Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and b. (a x b) a (a x b) b =

Q: 8. A bead slides down the curve xy 10. Find the bead's horizontal velocity at time t = 2 s if the…

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Q: Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If…

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Q: For the ellipse equation: 4x^2 + 9y^2 = 36 find the center, vertices, foci and graph it.

A: The given equation of ellipse is:4x2+9y2=36x29+y24=1

Q: Revenue The following spreadsheet gives annual production costs and profits at Gauss-Jordan…

A: To find the revenue in each sector in each year.

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A: The definite integral is ∫08225256-s2ds To evaluate: The value of the definite integral. Formula…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12…

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Q: Write the parametric equations for the tangent line to the curve of intersection of surfaces…

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Q: 6. Compute dy where xy = dx cos(x+y)-y x cos(x+y)+y x cos(x+y)-y x-cos(x+y) cos(x+y)+y x+cos(x+y)…

A: The equation is given by xy = sinx+y To determine: The expression of dydx.

Q: Find the derivative of y = x²ª dy/dx =

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Q: O stretch horizontally by a factor of 9, then shift down 6 units O shrink horizontally by a factor…

A: We will find the required

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

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Q: Differentiate. Please use positive fractional exponents of lowest terms rather than decimals in your…

A: y=-8t+6t5+9t6d dt(tn)=ntn-1

Q: f cos 4x√sin 4x + 1dx. O-(sin 4x + 1)³/2 + C O(sin 4x + 1)³/2 + C O-(sin 4x + 1)-¹/² + C O(sin 4x +…

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Q: Find the distance between the skew lines: z = 2 - 9t x = 6 +8t, y = 1+9t, x = 2-t, y = 8, z = 1+8t…

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Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

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Q: Find the critical points in the domain of the function f(x) = 8x³ - 7x.

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Q: evaluate using integration by parts

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Q: 9. f sin(In x) dx

A: The given integral is Sin(ln x).

Q: The region Rin the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y = x² + 1.…

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Q: For the function f(x) = e2x + 4x3 defined for all x ∈ R. Show that there is an inverse function for…

A: An inverse of a function exists if it is both one-to-one and onto. Inverse of a function f is…

Q: 2. (3-3Sin2x) dx seczx (cox-six) 1

A: We have to solve the given integration.

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Q: The curves F1(t)= (-4t, t², - 2t5) and F2(t) = (sin(3t), sin(2t), t - *) intersect at the origin.…

A: The given curves are:r1→(t)=-4t, t2, -2t5r2→(t)=sin(3t), sin(2t), t-π

Q: Determine the sum of the convergent series below. n=1 24n201-n

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Q: The total profit (in dollars) from the sale of x skateboards is P(x) = 30x – 0.3x² -250, for 0 ≤ x ≤…

A: Given Profit function:- Px=30x-0.3x2-250

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Q: fxex² sin x² dx

A: Given: ∫xex2sin(x2)dx

Q: b.) Tim X-8 X x - 8 √6-√x ² 2

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Q: K Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation…

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Q: Let R be the region in the first quadrant bounded by the graph of y vertical line z=1? A B (С) D T…

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Q: Q Search mail Given the function f(x) = -4x² Find the difference quotient f(x+h)-f(x) h f(x+h)-f(x)…

A: answers are in step 2.

Q: For each function a) find the critical points/numbers, b) intervals of increasing/decreasing c)…

A: Given function:- fx=3x2-4x+6

Q: 4. (a) Show that the function f(x) = Σ Σ (b) Show that f(x) = e*. m! is a solution of the…

A: (a) The given data is: Show that the function fx=∑n=0∞xnn!  is a solution of differential equation…

Q: Let F(t) = (²-2, 4e4t, 5 sin(- 5t)) Find the unit tangent vector T (t) at the point t = 0 0₁ T(0)=<…

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Q: Evaluate the given expression. Take 0-2 40-0 and C = 1 4A + 0.5C P 1 1 -1

A: We have given A=0-2-2021 and c=1-111-1-1

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Q: The position function of a particle is given below. s(t) = t³ + 6t² − 33t, t ≥ - 0 When does the…

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Q: Evaluate the iterated integral ] [18x²y³ 18x²y³dy dx.

A: A detailed solution is given below.

Q: A water tank is created by revolving the graph y=1/x about the y-axis, with the v(h) = √ ^ 72 dy.…

A: A water tank is created by revolving the graph y=1x about the y-axis with the bottom of tank at y=1.…

Q: Linearize ​f(x)=2−x for a=1 and use it to approximate the value of 1.8.

A: Given function is f(x)=2-x  for a=1

Q: Consider the function f(x, y) = 2ye" and the region R = {(x, y)|0 ≤ x ≤ 1,0 ≤ y ≤ x³}.

A: Given: f(x,y)=2yex7

Q: Determine the slope of tht line through the given points. (-7,-1) and (-5,9)

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Q: For each function a) find the critical points/numbers, b) intervals of increasing/decreasing, c)…

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Q: I. INTEGRATING FACTORS BY FORMULA 2 1/2 x 2x/x-2

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Q: y=2x R y=x²

A: To write an iterated integral for ∫R∫dA over the region R described  in the figure below. (a)…

Q: 4. In order to receive full credit you must show all of the steps you took to arrive at your answer.…

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Q: 1. Find the equation of the line: a. With a slope of-through the point (6,4) b. Through the points…

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