Find the gradient of the following functions a) F(x,y,z)= x2 + y3 + z4 b) F(x,y,z)= ex sin y ln z

Q: Consider the physical quantities m, s, v, a, and t with dimensions [m] = M, [s] = L, [v] = LT¹, [a]…

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Q: A sphere of radius r has surface area A = 4πr2 and volumeV = (4/3)πr3. If the radius of sphere 2 is…

A: a)The ratio of the areas, A2/A1

Q: a) Write down the metric and the inverse metric, and use the definitionrpµv = 1/2gpσ(δµgvσ + δvgµσ -…

A: The objective of the question is to find the metric and inverse metric for a sphere of radius a, and…

Q: If a varies directly with m and indirectly to x, and a=18 when m=24 and x=8, find m when a=26 and…

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Q: Please answer the following question(s): 1. The vector OP shown in the figure has a length of 9.0…

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Q: Evaluate and express in 3 sig figs 1. 12×10⁶/4 2. (3×10⁶)(8×10^-2) / (2×10¹⁷)(6×10⁵) 3.…

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Q: y h y = b2 h

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Q: 10. Change of basis Let us now construct the vector (matrix representation) for a function g(x) =…

A: Given : g(x)  = -2x+1

Q: dv B (а) = Ar +2, where A and B are constants, v and r are variables. At r = R1, v = dr Vo. At r =…

A: Given dvdr=Ar+Br Where A and B are constant So,…

Q: X(-) 9 5 kips 50° 60° 10 kips 3 Y(+) 0 Y(-) 25° 30° 8 kips X (+) 12 kips 2

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Q: If you were to plot F vs r on a log-log graph what would you expect the slope to be? The expected…

A: Expected relation between  F and r is given as  F=KQqr-2

Q: The height of a hill (in feet) is given by h(x, y) = 18(16 – 4.x2 –- 3y² + 2xy + 28x – 18y) where x…

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Q: 2. (a) Add 3.53103km and 4.53105m, express your answer in m with correct number of significant fig-…

A: 1st value 3.53103× 103 = 3531.03m 2nd value 4.53105m

Q: M Y Z N

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Q: Determine the following for a point with the rectangular coordinates (1.060, 2.930) m. (a) the polar…

A: Rectangular coordinates of a point = (1.06, 2.93) m to find : polar coordinates of this point

Q: An object is dropped from a height of 22 meters. Ignoring air resistance, how long until the object…

A: The objective of this question is to find the time it takes for an object to hit the ground when…

Q: Evaluate the integral. 5/t +² 2 dt

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Q: H'(0) = H"(0) =

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Q: Let u = (-7,3,-5) and 7 = (-1, 1, 0). Compute the following: ū x v- vx u u xu -9 (u × v) = u x (-97)…

A: The objective of the question is to compute the cross product of the given vectors in different…

Q: Simplify the expression（1+cotx）（1-cotx）-csc square x

A: The mathematical expression is given as  f(x)=1+cot x1-cot x- cosec2xThis mathematical expression is…

Q: Problem 3: A 500-kg dragster accelerates from rest to a final speed of 110 m/sec in 400 m (about a…

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Q: The primary dimensions of the constants (a, b) given in the equation F(y) = V (by – ab) are equal…

A: The unit of a quantity in terms of dimension is defined as MxLyTz Here x,y and z depend on the unit…

Q: Find the mass of the solid bounded by the planes x+z=1, x-z=-1, y = 0, and the surface y=√z. The…

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Q: FIG. 1. A displacement vector in the ay plane. A displacement vector in the ry plane is 15 m long…

A: The displacement vector resolve into two components X andY.

Q: Take two values, say 1 and 2 and use the relationship V(B) -V(A) =-SĒ dš

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Q: Given the following integral SV2-25 ox Determine the Trigonometric Substitution formulas that need…

A: The given integral is: I=∫x2-25dx Trigonometric relation used is: tan2x+sec2y=1 The given integral…

Q: Using the rules of significant figures, calculate the multiplication of A = 48.399 and B = 0.849:

A: To multiply A = 48.399 and B = 0.849 using significant figures, we follow these steps: Count the…