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Q: Write in scientific notation. In 1 year, a spaceship will travel 2,695,000,000,000 miles. 2,695,000,...

A: Mile is a unit used to represent distance or displacement of an object.  Scientific notation is a wa...

Q: Question * Let a and b be two positive integers such that gcd(a, a² – b?) = 1. Then, gcd(a + b, a² –...

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Q: Set up (DO NOT evaluate) a surface integral to find the surface area of a cone z = x² + y? inside th...

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Q: 6. Systems of first-order equations can sometimes be transformed into a single equation of higher-or...

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Q: The points A, B, C and O represent the numbers z, =, 1 and 0 respectively in the complex plane. Give...

A: We will treat A,B,C as position vectors to do the proof

Q: [1] An archer aims to a target 150m away, aiming 2 radians above the ground. The arc length of the t...

A: Given that, An archer aims to a target 150 m away, aiming 2 radians above the ground. We need to fin...

Q: 0. 1 Find the projection of the vector b = onto the column space of A = 4 1 2.

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Q: Let A be a 5 x 3 matrix and assume that N(A) is trivial, i.e.. N(A) = {0}. Find dim C(A).

A: Given that A be a 5*3 matrix. and N(A)={0}. we have to find the dim C(A)?

Q: Find the volume of the solid generated when the region bounded by y = x² – x and y = x - y2 is revol...

A: Introduction: If the area of the ring is A=πOuter radius2-(Inner radius)2, the volume of solid gener...

Q: If AB is a double ordinate of the hyperbola *- y =1 such b? a* that AOAB (O is the origin) is an equ...

A: Introduction :

Q: Given enough food and space, a colony of yeast increases at a rate proportional to its population. A...

A: Given that, A colony of yeast increases at rate proportional to its population. After an hour, it be...

Q: Find the series solution of xy' = (2x + 1) y

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Q: For each natural number n, the sum 1(2) + 2(3) + .…· + n(n + 1) is equal to: n(2n+1)(2n+2) n(n+1)(2n...

A: We will find out the required sum.

Q: Minimum distance between the parabolas y? – 4x –8y + 40 = 0 and x? -8x –4y + 40 = 0 is

A: Introduction :

Q: (a) How many ways can the letters of the word ANCESTOR be arranged in a row? Since the letters in th...

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Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

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Q: whether the following is true or false: c) (a, a, b, a, b, C.C.c, c) RUE, THEN CHOOSE Doğru ALSE, TH...

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Q: Turkish national swimming team coach is putting together a relay team for the 400 meter relay. Each ...

A: Let us solve the Assignment problem by Hungarian Method.

Q: Question * Let a and b be two positive integers such that gcd(a, a² – b?) 1. Then, gcd(a + b, a? – a...

A: Given that gcd(a,a^2-b^2)=1, we now check which of the following is/are true. 1.gcd(a+b,a^2-ab+b^2)=...

Q: Assume that there are 2 pairs of black socks (çorap),3 pair of pink socks, and 5 pairs of blue socks...

A: Given: Let us assume, ⇒ 2 pairs of black socks ( i.e  4 shocks) ⇒ 3 pairs of pink socks  ( i.e  6 sh...

Q: The inclination of the normal with positive direction of x- axis, drawn at another end of a normal t...

A: Introduction :

Q: 2 2 2 ithout calculation, find one eigenvalue and two linearly independent eigenvectors of A = 2 2 2...

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Q: "A proper subset of a set A is a subset of A that is not equal to A". According to this definition, ...

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Q: Question * If a and b are two integers such that a is even and b is odd, then gcd(a, b) # gcd(a/2, b...

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Q: For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. {(a, b, c, d...

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Q: |exp(2* + i) + exp(-iz?)| < e*-3ry? . Show that |exp(2* + i) + exp(-iz2)| < e*-3ay? + e2wy

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Q: In Section 2.5 we showed how integers can be represented by strings of 0's and 1's inside a digital ...

A: It is given that, integers can be represented by strings of 0's and 1's inside a digital computer. I...

Q: Find the area enclosed by the polar curve r = 3cose. Find the area common between the curves r= a (1...

A: First Part: Given function is r=3cosθ Since is an asymmetric function so the area formed under it ha...

Q: Question * Which of the following statements is true? If 2" – 1 is prime then n is prime. None of th...

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Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-...

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Q: Let the Maclaurin series be e ^ x = (check image); then the respective series of the function f (x) ...

A: To find- Let the Maclaurin series be ex = ∑n=1∞xnn!, then the respective series of the function fx =...

Q: "A proper subset of a set A is a subset of A that is not equal to A". According to this definition, ...

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Q: (a) By drawing a suitable diagram, prove the triangle inequality |z1 – 2| > |21| – |2|-

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Q: xyy' + 4x2 + y² = 0 b) (2x + y + 4)dx + (x – 2y – 2)dy = 0 а) - dy c) dx = 2 + (y – 2x +3)z - dy e s...

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Q: Refer to the data set: (1, 2.5), (2.5, 15), (0.5, 2), (-2, 0.5), (0, 1), (1.5, 5) Part a: Make a sca...

A: Use the following formulae, to obtain the solution. Let the regression line equation be y=a+bx. x¯=∑...

Q: Find the limit if the sequence converges and lim sup and lim inf if the sequences diverges (c and d)

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Q: You have 3 friends and you have 6 presents for them. How many ways can you distribute 6 presents to ...

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Q: Q2: Prove that the intersection of any two ideals of a ring R is also an ideal.

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Q: Use the theoretical probability formula to solve the problem. Express the probability as a fraction ...

A: Here  A fair coin is tossed two times in succession. The set of equally likely outcomes is HH, HT, T...

Q: y -0.5-

A: The graph of a function is the collection of ordered pairs of points (x,y) in the cartesian coordina...

Q: R(x): x can cook rice M(x): x can cook meat Universe of discourse is your family Express the sentenc...

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Q: You are given the system of linear equations, Aa b, in matrix form below. Follow the steps below to ...

A: To solve this problem using Gauss-Jordan elimination method first we find the reduced row echelon fo...

Q: Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In ...

A: Hi, It is multiple sub-parts, I am going to solve the first part only.

Q: Question Let a and b be two positive integers such that gcd(a, a? – b?) = 1. Then, ged(a + b, a² – a...

A: Given that a and b are two positive integers and gcd(a,a^2-b^2) = 1. We now check which of the given...

Q: Find an orthogonal basis for the column space of the matrix to the right. -1 7 1 -7 4 1 -3 7 1 -3 -3...

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Q: Question The cube of any integer may has the form: 9k + 8 9k + 7 O This option This option 9k + 6 Al...

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Q: Determine whether the graph is a tree. If the graph is not a tree, give a reason why. C D Choose the...

A: We have given a graph and we have to check this graph is tree or not.

Q: Show that the volume generated by revolving the area bounded by an arch of the cycloid x = a(0- sin0...

A: We have to show that the volume generated by revolving the area is 5π2a3.

Q: k] (where k is a real number), find all values of k where Bis diagonalizable. For the matrix B

A: Use the condition that,if the matrix has all distinct eigen values then it is diagonalizable .

Q: h+r 3- ) 2n+s 431

A: We have to find whether the series is absolutely convergent or conditionally convergent.