Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the volume of the tank is 10 cubic feet, how fast is the height of the water changing?

Q: The function f(x, y) = x² + 2y¹ + 8y² − 4xy² has stationary points at some of the following points.…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Create an equation or problem involving the Slope of a Tangent Line that is equal to 1.

A: Given slope of the tangent line is equals to 1  As we know that slope is denoted by dydx

Q: Question #1 -Let the revenue of a refrigerator be given by the equation R(x)=280x-0.4x² x = number…

A: Given:  Let the revenue of a refrigerator be given by the equation,  Rx=280x-0.4x2 where, x=number…

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: a=-1, 6, 5b=7,4,1

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Q: Find and sketch the domain of the function f(x, y) = In(-yr) √² + y²-4

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Q: The figure shows an open box with a square base. The box is to have a volume of 10 cubic feet.…

A: Given volume of box is 10 cubic feet. Volume of box = Length * Width * Height 10 = x * x * y 10 =…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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Q: Write the equation for the graph shown below. -4 -8 -2 6 -5- 4 3 2 1 4 -2 T 12 34 D

A: Equation of a line.

Q: Find the point at which the line intersects the given plane. x = t - 1, y = 1 + 2t, z = 3 = t; 4x y…

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Q: Q4 Integrate the following: (a) 4ln|x³| + C x3 dx (b)+C 4 (c)++C (d)+C

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Q: Water is leaking out of an inverted conical tank at a rate of 10100 cubic centimeters per min at the…

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Q: Three terms Four terms Five terms Six terms Seven terms Nine terms None of the above

A: Use chain rules then find the partial derivatives

Q: linear algebra Given 7 = 5 2 3 -10 find the closest point to in the subspace W spanned by and 40

A: We are given v,we have to find closest point to v in the subspace w spanned by u1 and U2.

Q: Consider the polar equations r = 1+sin'0 and r= 2 Area = Determine the appropriate values for a and…

A: Consider

Q: Find an equation of the plane. the plane through the point (2, 5, 3) and with normal vector 6i + 9j…

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Q: Question #22 In the following question, D(x) is the price (in dollars per unit) that consumers will…

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Q: Use the shell method to find the volume of the solid generated when the region bounded by: y=(1+x²)…

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Q: 2) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 4.2., # 8) A point on a…

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Q: Q.7. Find the value of the hypothenuse and the value of the angle 0 a) Expressing the exact value of…

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Q: Find the points (x, y) at which the polar curve 4 cos 0, horizontal tangent line. Vertical Tangent…

A: As we know ⇒x=r cos θ⇒y=r sin θHere r= 4cosθThen ⇒x=4cos2θ and⇒ y=4cosθsinθ⇒y=2sin2θ…

Q: Approximate the area under the curve y = x² from x=2 to x = 4 using a Right Endpoint approximation…

A: y=x^2 from x=2 to x=4. We have to find area using a Right end point approximation.

Q: Find a unit vector that has the same direction as the given vector. -6i+4j - k

A: Given vector, - 6i + 4j - k

Q: 41. f(x) = xV9 - x² and g(x) 0

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Q: Consider the following function where a is a positive constant. f(x) = x + a√√x (a) Select the…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: The function f(x) = sin(3x) has a Maclaurin series. Find the first 4 nonzero terms in the series,…

A: This is question of calculus  Here function given  We have to find maclaurian series for that.…

Q: Find the slope at the point (1,2) on the graph of the ellipse defined by 4x² + y² = 8.

A: Find slope at the point (1,2) to the ellipse 4x^2+y^2=8

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = -3x + 6…

A: Equation of the tangent line at the point (a,b) and slope m is  y-b=m(x-a)

Q: Let 7 be the plane given by 3x + y + 2z = 6. (a) Let be given by x = 2+1, y = 3t, z = t. Does…

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Q: Question 2.10c. Consider the following system x + y + z + w = 1; X Y Z W = 1; x + z = 1. Find the…

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Q: Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If…

A: Given forces are F1=350N & F2=600N  We have to find resultant vector R  Let theta be the angle…

Q: Solve that i tick by red pen

A: 2) We know that right angle triangles can be a scalene triangle when the other two angles or the…

Q: Solve 2 sin² (t) - 3 sin(t) + 1 = 0 for all solutions on the interval 0 < t < 2. Your solutions must…

A: given 2sin2(t)-3sin(t)+1=0

Q: Sketch the graph of the function f. √x - 6 -10 O -10 f(x): = -5 -5 -2x + 3 y 10 5 -5 -10 y 10 5 5…

A: According to question,Given Function,fx = x-6if x≤3-2x+3if x&gt;3

Q: Suppose the straight lines L₁ and L₂ have respective vector equations 4 5 9 -5 (99)-0) -3 +t = -…

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Q: For each of the following, decide if Bernoulli's Rule is appropriate for finding the limit. Then…

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…

Q: O-a³-3a²+4a

A: Simplify the same coefficient

Q: If f f(x) dx = 7 and f(x) dx = -7, then f(a) da

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Q: Question #16 - If I wanted to find the average rate of change for a function f(x) between x=2 and…

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Q: 3. Evaluate the definite integral by using the Fundamental Theorem √√x -3x x² .dx

A: ∫16x-3xx2dx

Q: 6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1).…

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Q: To enter cos(x), please type "cos(x)". Evaluate fx sin² x dx. +C

A: I=∫xsin2xdx

Q: Q13 Find the slope at x = 0 on the graph of f(x) = 3x² = 5x + 2xe*.

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Q: The absolute minimum value of f(x, y) = 4xy² = x²y² — xy³ on the triangular region in the xy-plane…

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Q: Minimizing Costs A pencil cup with a capacity of 36 in.3 is to be constructed in the shape of a…

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Q: π Find the equation of the tangent line to x(t) = 6 sec t, y(t) = 6 tant at t = in slope-intercept…

A: To find the equation of the tangent line to xt=6 sect, yt=6 tant at t=π4 in slope-intercept form.

Q: Given f(x)dx = 12 and g(x)dx = -2, find the following: S₂13³f(x) + 2g(x)]dx + f(x) dx O a.) 40 O b.)…

A: ∫-25fxdx = 12∫-25gxdx = -2

Q: A container of hot liquid is placed in a freezer that is kept at a constant temperature of 20°F. The…

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Q: a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation…

A: a. We need to find condition for D.E. to be exact. b. We need to solve D.E. c. We need to solve…