Draw a line to show how the white king can move out of check .Remember two kings can never move next to each other

Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where approp...

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and oth...

Q: 3. Consider the matrix B = a. Find its eigenvalues and the corresponding eigenvectors. b. Orthonorma...

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Q: A company is divided into 50,000 shares. An investor purchases 2,500 shares. What percent of the com...

A: Introduction: The percentage is very important in mathematics. The figure x% means that out of 100, ...

Q: Solve xy' (2y - 1) = y (1 - x)

A: Solve xy' (2y - 1) = y (1 - x)

Q: Solve the Bernoulli equation for y by making the substitution u = dy 3y + y°. dt Use the following i...

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Q: azu azu Consider the hyperbolic equation of at? 0sx<2,t 2 1 with boundary conditions of ди, u(0, t) ...

A: We are given the following hyperbolic equation ∂2u∂t2=∂2u∂x2;   0≤x≤2, t≥1 with boundary conditions ...

Q: Describe the conditions that would create an ambiguous case with two possible solutions.

A: Ambiguious case of law of sines. Now lets take an example. Now let angle A be 45 degrees, side a =9 ...

Q: 6. Use the shortest path algorithm to find the shortest path from A to G in the weighted graph below...

A: We will choose shortest path from starting point to reach the next point. 

Q: 7. Read about the Integral Test in Section 11.3 and, specifically, through example 2 to see how 1 th...

A: Series and sequences, integral test

Q: Q.2 Find the vertex point and show in graph: y=2x²-4x+4

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Q: Find an equation for the graph shown below. (Hint: use the form y = a(x – h)? + k) -6 -5 -4 -3 -2 -1...

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Q: 4. Use Laplace transforms to solve the following initial value problems. d?x "+2+4x = 0, x(0)=0 , x'...

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Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the stru...

A: Given that V be the vector space of polynomials of degree ≤2 with real coefficient, endowed with the...

Q: Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your p...

A: If gcd (a, b) =1, then there exist integers p and q such that ap + bq =1Here gcd ( 5,7) = 1 so there...

Q: Test for convergence the series 3.6.9 ... 3n ( 1 ) Σ n = 1 x" (x > 0), 7.10.13 ... (3n + 4) I1 = 2.4...

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Q: Let a be a real number. Consider the series where a, = cos(nr), 2n +1' n=0 (a) Is it possible to fin...

A: For  a series    ∑an   If L=limn→∞an+1an&lt;1 then series will be convergence  If L=limn→∞an+1an&gt;...

Q: +oo +oo n² – 1 n2 +1 (-1)" (a) Σ (c) )un where sn = u1 +... + un = n! n=1 n=1 +oo 1 - 11 n=1

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Q: s + 7 (s – 4) (s + 3)

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Q: Proposition 6. Consider the function g : Z? → Z² defined by g(m, n) = (m – n, n – 2m). The function ...

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Q: The value of the integral / (t tan-+3y+sin-r)dr + (cot-'y+e +7x)dy, where C is r +y =9 is %3D

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Q: T AppLiCATIONs 1. Schve for the orthogonal trayectories (a+x)y² = x*( 3a-x)

A: 1) solve for the orthogonal trajectories a+xy2=x23a-x                  ...i differentiate with respe...

Q: 1. Using the properties of determinants, solve with a minimum of calculation the following equation ...

A: We have,xaa1axb1abx1abc1=0Applying R2→R2-R1R3→R3-R1R4→R4-R1 we get,xaa1a-xx-ab-a0a-xb-ax-a0a-xb-ac-a...

Q: 1. Define Zero Divisor , Integral Domain. And one example of integral domain.

A: Zero divisors, Integral Domain

Q: 6. f(t) = (7- e^(12 – 3t))u(t-4). Perform Laplace transform by integration only. A. [(21 + 6s) / (s^...

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Q: Let F(n) be the function of the Fibonacci numbers, where F(n) is the nth lean of the Fibonacci numbe...

A: We will use fibbonacci sequence to find the limit.

Q: II| (x + y + z) dv, where E is the solid in the first octant that lies under the paraboloid z = 16 -...

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Q: Determine whether the system is consistent. x1 - x2 + 3x3 = -11 -4x1 + 4x2 - 12x3 = -2 x1 + 3x2 + x...

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Q: If X = {1,3,4,19}, Y = {2,3,4,7} and Z = {2,4,6,9}, then what Is X U (Y ∩ Z)

A: The union of two sets A and B is a set containing all elements in both set A or set B. The intersect...

Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 7. For any sets A, B, ...

A: Given that  for any sets A,B,D, if B⊆A then D-A⊆D-B We have to check that the above statement is tru...

Q: The lines / and m have equations r 3i- 2j+ k+1(-i+2j + k) and r 4i + 4j +2k + u(ai+ bj- k) respectiv...

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Q: Consider the initial value problem V5y – 7 6t2 - y(to) = y0 Existence and uniqueness is guaranteed a...

A: Given that y'=5y-736t2-4,   y(t0)=y0

Q: -6 5 4 The plot above is created with the paramet S«(t) = a cos(bt) ly(t) = c sin(dt) To acheive thi...

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Q: 5a+2b 3. Decide whether the set of all vectors of the form is a subspace of R³ or

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Q: Determine which vector from the options below is in the plane: 1 = S Omo

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Q: Proposition 13. For integers n > 1, 2 3 + + 4! 1 = 1– (n+1)!" 1 - 2! 3! (n+ 1)! Hint: Try induction ...

A: We can solve the problem by the method of mathematical induction. By mathematical induction we first...

Q: Suppose that you earn $39,600 per year. What is your monthly salary? $ 3300 Assume that you deposit ...

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Q: Consider the initial value problem, (6z – ly)y' = (x – 8) o + 2, y(z0) = y0 If ro - 7, then for what...

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Q: In a mechanical system, acceleration a, velocity v, and distance S, are related by the simultaneous ...

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Q: The graph below represent the domain of the function O f(r, y) In(1 -+y) Of(r, y, z) = VI+y-1 Of (r,...

A: The given graph represents x+y&gt;1. The domain of ln(1-x+y) is 1-x+y&gt;0⇒-x+y&gt;-1⇒x-y&lt;1. So t...

Q: How does an earthquake of magnitude 8.4 compare to an earthquake of magnitude 3.7? Round answer to t...

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Q: 4. f(t) = e^(5t)(t^3) A. 6/ (s-5)^4 B. 6/ (s+5)^4 C. 6/ (s-5)^3 D. 6/ (s+5)^3 %3D

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Q: Make a concretr example of secant method then show your solution with explanation.

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Q: Proposition 6. Consider the function g : Z² → Z² defined by g(m, n) = (m - function g is a bijection...

A: Consider the function , g : ℤ2 → ℤ2 defined by ,  g(m,n) = (m - n , n - 2m). We need to show that , ...

Q: Give the Maclaurin series expansion of f(x) = ln(3 − 2x). Determine its interval of convergence. App...

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Q: Find the general solution of the differential equation: ip dt t. Use lower case c for constant in an...

A: Solution of linear differential equations

Q: f(t) 1 2π

A: Graph of periodic function is given. We determine b4.

Q: Given a universal set U for a set X , if AC X , then (U – X) n A = Ø

A: Given a universal set U for a set X and A⊆X We shall prove it by contradiction method. Let us assume...

Q: Proposition 5. Consider the function f : Z² → Z² defined by f(m, n) = (mn, m+n). The function f is n...

A: Remark: Let f be a function from a non-empty set A to another non-empty set B. Then f is Said to be ...

Q: Dylan wants to accumulate at least $60,000 by depositing $1,400 at the end of every month into a fun...

A: Dylan is depositing $1400 per month to get $60000 where interest is compounded monthly formulae for ...

Q: A certain radioactive substance decays by 2.2% each year. Find the half-life of the substance, to 2 ...

A: Given: Decay rate of a substance is 2.2% per year. To find: Half-life period of radioactive substanc...