1. Let a force F be given by F = Fo(i+ 4j + 8k) where Fo is a constant. Determine the scalar component of F in the d = 6i + 3j + 2k direction.

Q: Let a, b be integers. What does it mean for a = b (mod 17)? Describe the elements of Z17. Compute [5...

A:  a ≡ b (mod 17) means that a − b = 17k for some k ∈ ℤ. ∴  b − a = −17k = 17(−k); henceb ≡ a (mod 17...

Q: Which of the following functions form a fundamental set of solutions of the differential equation 3y...

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Q: a) Show that u and v are orthogonal. b) Find the value of a for which w is orthogonal to v c) Find p...

A: Given, u=1,-2,6,v=2,-5,-2 and w=a,2,-1 We have to find projvu and  projwu.  

Q: 10z2 - Find the volume of the solid obtained by rotating about the y-axis the region bounded by y an...

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Q: Let S be the surface 7(x, y) = (x² + 2y, 3x, xy), (x, y) E D = [0, 2] × [0, 3]. The area of S is: /|...

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Q: 4) Sketch the region and find the area bounded by + = 1, y = ±3 and y = x + 4 using double integrati...

A: We have to find the area of the region.

Q: L 3 S

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: Determine the total work, by Green's theorem, done by the force field F(x,y)=, on a particle followi...

A: As per the question we have to find the line integral of the force field F = ⟨2x+y2 , 2x2y⟩ Along th...

Q: A model for the yield Y of an agricultural crop as a function of the nitrogen level N and phosphorou...

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Q: Find the dimension of the subspace U = {[x, y, z, t]|x+4y-z = 0; x-2z+ t= 0}. Select one: a. 4 b. 2 ...

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Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =...

A: Reflexive relation: A relation R on a set A is said to be reflexive if every element of A is related...

Q: - y = 0 is a third order ordinary differential equation False O True

A: Given differential equation is x3d2ydx2 - xdydx4 - y = 0

Q: uments a, b, c or d below) A. Modus ponens B. Modus tollens

A: In this question, the concept of argument is applied. Argument Every argument having true premises a...

Q: Consider an ICE operating at constant rpm because it powers an electricity generator. Does this engi...

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Q: Solve for x. If necessary, round to the nearest ten-thousandth. (If there is no solution, enter NO S...

A: Given expression is log6x + log6(3x - 2) = log621

Q: 14 is 2 times as many as 7

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Q: 4. Find the resultant using (a) the head-to-tail method, and (b) by summing up components. For the v...

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Q: DO NOT include spaces in between characters. * Find an equation of the tangent line to the graph of ...

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Q: How do you create Pascal's Triangle?

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Q: 1. y" – 2y' = sin 4x 2. y" + 6y' + 9y = 1+x 3. y" + 2y' + y = xe-* 4. y" + y = e* + x3 y(0) = 2; y'(...

A: 1.) y''- 2y'= sin4xAuxiliary equation is m2-2m=0⇒m(m-2) =0⇒m=0, 2y(x)= c1+ c2e2xPI= sin(4x)D2-2D= si...

Q: (d) How many subsets V of A are there so that 1 € V or VOB= Ø? Explain.

A: This question related to set theory . Solution is given below.

Q: Show that the polynomial 1+x+x2 +...+xP-1 , where p is a prime number, is irreducible over the field...

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Q: Determine the limit superior and limit inferior of the following sequences: {1 1 1 (a) = 4 5

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Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)...

Q: The solution of the Bemoulli equation y' +2-Vy= 0 is:

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Q: Which of the following is true about ƒ (x) = [x]? A. The function is continuous at r= 0. B. The func...

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Q: Consider the following. f (x) = 7 log, r Which table of values could be used to graph the logarithmi...

A: Let us consider the logarithmic function f(x)=logab Domain of the function is all positive real num...

Q: Approximate the roots of the following functions. 1. f(x) = x3 + x - 3

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: Consider the equation u' = (1 – b)u – au³ where a and b are fixed positive constants and 1 is a para...

A: Given: The differential equation, u'=λ-bu-au3 where a and b are fixed positive constants and λ is a ...

Q: Let {v1 = (1,2,3,5,9), v2 = (3,1,2,8,9), v3 = (2, -5,5,9,4)} and {u1 = (0,1,1,1,2), u2 = (0,2, -2, -...

A: The given question is related with vector space. Given that , v1 = 1,2,3,5,9 , v2 = 3,1,2,8,9 , v3 =...

Q: You know f:J→J and g: J→J Select the choice with algebraic expression for f and g such that f(g(x)) ...

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Q: The line segment x = p – y, 0 <y < p, is revolved about the y-axis to generate the cone as shown in ...

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Q: Integrate the following: 3x2 ( 15x3 + 102 )0.7000000000000001 within the range 5 and 7.

A: To integrate 3x2 (15x3 +102 )0.7000000000000001for 5≤x≤7. Let I=∫57x2 (15x3 +102 )0.7000000000000001...

Q: What formula would be used to calculate the right rectangle approximation of Si – 2x +3)dx using fiv...

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Q: g(f(x)) = 18x² + 36x + 18

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Q: Which of the following functions form a fundamental set of solutions of the differential equation 3y...

A: Given differential equation is 3y'' + 2y' = 0

Q: able functions f1 and f2: fi = 7 · fi – 5 · f2, f½= 10 · f1 – 1

A: In this question, the solution of the differential equation is determined using the eigenvalue of ma...

Q: quation correspo = (a + bx) e3× is c

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Q: Find the Laplace Transform of f () =2 sin a +3 cos 2z.

A: This is question of laplace transform . Solution is given below

Q: Given the following simultaneous equations: 7.8x1 + -1.6x2 + 9.1x3 + -8.2x4 +-2.7xs+-4.8 0 -3.5x1 + ...

A: The system of equations given is as follows: 7.8x1-1.6x2+9.1x3-8.2x4-2.7x5=4.8-3.5x1-8.5x2-9.3x3-3.2...

Q: Find the dimension of the subspace U= {[x, y, z, t] | x+4y-z = 0; x-2z+ t= 0}. Select one: а.4 b. 2 ...

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Q: Let M1 = ( S1, Ih) and M2 = ( S2, I2) be two matroids with disjoint ground %3D sets. Prove that the ...

A: Given: Two matroids M1=S1,I1 and M2=S2,I2 with disjoint ground sets.   To prove: The subset system M...

Q: Using Reciprocal Substitution * dw For f (w²+4)ž --S tdt tdt = Ja + 4t²)v1+ 4t² V1+ 4t² O Option 1 O...

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Q: y= 6. 30 18/3/2 Sin(8)= Cos(8)D Tan() = %3D Sin(A)-

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Q: Express your answer in rectangular form both in EXACT value and approximate value. Round off approxi...

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Q: Q3 Find the PA=LU factorization of the following matrices: 2 4-2 6 0 2 4-2 6 0 4 2 A = 3 В - 3 4 2 4...

A: PA=LU Decomposition: Suppose an m×n matrix A is carried to a row-echelon matrix U via the gaussian a...

Q: 8-1 Find the inverse Laplace transform, y (t), of L-'[ using the first shift theorem: 282+5s+2 If L-...

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Q: Find the dimension of the subspace U= {[x, y, z, t] | x+4y-z = 0; x-2z+ t= 0}. Select one: a. 4 b. 2...

A: We  first find a basis for U and then we will determine the dimension of U.  To do this we use the c...

Q: 3) Show that the irreducible polynomials in R[T] are the following: (a) Linear polynomials, i.e. pol...

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Q: Evaluate xy dA, where S is the region shown in Figure 16. (2, 4) 2 Figure 16

A: Let us consider the double integral ∫S∫f(x,y)dxdy, ∫s∫f(x,y)dydx,  To solve the double integral  In...