Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis. y=x², y=6-5x, x=0, for x ≥ 0

Q: Assume that x and y are both differentiable functions of t. Find the required values of and dy dt…

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Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

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Q: A horizontally outstretched arm supports a weight of 21 lb in a hand (see figure). If the distance…

A: Solution: (a) The magnitude of the torque about the shoulder can be calculated using the equation…

Q: Use Gauss elimination method to solve : x + 3y - 4z = 3 2x + 5y-z = 11 4x - 3y + 2z = 0

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Q: 10 10 Ꮎ – 11 10-0 (el°-° - 1 ) dᎾ

A: Given,             ∫010θ2e10-11e10-θ-1dθ

Q: -x+2y = -5 (-2y = ²/x + 6 1.x3 7x+4y=17 3.0 7x+5y = 5 (12y=7x+12 4.R15y=7x+7 (3x-5y=-3

A: Given :1. 13x+2y=-5                 -2y=23x+6 2.13-3x=-4y 7x+4y=17                3.7x+5y=5…

Q: Find the divergence of the vector field F. F(x, y) = 5x²i + 3y²j

A: To find the divergence of given vector field.

Q: Evaluate the integral. (Use C for the constant of integration.) | نام (7-e4)² du

A: The given integration is ∫eu(7-eu)2 du We have to find the integration.

Q: Evaluate the integral: 0x = x = (A) Which trig substitution is correct for this integral? 7 6 O: x =…

A: We are required to solve I=∫36x2-49x3dx      The following formuls has been used to solve this…

Q: Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) =…

A: To find the unit tangent vector and the curvature.

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: given  r(t)=(5cost)i+(t2-sint)j+(4e4t)kat t=0x=5costy=t2-sintz=4e4t

Q: For what point on the curve of y=9x² - 2x is the slope of a tangent line equal to 88?

A: To find a point on the curve with given slope of tangent.

Q: Find Vw. - xe2% sin 4z NOTE: Give your answer in unit vector notation; that is, in terms of i, j,…

A: According to bartleby guidelines we supposed to do the first one of multiple qurstions kindly repost…

Q: -3x <-5. (Enter your answer as a comma-separated list of equations where x and y are Find parametric…

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Q: Find the Solution logx16 = 2

A: Solution: logx16 =2 Apply log rules 1log16(x)=2

Q: Where did the negative 8 come from ?

A: We need to clear the doubt.

Q: 14. d dt t-π²²

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Q: The line graph shows the cost of inflation in some country. What cost $10,000 in 1975 would cost the…

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Q: For f(x) = 8x3, construct and simplify the difference quotient f(x+h)-f(x) h (Type in descending…

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Q: Find the distance between planes x + 2y + 6z = 1 and x + 2y +6z = 10.

A: We know that Distance between two parallel plane ax+by+cz+d1=0 and ax+by+cz+d2=0 is d2-d1a2+b2+c2…

Q: 1. ƒ (x) = 10x² + 6x f 7

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Q: 2 31. x² + y² = 4, z = -1

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Q: Differentiate the function G(x) = 7x−7 + 5x−⁹. Answer G'(x) =

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Q: Write the equation for the graph of g(x) as a transformation of the equation for the graph of f(x).…

A: Write the equation for the graph of gx as a transformation of fx in the form of y=afbx-h+k

Q: The velocity v of blood that flows in a blood vessel with radius R and length / at a distance r from…

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Q: 2. R(z) = = -5/3 – 4z³/ - N Hint: Simplify.

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Q: 13. Differentiate the following functions: a)y=e(cosx+sinx) b)y=(x²)2* c) y= tan’(cosx)

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Q: Find an equation of the line where the planes Q and R intersect. Q: - 2x + 3y - 4z= 1; R: x+y+z=0

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Q: Find the angle between the velocity and acceleration vectors at time t = 0.

A: Here is the solution:

Q: O True L

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Q: 10x + 5x2 to answer the following questions. Note the denominator factors as (3x+1)(x+2) 3x² + 7x +…

A: Given: g(x)=10x+5x23x2+7x+2

Q: Complete the table and investigate the limit. lim (x + 4) X-3 X f(x) = x + 4 2.9 x approaches 3 from…

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Q: 5. Using the definition of the derivative, find the slope of the tangent to the given curve at the…

A: (a) y=2, (1,2)from defination of derivatives f'(x)=limh→0f(x)-f(x+h)h

Q: If f(x) = 3x + 4 and h(x) = 3x2 + 3x + 1, find a function g such that f ∘ g = h.

A: Find function h

Q: Solve this differential equation: dy dt y(0) = 2 y(t) = 0.06y(500 - y)

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Q: -6(-4) - 3(-7) + 5(-5) =       5(-4)+ (-2)7 - 8(-4)      5(-4) + (-17) + 9 – 6(-3) =

A: see below the answer and calculation

Q: If 3x − 4 ≤ f(x) ≤ x² − 3x + 5 for x ≥ 0, find_lim_f(x). - - X→ 3

A: Given 3x - 4 ≤ f( x ) ≤ x2 - 3x + 5limx→3f( x ) = ?

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 7 Lim ( √√² + 1 - 7) t→0…

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Q: d Use the Product Rule to find the derivative [(x + 2)(5x + 6)]. dx Answer

A: The objective of the question is evaluate the derivative using product rule.

Q: A missile is fired from ground level with an initial velocity of (0) - (1000, 1400, 368) measured in…

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Q: 30. f(x) = 4 — x², - a = -1

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Q: Formulate a system of equations for the situation below and solve. A manufacturer of women's blouses…

A: A manufacturer of women's  blouses makes three types of blouses: sleeveless, short-sleeve, and…

Q: A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of…

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Q: Solve y'= 10xy - 2x, y(0) = 5 y(x) =

A: To solve the following initial value problem. y'=10xy-2x, y0=5

Q: (a) Compute the following values. f(0) = 100 f(10) = 75 Amazing work! Amazing job! (b) How many days…

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Q: Graph the function and then find the specified limits. If necessary, state that the limit does not…

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Q: -2 8- y = f(x) y=√√√x+1 y = 3x - 23 P(9,4) 13 What is the right-hand derivative of the given…

A: Solution: y = 3x -23 limh→0+f(9+h)-f(9)h

Q: Consider the function f(x) = 5x³ + 3x² + 8. For what values of k does the Intermediate Value Theorem…

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Q: Given that f(x) = x³h(x) h(-1) = 4 h'(-1) = 7 Calculate ƒ'(−1). Hint: Use the product rule and the…

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