1. Derive the law of sines using the triangle shown below. Suggestion: Try writing the length of the altitude (height) of this triangle in two different ways. Then do the same for a different altitude of the triangle. A

Q: Solve the initial value problem below using the method of Laplace transforms y" + 36y=144t² - 36t+…

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Q: 1. Answer the following for the given equation Ax = 0. (a) Find a basis for ColSp(A). (b) Find a…

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Q: 6. How many permutations of {0, 1, 2, 3, ..., n,} leave at least two numbers fixed?

A: How many permutations of {0, 1, 2, ...., n} , leaves at least two number fixed ?

Q: Find the flux of the vector field F = (-y,x,1) across the cylinder y = 3x², for 0≤x≤ 4, 0≤z≤3.…

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Q: The graph of a rational function is shown be- low. Write the equation that represents this function.…

A: Here, we have to find functions from the given graph.

Q: Find all local constrained extrema of f(x, y) = x² + 2y - z² + z under cionstraints 2x - y = 0, x +…

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Q: The State Government have built a new express transport system to connect the CBD to the town of…

A: The given transition matrix is T=0.90.10.30.7 The share matrix is S=01.   The steady state vector of…

Q: n Use induction to prove: for any integer n ≥ 0, Σ2 · 3³ = 3n+¹ − 1. j=0 Base case n = Σ2.30 j=…

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Q: Find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7. Write down the…

A: We are to find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7 Write…

Q: [15] (4) GIVEN: z = f(x, y) = x²y, where (x, y) is subject to the constraint: T: x² + xy + 7y² 27, x…

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Q: Gregg filled a box with 6 cubes that each had a side length of 1 foot. Which statement correctly…

A: Gregg filled a box with 6 cubes that each had a side length of 1 foot. We have to find the volume of…

Q: A function f(x) is (g(x)) if and only if there are positive constants k, C₁, and C₂ such that…

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Q: 1. Is V = why not? 1:0 20 and b≥( a vector space? Draw the graph and explain why or

A: By the answering guidelines we have to do first question is multiple questions are given so I am…

Q: Problem 3: Show that for n ≥ 1, dx Lo (1+² (1+x²)n+¹ 1.3.5... (2n-1) 2.4.6...(2n) π.

A: Beta function: β(p,q)=∫0∞xp-11+xp+qdx for p&q>0 Even function: f(x) is said to be even…

Q: The value of a new sports car (Lamborghini) appreciates at a rate of 3% per year. If the vehicle was…

A: Given that, The value of a new sports car appreciates at a rate of 3% per year. ⇒If the vehicle was…

Q: Partial derivative. Compute fxyxzy for f(x, y, z)= y sin(xz) sin(x + 2) + (x+2²) tan y + x tan (²+ =…

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Q: Laplace transform a. L- (¹) 48 b. L-¹ { 1/2-) S5 C. 1 L-1 (2435) s²+3s. :-1 (432 +1} d. L-1

A: We have used standard formulae of Laplace transform.

Q: arsh 20 underwater substation can be built. The scuba diver finds a mysterious underwater cavern…

A: Given the water pressure y in pound per square feet increases exponentially as the depth below sea…

Q: Determine the truth values of each of these statements if the domain for all variables consists of…

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Q: (a) Find the arc length function for the curve y = In(sin(x)), 0 < x < π, with starting point (7,0)…

A: Here, the given curve is y=ln sinx with starting point π2,0. To Find: Arc length .

Q: 14. Use spherical coordinates to set up an integral that would give the volume of the region…

A: Integrals calculus

Q: 30. x²y" - 5xy + 8y = 8x6, y ³ (²¹) = 0,✓ ( ¹² ) = - y = 0 2

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Q: The general form of Newton's Law of cooling is: T(t) = T₂+ (T(0)-Tale-kt where I is the temperature…

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Q: Encode the message "CRYPTOGRAPHY" using matrix A. Remember to partition the numerical message into…

A: Given that: Matrix 1213. Message- CRYPTOGRAPHY.

Q: Arrange the given steps in the correct order to prove that +23+++1)=+1 is true for all n> 0 using…

A: We have to arrange the statements according to the correct order to prove the statement…

Q: Explain why the system cannot be solved by matrix inverse methods. Discuss methods that could be…

A: The given system of linear equations, x1+5x2+4x3=92x1+4x2+7x3=2x1-x2+3x3=-7 We have to find a…

Q: The matrix M = =[₁ 0 1 O 5 7 4 -3 -1, has eigenvalues λ = 1 and λ = 5. What is the eigenvalue for…

A: M=74-3-1 The eigenvalues of M are: λ=1 and λ=5. We have to find the eigenvalue for the eigenvector…

Q: Problem 2 M, A, T, H are four positive integers in the following vertical addition. MA T H A T H T H…

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Q: Suppose A, B and Care 3 x 3 matrices with det (A) = 3, det (B) = -2, and det(C) = 3. Find det…

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Q: The graph of f'(x) is shown in the figure below. This is not the graph of f(x). 1 (a) List the…

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Q: A 10-year annuity is payable continuously at the annual rate of $1. 2 Find the present value of this…

A: Annual rate=$1Force of interest at time t is δt=2100+5tTime=10 year

Q: 2. State the converse of the statement "\emph{lf x ≤ y and y ≤z, then x ≤ z.}".

A: if  P and Q are two statement such that  P→Q then converse of statement is Q→P

Q: Ise the given transformation to evaluate the given integral, where R is the triangular region with…

A: We have to find given integral, using triangular region R.   ∬(x-6y)dA, x=5u+v &amp; y=u+5v

Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

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Q: [15] (4) GIVEN: z = f(x, y) = x²y, where (x, y) is subject to the constraint: I: x² + xy + 7y² 27, x…

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Q: n Use induction to prove: for any integer n ≥ 1, Σ(6j – 4) = 3n² – n. j=1

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Q: This exercise is based on the following data on four bodybuilding supplements. (Figures shown…

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Q: 3. a) Describe the transformations on y = 3* to sketch y = −4(3-×-2) + 4.

A: Curve or equation, y=3x

Q: Let S(x) be a clamped cubic spline that passes thorugh the points (0,0), (1,1), and (2,-1).…

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Q: Use the change of variables X1 X2 X3 X4 = = G(r, 01, 02, 03): = to compute the content of the 4-ball…

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Q: 1. Prove the following statement. If (rn), (Sn), (tn) are sequences of real numbers such that then…

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Q: Find a decimal approximation to 100 sin (65) correct to 38 significant figures and enter your answer…

A: The expression given is 100sin65. To find- The decimal approximation of the given expression correct…

Q: A weight of 600 pounds is suspended from two cables as shown in the figure. What is the tension in…

A: I have explained everything with in the solution. Please go through that.

Q: Consider the vector function given below. r(t) =   7t, 5 cos(t), 5 sin(t)   (a) Find the unit…

A: rt=7t, 5cost, 5sint

Q: Click and drag the steps to their corresponding step numbers to prove that the given pair of…

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Q: Researchers conducted a study to learn how early childhood education relates to a child's future…

A: Early childhood education refers to the educational programs and activities that are designed for…

Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

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Q: The curve X = | y² - 1 ln y, y = [0, 6] is rotated about the x-axis. Then ds and the area of the…

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Q: 4. Determine m E Z with 0 <m <3 such that m = 12103 mod 4.

A: The congruence equation : m≡12103 mod 4, m∈ℤ with 0≤m≤3.

Q: Solve the initial value problem below using the method of Laplace transforms. -(1)-1( ) = 0 = 1, y'…

A: Solve the initial value problem below using the method of Laplace transforms.   y''+y'-6y=-7 cos…