3. Consider the problem of finding the point (s) on the plane 2x - 2y-z = 36 closest to the origin. This problem will be solved using the method of Lagrange multipliers. Do not use a different method for this problem.

Q: 4. Evaluate the iterated integral: LIE dyda.

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Q: 1. Find the solution of the initial value problem y" + y = 8(t− n) +8(t−2π), y(0) = 0, y'(0) = 0.

A: By Laplace transform

Q: Given f(x)=16x+8 Find ¹(2). Write your answer as a whole number or as a fraction. f¹(2)=

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Q: - 4 Y 5 Let & be the line with symmetric equations =-z-4. Let P be the point (1, 2, -3), which is…

A: Point normal form of a plane . If normal to the plane is n→ and a point on the plane is a→ then…

Q: Find a basis for the plane x -2y + 3z = 0 in R3. Then find a basis for the intersection of that…

A: Given an equation of plane x-2y+3z=0. To find the basis for the plane x-2y+3z=0 in ℝ3. Here vectors…

Q: Find the flux of the vector field F = (0,0,-2) across the slanted face of the tetrahedron z = 1-x-y…

A: Given: F=0, 0, -2 , z=1-x-y To find: ∬S F·n dS=∫∫R dA

Q: The solution of the system x - 4y +z = 9 A B C D y 3z = -1 - x = 11m +5, y =3m +1, z = m, None of…

A: Answer  The solution of the system  x-4y+z=9 y-3z=-1 When we solve we found that option D correct.

Q: d =489 dx Where operator D = Find the GS of (D+1)³y = ex

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Q: 1. Given that f is the function defined by f(x, y) = 2¹+y²-²-2y, determine the relative extrema of f…

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Q: What is the slope of the given slide? The slope of the slide is (Type an integer or a simplified…

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Q: 19- y" + y = 0 y(0) = 1 find the value of OA) 0 OB) -2 OC) 2 OD) 1 OE) -1 Y().

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Q: Compute the simple interest INT for the specified length of time and the future value FV at the end…

A:

Q: Given f(x)=18x-9 Find the inverse ¹(x). F¹(x)=

A: Inverse of the function

Q: (a) (b) Prove that 2n²-3n+7 € O(n²) by constructing a c>0, non no : 2n²-3n+7 0, no 20:3n > no…

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Q: Solve the following Exact ODE

A: This is a problem of DE.

Q: A diver is standing on a platform 28 feet above a pool. Their jump to the pool can be represented by…

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Q: Q1: Given that totient (337) is 336, what is 69^673 (mod 337)?

A: Here in question totient function is used it is nothing but same as eular phi(∅(n)) function which…

Q: What lump sum do parents need to deposit in an account earning 12%, compounded monthly, so that it…

A: Let, the needed deposit is $P. Then, at a rate of 12% per annum compounded monthly, the lump sum…

Q: 1. In a room there is a series of four light switches. How many on/off positions can these four…

A:

Q: What is a derivative table?

A: What is derivative  table ?

Q: 5. Consider the tetrahedron in the first octant (where each coordinate is positive) bounded above by…

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Q: an = 2n dn= (n)² २

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Q: 3. Find the area bounded by the curve a² + 4y = 4, its tangent (1,7). and the x-axis.

A: !st we need to find equation of tangent line to the given curve at given point , then  draw the…

Q: f" (ro) = lim Δr-10 2f(xro - Δ.) + 2f(xro + Δz) + af(x0) b(Δ.)2

A: The given equation is, ⇒f''(x0)=lim∆x→02f(x0+∆x)+2f(x0-∆x)+afx0b∆x2. To Find: The values of a and b.

Q: 3. Let R be the region enclosed by the curve r(t) 27. Find the area of R. You may = (5 cost, - sint…

A: Given: r→t=5cost, -sint+cos4t , 0≤t≤2π To find: Area of R.

Q: What is a derivative table?

A:

Q: 1. For each of the following, is it an equivalence relation? Prove or provide a counterexample. (a)…

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Q: 2. Consider the surface S₁ with equation 2² -4 = 22. a) Sketch the graph of S₁ in R³. Indicate…

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Q: e 1. Consider the surface defined by z = x² + eln(x - y). Let f(x,y) = x² + ³y ln(x−y). (a) Compute…

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Q: Given f(x)=x+2 Find the inverse f¹(x). Use fractions in your answer. f¹(x)=

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Q: Find the center mass of the solid bounded by planes x+y+z= 1, x = 0, y = 0, and z = 0, assuming a…

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Q: 81. Pharmacology When a drug is administered orally, the amount of the drug present in the…

A: The graph of a function is the collection of ordered points (x,y) in the cartesian coordinate system…

Q: Consider the series [₁ n=1 Compute an where In this problem you must attempt to use the Ratio Test…

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Q: Which of the following graphs have hamiltonian circuits? E OA Y C Z R U B M R

A: Given graphs are: We have to explain which of the graphs have a Hamiltonian circuit.

Q: The sultan has 100 prisoners and 100 prison guards. Today is the Sultan's birthday and he wants to…

A: Given there are 100 prisoners and 100 guards. On sultans birthday sultan want to free some…

Q: 4. Urn R contains n red balls and urn B contains n blue balls. At each stage, a ball is selected at…

A: Given Data: To show that the mean number of red balls in urn R after stage k is 12n1+1-2nk

Q: In Exercises 7-10, calculate the relative frequency P(E). 7. Two coins are tossed 50 times, and two…

A: Two coins are tossed 50 times and two heads come up 12 times.   Let E is the event that at least one…

Q: (1 point) Let f(x) = 22. Find (a) the intervals on which f is increasing, (b) the intervals on which…

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Q: The annual domestic revenue (in billions of dollars) generated by the sale of movie tickets can be…

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of…

Q: 5. What is the Laplace transform of the given function f(t) = cos³ (t)? 3 S - . 4 s² +9 A) F(s) B)…

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Q: If u = 2 + i and v = 2 - 2i, then what would v be expressed in exponential form? Once found,…

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Q: SSF F = (3ry?, re*, z3) S is the surface of the solid bounded by the cylinder y2 + z² = 9 for 3 ≤ x…

A: Given: F =3xy2 , xez , z3 , y2+z2=9 , 3≤x≤4 To find: ∬S F ·dS

Q: Use a proof by induction to prove that for all n EN, 1+3+5+...+(2n-1)= 1 (2j-1) = n². 9. (9 n², that…

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Q: The population of India can be modeled by the function P(t) = 1462(1 + 0.0177) where P(t) measures…

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Q: Given f(x)= x)==-3x+5 Find f¹(3). Write your answer as a whole number or as a fraction. f¹(3)=

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Q: 5 Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), −5 ≤ t ≤5 b) r(t) = √2ti +…

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Q: Select the row of A and the column of B whose dot product is the entry AB5,4 in the product AB. J 1…

A: Two matrices can only be multiplied, if the number of columns of the multiplicand matrix is equal to…

Q: = Given: A is a symmetric 3 x 3 matrix with eigenvalues 1 and 4 and corresponding eigenspaces E₁…

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Q: In Example 2 we saw that Airbus A330-300s seat 330 passengers and cost $250 million each, Boeing…

A: Given that  Airbus A330-300s seat 330 passengers and cost $250 million each, Boeing 767-300ERs seat…

Q: A sample of a radioactive substance has an initial mass of 761.7 mg. This substance follows a…

A: