Find the directions in the xy-plane in which the function f(x,y) = 6 - x² - y² has zero change at the point P(1,2,4). Express the directions in terms of unit vectors. What is the unit vector in a direction of zero change with a positive x-component? 10 (Type exact answers, using radicals as needed.) What is the other unit vector in a direction of zero change? (10 (Type exact answers, using radicals as needed.)

Q: Solve the following system of equations by elimination. 4x=2y+10 2x - y = 5 O (3,1) The system is…

A:

Q: exact value of cos (-15)

A:

Q: Find an angle in each quadrant with a common reference angle with 154º, from 0°<0<360° Quadrant I:…

A: An angle made by the terminal side of the given angle with the -axis is called the reference angle.

Q: t=a v= t = 1 t = 2 t = 3 v = || V = m/s m/s m/s m/s

A:

Q: -7 -6 -5 -4 -3 1 2 3 J 4 5

A: We have a graph of f(x)We have to sketch graph of f'(x)

Q: A large corporation borrows $750,000 to expand its product line. Some of the money was borrowed at…

A: To find the money borrowed at 8% intrest.

Q: Consider the following. f(h, k) = (32h³ + 15h² - 10h + 47) (43k +15) when h = 4.3, k = 3.5, and Ak =…

A:

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

A:

Q: Florida Faculty of Science Determine the volume of the solid obtained by rotating the region bounded…

A:

Q: The temperature at point (x,y) on a metal plate is T(x,y) = 144x² - 144xy +36y². An ant on the plate…

A:

Q: ta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago (t = 0)…

A:

Q: Solve the following system of equations in terms of x: (1) x-3y+z= -2 (2) -4x+9y=7 * Student can…

A: NOTE: Refresh your page if you can't see any equations..The given system is,

Q: Given the complex number 2₁ 30 (cos 17+ i sin 177) and 10 10 22 = 5 (cos+ i sin ), express the…

A:

Q: 5. The position function of a particle is given by s (t) = t³ - 6t² + 9t, 0≤ t ≤ 4. Position units…

A: NOTE: Refresh your page if you can't see any equations..The given position function is,To find the…

Q: NYY - BOS In 3 hours FI Solve the following system of equations: (1) 2x-y+z=3 (2) 7x - y - -z = 8 2…

A: To solve the given equations.

Q: Find the length of side x in simplest radical form with a rational denominator. Answer: x = X 60° √8…

A:

Q: Which of the following is the magnitude of a vector whose initial point is (0, 0) and terminal point…

A: Let, A=(0,0) and B=(5,0)

Q: a) The cost of first-class postage stamp was 6¢ in 1961 and 66¢ in 2010. This increase represents…

A: “Since you have posted multiple questions we will solve the first three subparts for you. To get the…

Q: Solve the following system of equations: (1) -x+2y+ 6z=10 (2) -10x+20y+ 60z = 100 O Ø (the null set)…

A:

Q: Perform the indicated operations and simplify the expression. (8 - 4x)²

A: Perform the indicated operations and simplify the expression.(8 - 4x)2

Q: Find the derivative of the function. y = sin−1(cos−1(t))

A:

Q: 2) x² + x²³₂²2²-√²³=5πe b) xsiny-y(os₂x = xy C) (os(xy) = sin(xy) 3.2

A:

Q: The following set of equations has how many solutions? y+ x² = 4 y-x=4 3 O infinitely many 0 1

A:

Q: Perform the indicated operation and simplify the expression. 4x + 7 x²-9 X 3-x +

A: The given expression is,

Q: 7. If y == f(x²), ƒ' (4) = 3, ƒ (4) = 12, then y′(2) = a. 0 8. If y=x then y' (4) = a. 2√2 2 + In 2…

A: Firstly use differentiation property both side

Q: Find the locus of the midpoints of chords of hyperbola            3x2-2y2+4x-6y=0  parallel to…

A:

Q: The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t) =…

A:

Q: For the following vector v, find |lull, the unit vector with the same direction angle as v. V = -25j…

A:

Q: X = 4x²9x + 2 = 0

A:

Q: Find an equation for the tangent line to the curve y = x-1/3 at the point (8, 1/2).

A: curve : y = x-1/3point : (8, 1/2 )

Q: Evaluate O x3+4x²+ 6x Select the correct answer below: -1 2² ) ) + 0 O (2 In [x]-In (x² + 4x+6) +…

A: Given thattaking firstly using the partial fraction decompositionon comparing the like terms

Q: Find My My, and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.…

A:

Q: Evaluate JJJ y² dV, where E is the solid hemisphere x² + y² + z² ≤ 4, y ≥ 0.

A: We find the given integral value using spherical coordinate.

Q: Convert the rectangular coordinates (9, -3√√/3) into polar form. Express the angle using radians in…

A: Lets find the angle using radians in terms of pi over  the interval .

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: ,

Q: Write down the first five terms of the following recursively defined sequence. a1 = 3; an+1 = a1 =…

A: ................(1)

Q: Evaluate the line integral, where C is the given space curve. Sc(+2. (x² + y² + z²) ds, C: x = t, y…

A:

Q: 21 A father makes a deal with his son regarding his weekly allowance. The first year, he agrees to…

A: Given:We are required to find:

Q: Solve and graph 12x² <7x+10

A:

Q: Σ n=1 4n2 + 6 8n1 + n + 1

A:

Q: What is f'(x) when f(x) = log5 x cos x 7x²+2x+7

A: Here we are given that f(x)=we need to calculate f'(x)

Q: Which of the following limits is equal to f1(x) (i.e. derivative of f), where f(x)=√x² +1 − 2x lim…

A:

Q: 4. The inverse function of y=x²-2x+2 is ƒ'(x)=-1+√√x-1 c. f¹(x)=-1+√√√x-1 2 5. cos¹ (cos 8. x2-1 721…

A:

Q: Determine whether the following series converges or diverges: n=1 2n 1 n+1

A: Consider the series .If is non-zero or does not exist, then the series diverges.

Q: Solve the initial boundary value problem for the given heat equation: u₁ = 3u 00 u(0,1)= u(2π,t) =…

A: The initial boundary value problem of the heat equation is ut = 3 uxx ; 0&lt;x&lt;2πu(0,t) = u…

Q: x² Find the volumes of the solids generated by revolving the region between y = 4√√x and y = about…

A:

Q: D. 22√2) 3 2√3) 9. if f(x) is even function and g(x) is odd function then a. 18 b. 24 (f(x) g(x) +…

A:

Q: -5 -14 -2 Find lim -1- Find lim 2 ●1 #4-1+ J f (x) f(x) Find lim f(x) HI-1 -2 03 -$+ 2 Find f (-1)…

A: Explanation of the answer is as follows

Q: Which of the following is the magnitude of a vector that has an initial point of (-4, -1) and…

A: Magnitude of a vector having initial point  and terminal point  is given by

Q: For the following vector v, find |lull, the unit vector with the same direction angle as v. v = -i +…

A: Given vector,