10x + 8y 4x-3y 4x-7y 2x 3y-3x…

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. ey O eLny °A O D.Y O…

A: given    y(x+y+1)dx+x(x+3y+2)=0

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

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Q: Which of the following equations can be made into a linear diff O A. (x² + xy)dy - (lnx - Iny)dx = 0…

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Q: Solve the following equations. Leave answer in exact form. 1. e³x = 5 2.5e-7 = 8

A: Given, e3x=5Taking ln on both sideln(e3x)=ln(5)We know that ln(ab)=bln(a)3xln(e)=ln(5)We know that…

Q: Find the particular solution of each of the following. (4+sine)y'=e*(6soc² e* - ycose); y(ln x) =…

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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: If f(x) = f'(x) = = f'(4) = 3 tan x, then -sin(x) - 3 sec²(x) COS X >

A: we need to find out the derivative for the given function

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Your option is incorrect but my solution is correct .

Q: Find the area of the region bounded by the curves y = x² 3 x - 3x and y= 3 x 1 - 3x on the interval…

A: Let's find area of region bounded by two curves.

Q: A central angle in a circle of radius 8 is subtended by an arc oflength 10pai. Find the angle’s…

A: Given: Length of arc, l=10π units Radius , r=8 units To find the central angle’s radian and degree…

Q: Find the derivative of the following function. f(x)=√coth (2x)

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Q: Question 20 Obtain the differential equation whose general solution is y = C₁ + c₂e³x A. B. D. E. y"…

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Q: If y=f(x)=7e^x + 3x^4 - 20x - 5, Find the equation of the

A: Using derivative first find slope m,

Q: N 10 9 8 7 6 5 3 2 1 2 Based on the graph above, estimate to one decimal place the average rate of…

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

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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: Which of the function is not an exact equation of the first order? O A. (ey + ycosx) dx + (xey +…

A: To find the non exact equation.   Option c and d are correct

Q: Integrate. S2x² sin (12x) dx = +C

A: Given query is to find the integral.

Q: The figure shows the positions of an object as a function of time t. S 10 J540 501 + 20 30 40 50 t…

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Q: Let P = 1x, y2 be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: a. Graph the functions ƒ(x) = x/2 and g(x) = 1 + (4/x)together to identify the values of x for…

A: Given:-f(x)=x2g(x)=1+4x

Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

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: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Use the Gauss-Jordan method to solve each system of equations. 4x + 4y-4z= 36 2xy + z = -3 x - 4y +…

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Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: 4. Find the limit. lim x-0 lim X-0 5+5x+ sin x 6 cos x 5+ 5x + sin x 6 cos x CA. Yes, lim f(x)…

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

A: Exact differential equation A first order differential equation M(x,y)dx+N(x,y)dy=0 is called an…

Q: Which of the following is a non-homogeneous function? O tan³y/x xLnx − xlny x³ − xy + y² 3 2 - (y² +…

A: function f(x, y), if it can be written  by writing x = kx, and y = ky to form a new function f(kx,…

Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: Evaluate the integral π/ 10 S 3cos 5t sin 5t dt. 0

A: Please see the below picture for detailed solution.

Q: Graph the function y = sqrt(|x|)

A: Given data:- The given function y= sqrt(|x|)

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: dy Solve for the value of C in the equation: + ycotx dx OA. -5 B. 5 OC.-4 D. 4 E. None of the…

A: The given differential equation is dydx+ycotx=5ecosx, yπ2=1 This is a linear differential equation…

Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt