Find the area of the shaded region: 6 y=x²-15 x 64 -128 128 2 20 10 -10 -20- 2 4 y=x 6 X 0

Q: 2 x² dx √4-x² 2

A: Let's solve given integration.

Q: A pool shaped like the bottom half of a sphere is being filled at a rate of 22 cubic feet per…

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Q: Consider the following. lim x4/x X18 (a) Describe the type of indeterminate form (if any) that is…

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Q: Show that (csc(x)) = -csc(x) cot(x). d dx d dx -(csc(x)) H = = d dx sin²(x) 1 sin(x) 1 = -csc(x)…

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Q: ey = 25e4x-z+w 10z - w + 3x = -23 8y + 3w - x -z = 5 x+y-z + 4w = -10

A: The objective is to rearrange the  equations so that their associated matrix is ​​diagonally…

Q: Evaluate the definite integral. 1 lis 0 (5* −_4*) dx

A: solution:-∫015x-4xdx=∫01exln5-exln4dx=exln5ln5-exln4ln401=e1ln5ln5-e1ln4ln4-e0ln5ln5-e0ln4ln4=5ln5-4…

Q: Find the values of the following limit. If a limit does not exist, type DNE in the entry box. x-3…

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Q: dx dt Please give an exact answer. If z³ = x³ + y², = dy -2, = dt dz dt Provide your answer below:…

A: To find derivative.

Q: Oct 23, 9:35:15 PM A particle moves along the x-axis so that at time t 0 its position is given by…

A: Given query is to find interval where speed is decreasing.

Q: A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base…

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Q: Determine the area of the region bounded by two the curves f(x) = x² - 18x +36 and g(x) = 9x + 18.

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Q: A rational fraction of the form g(x) = 0. Select one: O True O False f(x) is called a proper…

A: We know Rational fraction=fxgx, gx≠0

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A: we will find the required.

Q: Answer the following Questions: 1. Evaluate the integral using partial fractions method: ²+1)…

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Q: 1. Find the arc length of the following function 3 - (x² − 1) ² - 2 - 3 1≤ x ≤ 3

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Q: Use a scalar projection (NOT A FORMULA- unless you derive that formula as part of your solution) to…

A: Here we have to find the shortest distance from the point (1,−2,5) to the plane given by…

Q: ← The following table gives the monthly premiums for an insurance policy on people of various ages.…

A: The given data is: age monthly premium       35 127       40 164       45 242       50…

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, 1, -3) and the direction in…

A: Please see the below picture for detailed solution.

Q: What is one solution to the trigonometric equation 3cosx - sinx + 3 = 0 in the interval [0, 2m]? 0 O…

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Q: W 1 2 y concave upward 3 concave downward Determine the intervals where the graph of f is concave…

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Q: For the right triangle below, find the measure of the angle. Please show your answer to one decimal…

A: Given query is to find the measure of the Indicated angle.

Q: 3. The slope of a curve at the point (x, y) is given by 3x²y + 2y. Find the equation of this curve…

A: To find the equation of the curve with given slope

Q: An object of mass 2 [kg] is tossed up with upward velocity 10 [m/sec]. Assume the gravitational…

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Q: In each of Exercises 1-14, D(x) is the price, in dollars per unit, that consumers are willing to pay…

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Q: A particle moves along the x-axis so that at time t > 0 its position is given by x(t) = 3t³ - 27t² +…

A: Given that , xt=3t3-27t2+45t-33 find the total distance traveled by the particle from 0≤t≤6.

Q: What initial investment at 8.5% compounded semiannually for 3 years will accumulate to $15,000?…

A: Let $P amount be invested at r% interest rate compounded semi annually then after t years it will be…

Q: [(5x²³ -2.r²+3)dx

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Q: X y f(x): || 1 2 968 1662 Use exponential regression to find an exponential function that best fits…

A: use the calculator to find the exponential regression in your calculator press STAT select edit by…

Q: Let y (9x+3)(x² - 8)6 Use logarithmic differentiation to determine the derivative. y' = =

A: Need to find out the logarithmic differentiation.

Q: 2x²-2 limx→-1 ²+3x+2 =

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Q: The Total Revenue is decreasing when the demand is elastic and the price is increased slightly. O…

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Q: g(x) = 2 x²_4 3x²+x-4

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Q: Find the linearization L(x,y,z) of the function f(x,y,z) at the given points. f(x,y,z)= ex+cos (y+z)…

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Q: Find the tangent, unit tangent, and unit normal vectors for the curve r(t) = (2t²+1, 2 sin(t),…

A: Given that, r(t)=<2t2+1,2sin(t),ln(cos(t))>We need to find tangent, unit tangent and unit…

Q: Prove that the following differential equation: (1 + x2)y'' + 2xy' - 2y = 0 has the following…

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Q: Find the derivative of the function. -0 f'(x) = f(x) = (2x - 5) 4(x² + x + 1)5 x

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Q: 4. How far from y-axis is the center of the circle 2x² + 2y² + 10x - 6y - 55 = 0? 5. How far from…

A: Given the equation of a circle, 2x2+2y2+10x-6y-55=0

Q: Let C(x) represent the cost and R(x) the revenue, in dollars, associated with producing and selling…

A: Given data÷ C(x) = cost function R(x) = revenue function x = number of units of book C'(30) = 66…

Q: Find the derivative y'(x) implicitly for the equation y' (x)= 4x + 3 y 2x + ³.

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Q: 7x – 4x − X

A: Topic = Integration

Q: Evaluate the definite integral. JO In 2 tanh x dx

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Q: A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 L/min. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: Find the distance the Point PC9₁-6, 37 is to lline through the two Points. 1Q (5-=-= 3,01 and R…

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Q: 7x sin²(x) dx =___________ (Apply integration by parts method) O 7x tan(r) 7x cot (x) 7x In(sin(x))…

A: Topic = Integration

Q: Find the equations of the tangents to the curve x = 9t2 + 9, y = 6t3 + 3 that pass through the point…

A: To find the equation of tangents to the given curve.

Q: A function f (x) is continuous at x = a if: 1.a is in the domain of f (x) II. lim f(x) exists x→a…

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Q: 2. Let a be a real number, and consider the function h: (-∞, a) U (a, ∞) → R defined by h(x) A. The…

A: The limit of a function f(x) at x=a exists if and only if the right hand limit and left hand limit…

Q: If S (x − 1) (x − 3)(x + 7) 10 3 7 1 Adx de = [ 2015 ] dx + X 3 Bdx x + 7' then A+B =

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Q: limx→3 0 4 01 O O 3-x 4-√√²+7 O None of the above

A: We need to find: limx→3 3-x4-x2+7

Q: Evaluate the function for the given values of x. h(x) = Part 1 of 5 3 for -3 <x<-2 2 for -2<x<-1 1…

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