(f) Consider the functions y= V7 and y = r² on 0

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Q: Solve using separable first order different equations? Solve for K of YEAR 1990-2000 Population…

A: We need to find the value of K for the term 1990-2000.  So our starting or initial year is 1990. The…

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Q: 43. Let {rn}-1 be a bounded sequence and {y„}=1 be a sequence tending to 0. Pro that x„yn → 0.

A: We have given that , xn be a bounded sequence. Also , yn be sequence tending to 0. We need to prove…

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A: We have to find the day when the rabbit dies.

Q: What is the field of fractions of Z[x], the ring of polynomials with integer coefficients?

A: Please check the answer in next step

Q: Find the Fourier Sine series of the function f(x) = 1, x € [0, 7]. f(x) = cos x, x E [0,7] (i) (ii)

A: (i)  We have given , f(x) = 1  , x ∈ 0 , π We know  that , Fourier sine series of fx on 0 , L given…

Q: 5. XCt) Ct +2)Sin Ct - 4) %D

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Q: Evaluate In [(1+ i)']

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Q: A" A is invertible if and only if A has linearly independent columns.

A: ATA is invertible if and only if A has linearly independent columns.

Q: 2. Suppose T : R³ → R³ is a linear transformation where the images of the standard basis are 3 T(e1)…

A: We have to find the standard matrix for T and we have to find T321

Q: 14. What does it mean that a sequence {xn} tends to infinity?

A: What can we say if the sequence tends to infinity .

Q: Find the solution of the following heat conduction problem using the variable separation method. ôT…

A: The given problem is to find the solution for the given heat conduction problem with given initial…

Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,

Q: You decide to quit using your credit card and want to pay off the balance of $9,600 in 4 years. Your…

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Q: Find the area of the shaded region. r = V cos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find the area under the curves r=cos 2θ and r=9 cosθ

Q: 32 Find the z values for each of the following x values for a normal distribution with mean = 16 and…

A: Give in question  Mean  = 16 Standard deviation =sd =3

Q: Use Limit Comparison Test to find the condition on p that determine the convergence or divergence of…

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Q: Exercise II.43. Let A be the transformation S4+.+ • T(4,2,0) · What is A((0,0,0))? Give the 4 x 4…

A: Since A takes the point from R³, so the representation matrix will be of order 3×3. For the deatils,…

Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

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Q: The local computer store has the following ad placed at their doorstep: We do not ensnare our…

A: The local computer store says, they will divide the price of their product by 13. And the customer…

Q: for the curre y=: f(n) = n*, 0 sM 32 find the curve'slength given by: 1. 2 It dn

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Q: A - (BUC) = (А — В) n (А — С) (A – B) UC ) Option 3 O Option 4 (А - В) U (A — C) (А — В — С) Option…

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Q: Given the z value, find the are unde the normal curve for the given parameter: To the right z = 0.97

A: Given: z=0.97 To find the area under the normal curve

Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: Q2: (a) Determine which of these functions are injective, surjective, and bijective. The function f…

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Q: 1. (a) Sketch the set S of points in the complex plane satisfying the given inequality. Determine…

A: We will find domain and then  draw region of each in equation to find type of region

Q: yct)= sin 2t cos 34

A: Given: y(t)=sin2t cos3t

Q: If x = P(7, 4), y = P(8, 4), and z = P(8, 3), arrange X, y, and z from smallest to greatest. O x, y,…

A: We know from permutation formula,       P(n,r) = n! / (n-r)! and n! = 1*2*3*..….......*(n-1)*n…

Q: 4. In the differential equation (6x-3y+2)dx-(2x- y-1dy=0, we let the substitution dx =

A: According to guidelines we solve one question.thanku

Q: OLet W, X, Y, and Z be invertible square matrices. Show that if WY = YW, then det Y det(W Z –YX)

A:

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(r – 1) +2" – r has a critical number between…

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Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

Q: Give an example of a sequence of real numbers {xn}® such that its limitpoint set is just the set of…

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Q: Assuming that no one has more than 1,000,000 hairs on the head of any person and that the population…

A: We can use Pigeonhole principal to answer this question.

Q: Questión 2 (a) Consider the following initial-value problem dy +3y= 2r +1, 1siS2, y(1)=5. Use…

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Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

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Q: Please do Exercise 14.3.17 part A,C,E and please show step by step and explain

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Q: So I need to keep the 4 and the cubed in the integral??

A: Yes, you have missed the "4" and the cube.

Q: Exercise 14.4.3. Compute each of the following: (a) (125843)² (c) (125843)4 (e) (125843)6 (b)…

A: To find the value of the given element . Since it is the element of the permutation group s8 . So…

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Q: If A and B are sets; A and B denote the complements of the sets A and B, then set (A- B)U(B –…

A: Using venn diagram we solve this question.

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that…

A: Given that                    f be continuous and differentiable everywhere. Suppose that f has…

Q: 38. Let F be a closed set in R. Let y ¢ F. Show that there exists some ɛ > 0 such that the…

A: We have to prove the above statement.

Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: M L ´N, K 4o0 S P 350

A: Concept: Given that line m and n are not parallel. Here only suplementery angles that are formed on…

Q: Evaluate / f(z)dz when ) f(z) z+1 and y = TR (R > 0) z2 (ii) f(z) = (z+1)³ sin(z2022) and y = r(0;…

A: Given function i fz=z+1z2 and γ=ΓRR>0iifz=z+15sinz2022 and γ=γ0;1

Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

A:

Q: 10. Solve the problems. Use the graph for the standard deviation points. In a fishing contest, the…

A: Given that: Mean = 16.40 in Standard deviation = 4.71 in  To determine the percent of the fish…

Q: 6 5- 4 y 3- 2- 1 3 4 5 2.

A: Given is a figure showing the region which is to be revolved about the y-axis and then we need to…