Find the dimensions of a rectangle with an area of 144 square feet that has the minimum perimeter. The dimensions of this rectangle are ft. (Simplify your answer. Use a comma to separate answers as needed.)

Q: If the statement is true, write "T" in the box on the right, which the statement is false. The limit…

A: As  per the guidelines I am supposed to solve three sub-parts of the given problem.

Q: An object is moving along the parabola y² = 18(13 - x). When the object is at the point (-1,6√7),…

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Q: Find the center of mass of a thin plate of constant density & covering the given region. The region…

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Q: Every quotient group of an abelian group G  is abelian but converse is not true.

A: Every quotient group of an abelian group G is abelian but converse is not true.

Q: Let TEL(V). If S is a 7-invariant subspace of V must there be a subspace T of V for which (S, T)…

A: In linear algebra, a T-invariant subspace of a linear operator T on a vector space V is a subspace W…

Q: Solve the initial value problem y' y(2) = 3. = 2 - xy 2 y with help (equations)

A: We have to solve the initial value problem y' = (x2 - y2)/xy with y(2) = 3

Q: Proof: For any n ∈ Z, 3 | (n3 - n)

A: We see,       n3 - n = n(n2 - 1)                 = n(n - 1)(n + 1)  Now, there may be three cases.…

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Q: Suppose y = Σ and" on an open interval I that contains the origin. Express the following as a…

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Q: Let f(x) = 0 if x < -5 3 if -4 if 0 and g(x) = f(t)dt T -5 -5 ≤ x < 1 1<x<5 if x ≥ 5 Determine the…

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Q: Find the norm of f(x) = √√1-x² on the interval [- 1, 1] . √3 a|m O 2 P 3 2√3 3 2

A: A norm is a function that assigns a non-negative length or size to each vector in a vector space.…

Q: Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 12z) k C is the line segment from (3, 0,…

A: Introduction: To find the potential function for a given vector field first use the derivatives and…

Q: 1. COMPUTE USING FLOATING POINT MATH поїхаж Х 23 AND 1.1x23 - liolxay www

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Q: 5. Calculate the divergence of F = (7x², 9y, -52).

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Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

A: t (years) Length (mm) 0 88 4 93 8 99 12 103 16 108 scatter plot: t=0 for year 2000.…

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Q: Compute the curl of F = (3y2, ay, 22).

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Q: Evaluate the iterated integral O 4 sin (2) 01 cos (4) O 3-3 cos (4) 01 3 2 - 2 sin (2) 0 sin (x²)…

A: Given integral is  ∫02∫06∫0sinx2 x dz dy dx…

Q: Salicylate is active in aspirin. The following table shows the amount of salicylate in the…

A: Time (min) Salicylate (mg) 0 200 20 177 40 157 60 144 80 123 100 114 120 99

Q: classify the following sequence 28, 21, 15, 10, 6, ...........

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Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x − y, 5y − x), B' = {(1,…

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Q: Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformation T: R→Rm…

A: (.)   Define linear transformation                       T : ℝn → ℝm  by   T(v) = Av . where   A =…

Q: Let f be a positive, continuous, and decreasing function for x ≥ 1, such that a = f(n). Note that if…

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Q: dw r = u = w-wr, and dr u -r + rw. (a) What are the (non-zero) nullclines for this system? w = (b)…

A: Given Data: Let us consider the given  system is, dwdt=w-wrdrdt=-r+rw

Q: b) Show that if o is a written as a product of disjoint cycles 0₁,...,0 of lengths 1₁,..., lk. Then…

A: Given, f is written as a product of disjoint cycles f1,f2,f3,.....,fk of length r1,r2,r3,.....,rk.…

Q: 13. Find a unit normal to the surface cos(x,y) = (² e-2 at (1, 7₁0).

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Q: Are there more than one potential function for F? Explain why or why not.

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Q: f $2000 is deposited in a savings account that earns interest at an annual rate of 4.5% interest…

A: The formula for continuous compounding is given by:         A = Pe^{rt}

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Monty Find two other…

A: To obtain (r,θ) ; move θ first then move r units in the radial direction of θ. If θ  is positive…

Q: A stock increased in value 400% over the past 3 years. This was an increase of $1,240. What was the…

A: Stock increased is 400% over the past 3 years. Increase of $1240. The formula used is: Percentage…

Q: Suppose you know that ƒ(x) = |x| = ¼ − ½ Σn=1 (2n-1)² cos [(2n − 1)x] for all x € [-^, π]. - π² Use…

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Q: The function f(x) ∞ f(x) = CnX¹. = CO= 6x arctan (3x) is represented as a power series n=0 Find the…

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Q: Determine {f}, where f(t) is periodic with the given period. Also graph f(t). f(t)=t, 0<t<1, and…

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Q: On paper, sketch the solid obtained by rotating the region bounded by y=z³,z=1, and y=-1 around the…

A: Volume ≈∑πR2Dx=∑π{x3-(-1)}2Dx=∑π(x3+1)2Dx

Q: Problem 5. and Define transformations 7 and p on R² = {(x, y): x, y = R} by T(x, y) = (y,x) p(x, y)…

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Q: FA тов FB Find the magnitude of the resultant force (FR) and the angle (6) it makes measured…

A: Since you have posted multiple questions according to company rule we are supposed to provide…

Q: An investor is presented with a choice of two investments: an established furniture store and a new…

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Q: order 12 in the symmetric group S4 on four elements. Find the elemen

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Q: the question says without using Cauchy Riemann equations.

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Q: a) Find eigenvalues og eigenvectors to the matrix -1 2] A = 0 2 0 b) Diagonalize matrix A if…

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Q: etermine whether the following individual events are independent or dependent. Then find the…

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Q: Consider the following line integral. $² xy dx + x²y³ dy, C is counterclockwise around the triangle…

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Q: Question #3. Find convolution f * g when f = sint and g = t. Also verify that L{f} x £{g} = £{f*g}.

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

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Q: 2. Prove that the chromatic number of K3, 4 is 2.

A: I have explained everything with in the solution, please go through that.

Q: The effect of adding p to a vector is to move or translate the tip (endpoint) of 7 in a direction…

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Q: Use Stokes Theorem to evaluate F = (+22)i F = (²+20)i + ( 3 0 0 1 SF. C (1,0,0), (0,1,0), (0,0,1)…

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Q: suppose Σ 00 α n=0n on an open interval / that contain the origin. Express the following as a…

A: Differential equations

Q: (b) Your nullclines divide the phase plane into four regions. Give a sample point in each region,…

A: Given Data: Let us consider the given  system is, dwdt=w-wrdrdt=-r+rw