PROBLEM 1: A spherical balloon is filled through an area A₁, with air flowing in at a velocity of V₁, and constant density p₁. The radius of the balloon, R(t), can change with time, t. The average density within the balloon at any given time is pb (t). Determine the relationship between the rate of change of the density within the balloon and the rest of the variables.

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A: Given matrix:   We have to find the value of  such that is singular.

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Q: Which of the following notations given below is NOT equivalent to ? ni Note: There is a 'double-dot'…

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Q: 17. Describe the surface that has the following parametrization, and com- pute the Jacobian…

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Q: 段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI…

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Q: Use the graph to state the absolute and local maximum and minimum values of the function. (Assume…

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Q: 1. Let {v₁,..., Vn} be a linearly dependent set. Prove that there exists some j with 1 ≤ j<n such…

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Q: For n ≥ 1. Suppose u ∈ C^2(Rn ×[0,∞)) solves the heat equation u_t − ∆u = 0. Let u(x, t) =…

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Q: Nice! You have shown that L(y) side of this equation. L(y) = = 7+3s s(s+2) Find the partial fraction…

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Q: Let f: R³ R be the function defined as x² + y² + 2², -p+212 f(x, y, z) = if (x, y, z) = Q³,…

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Q: ♡ Determine if w= 2 is in Nul A, where A = 1 -4 5 7 -1 -19 -7 1 19 Is w in Nul A? Select the correct…

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Q: Let f be the function whose graph is given below. (a). Use this graph to find the largest number &>…

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Q: 2. In each case, show that there exist constants C and k such that f(x) ≥ Cg(x) for all x > k. Note…

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Q: 6. Find all of the subgroups in A4. What is the o

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Q: For each real-valued sequence, explain whether limn→∞ Sn is convergent, divergent to to, or…

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Q: let glo) be equal to [x] 2202 R x h(x) =1g (f(x)]" them [²+1] is was in contines at x=0 or not?

A: Let   then , we have to check that h(x) is continouos at x =0 or not ?

Q: Sketch the root locus for the characteristic equation of the system for which (s+2) L(s) 3²(x+5) and…

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Q: Consider the quadratic form F(X₁, X₁₂, X 3) = 25X² +34X² +41 X² - - 24 X₂ X3 at while I as = [X²…

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Transcribing the text in digital format

Q: Solve the following linear program graphically. 5X + 7Y (x, y) = Max s.t. 1X ≤ 9 2X + 3Y≤ 18 X + Y≤8…

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Q: 19. Prove that if {A₁, A2,. Ak} is a linearly independent subset of Mnxn (F), then {(A, A₂,..., At}…

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Q: 段階的に解決し、 人工知能を使用せず、 優れた仕事を行います ご支援ありがとうございました SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI…

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Q: A lumber store stocks dowels in one standard length of 150 cm. Each dowel costs $20. A customer…

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Q: 1. Prove or disprove: U(8) Z4

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Q: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. K

A: A contour map of a function is shown :To Find:Use it to make a rough sketch of a graph of f.