21. A parabola has a span of 30 m and a height of 20 m. Determine its area.

Q: Which of the following is equivalent to plq (d(bb)¡((bb);(b<-d))b

A: To find the logical equivalency, lets use truth table. We know p|q is used for (NAND operator) which…

Q: Show that √3 € Q [√6].

A: Let 3∈Q6 Then there exists rationals a,b such that 3=a+b6 Consider:…

Q: (a) Is Q (√6) ≤Q (√2 + √3) ? Justify your answer.

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: The graph below shows the derivative F'(x) of a function F(x) and the values of some areas. The…

A: 1. Consider the graph given in the problem, We know that, Fx=F0+area under the F'x curve Since, we…

Q: Prove or disprove the following statement: the product of any 4 consecutive integers is divisible by…

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Q: Determine whether the set S is linearly independent or linearly dependent. S = {(2, 6, 1), (3, -1,…

A: When two vectors are linearly dependent one vector can be written in scalar multiple of other.

Q: Suppose an undamped forced spring mass system is driven by the equation d²x +49x = f(t), di where…

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Q: Given are five observations for two variables, and y. Excel File: data14-25.xlsx What is the value…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Given,  The coordinate matrix of x relative to a (nonstandard) basis for Rn B = {(1,0,1), (1,1,0),…

Q: Let B=[u, be a base for V=R², where = (1,2) and =(-1,1). We know that every vector in V is a linear…

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Q: Solve for the power series solution of the given differential equation. (x² - 1)y" + (x + 1)y'- y =…

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Q: Find the limit of the sequence πρὖ + 4 πρ4 +5 c3 - 2e { where - e CER+ and n " cn+1 - ne 0 for any…

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

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Q: Construct an element of multiplicative group of the finite field elements.

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Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

Q: The surface S is parameterized by r(u, v) = (u, 2 cos(v), 2 sin(v)), 1 ≤ u ≤ 3,0 ≤ v≤n. 1. Identify…

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Q: Exercise 8.7. (a) Determine the number of cyclic subgroups of order 10 in Z30 Z120. Find all the…

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Q: 25. Solve(1 Point) L-1 3s+16 s²-s-6 O4e³t - 3e-2t 3e³t-4e-2t O5e²t - 2e-3t O 5e³t - 2e-2r…

A: Solution:

Q: The function f is defined as follows: f: R² R² with f(x, y) = (2x, x+y) Which statement is correct?…

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Q: In cylindrical coordinates, a particle has position vector F = rê, + ze = r cos(0)i +rsin(0)j + zk.…

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Q: 6) Approximately how long will it take for $10000 to become $20000 at 4%. ||

A: The solution is given below

Q: The function f(x) = x² − 3x³ − 4x² − 400x + 150 is unimodal on the interval [-8; 11]. Make use of…

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Q: Consider the following points. (2, 4), (3, 6), (5, 10) (a) Determine the polynomial function of…

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Q: Using these sets, find the following: DU (EU F) D = {b, a, c, k} E = {t, a, s, k) F = (b, a, t, h).

A: Given, D=b,a,c,kE=t,a,s,kF=b,a,t,h D∪E∪F is to be determined.

Q: 3. Let S be the subset of Mmn containing all matrices A such that (A)₁1 = 0. Determine whether or…

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Q: A scientist satisfies the equation: (a) (b) (c) Q(t) of a substance present at ti 40"(t) + 4Q'(t) +…

A: The amount of a substance present at time t≥0 satisfies 4Q''(t)+4Q'(t)+Q(t)=0

Q: Let B be a subset of R¹. Which of the following statements are correct? O If B is a base, then |B| =…

A: Let V be a subspace of Rn for some n. A collection B = { v 1, v 2, …, v r } of vectors from V is…

Q: Which of the following is true about the sequence In (3n² − n² + 1) − ln(n³ + 2n¹ + 5n)? = an The…

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Q: 2. Using h = 0.1, approximate the value of y(0.5) for the given differential equation using a) Euler…

A: Given :   y'=y+2x-x2                      y0=1                 h=0.1 To Find : (a) Euler method y0.5…

Q: Use the definition of a Maclaurin Series to express f(x) = as a Power Series. Give the 8th degree…

A: We have to express f(x) as a power series by using the definition of Maclaurin Series, where f(x) is…

Q: Consider the set (Z;. x), where x is multiplication mod 9. Which of the following state- ments are…

A: 1st Statement is Wrong :   an element [a] in (Zn*, ×) has an inverse if and only if gcd(a, n) = 1 .…

Q: Refer to Figure below; disregard the differential lengths and imagine that the object is part of a…

A: We need to calculate the surface area of ABCD.

Q: 13. If all even numbers from 2 to 104 are added, what is the sum? O 1098 O 1568 2756 O4572 O5122

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Q: 22. A diving pool can be filled by a pipe in 10 hours if the drain is opened. If the pipe was…

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Q: II. Use the Remainder Theorem to find the remainder when each polynomial is divided by the…

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Q: 4. Is R5 an under- or over-estimate of the total distance the car has traveled during the ten…

A: given data  time (sec) 0 2 4 6 8 10 velocity (ft/sec) 20 30 38 44 48 50 (4) is R5 an under…

Q: The Maclaurin series expansion for e* is ∞ i=0 (-1) Find the Padé approximation to e* of degree 5…

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Q: n=1 (−1)n-¹(x − 1)n n2n

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Q: Activity 1: Analyze the following and construct a graph. (Apply what you had learned in your…

A: We have: Year 2010 2011 2012 2013 2014 2015 Cost 1.40 1.55 1.61 1.65 1.78 1.90

Q: Let u, 1₂" orthogonal to u, and u The nonzero vector v and u Note that u, and u, are orthogonal. It…

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Q: Consider the rectangular box enclosed by the planes x=0, x=3, y=0, y=5, z=0, and z=2. Let S₁ and S₂…

A: Normal of the planes are parallel to axis (positive or negative)

Q: In how many ways can 10 people be seated in a row of 10 chairs if Janet insists on sitting in the…

A: The main objective is to find the permutations for the given problems.

Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

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Q: (a) (b) x1 + x2+2x3 = 8 - x1-2x2 + 3x3 = 1 3x17x2 + 4x3 = 10 2x1 + 2x2+2x3 = 0 - 2x1 +5x2+2x3 = 1…

A: Gaussian elimination is also know as row reduction. In these we can solve the system of equations by…

Q: Let R be the region, 4 ≤ x² + y² ≤ 25 with the positively oriented boundary R. Let f(x, y) be a…

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Q: Verify that λ, is an eigenvalue 8 -1 3 0 6 1 07 0 Ax₁ = Ax₂ = A 8-1 3 0 61 0 0 07 0 8-13 0 0 6 1 2…

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Q: Lercise 8.13. (a) Is S₁ ≈ Z4 U(7)? Justify your answer. Is S4 Z6 U(5)? Justify your answer.

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Q: Use the method of your choice to find the volume of the solid generated by revolving the region…

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