Trigonometry is used in a rich variety of real life situations. Scientists, designers and other professionals use angles in their daily work. Research the internet to find an example of how Trigonometric function are used in the 'real world' and create or find a problem related to it. Provide a solution to the problem.

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0 =…

A: Solution:Given the differential equation:36y′′−y=xex/6,y(0)=1,y′(0)=0Step 1: Solve the Homogeneous…

Q: Instruction: Course Name: Calculus with Analytical Geometry-1 Course Code: MATH 132 Do not use…

A: Let's denote the side of the square to be cut out as x. After cutting out the squares at each…

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A: The matrix A^ given is:A^=⎝⎛​00−i​010​i00​⎠⎞​  Step 1: For the EigenvaluesThe eigenvalues λ of the…

Q: Instruction: Course Name: Calculus with Analytical Geometry-1 Course Code: MATH 132 Please do not…

A: Step 1:Step 2: Step 3: Step 4:

Q: 1.4-5 Theorem (Convergent sequence). Every convergent sequence in a metric space is a Cauchy…

A: Required python code for graphs:import numpy as np import matplotlib.pyplot as plt # Define the…

Q: If a connected planar graph with n vertices all of degree 4 has 10 regions, determine n. Ex- plain…

A: Step 1: Step 2: Step 3: Step 4:

Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs…

A: Required code:# Adjusted plot to avoid issues with LaTeX expressions # Define points for a sphere…

Q: Find the value of a so that the work done by the force ♬ = (y² + 1)² + (z+y) in moving from (0,0) to…

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Q: Need help with probability.

A: (a) Determine if X and Y are independentFor X and Y to be independent, their joint probability…

Q: The graph of the function f() is (the horizontal axis is z.) Consider the differential equation z' =…

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Q: Find the eigenvalues and eigenfunctions for each of the following Sturm-Liouville boundary value…

A: For problem (a): y'' + λy = 0,  y'(0) = 0,  y(7π) = 0 1) The general solution y(x) = A cos(√λx) + B…

Q: Answer the equation and it's a different equations problem

A: Step 1:The provided differential equation is:x2dxdy​=y−xy   .........(1)with the initial condition:…

Q: Question 1 Convert the following numbers to binary. Show all working clearly. (a) (i) 75.62510 (ii)…

A: Question 1a) Convert the following numbers to binary:i) 75.62510Integer part:We repeatedly divide…

Q: Review of complex numbers 1=Re 22=R₂e z= 212=R₁ Re(+2) Cz-Re(6+2x/8) The complex conjugate of z =…

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Q: These integrals are transformations to solve differential equations, and there is a relationship…

A: Step 1: solution of answer (1)      Step 2: solution of question (2) Step 3: Step 4:

Q: Determine whether the transformation is one-to-one and/or onto. PROVE YOUR ANSWER. 3. Let 7: R4 → R³…

A: Step 1: To determine whether the linear transformation  (T:R4→R3) defined by  (T(x)=Ax), where the…

Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs…

A: Required code:# Visualization of a linear functional on the unit ball in R^2 # Define the unit…

Q: Q1/ Use Elzaki Adomian decomposition method to solve the following nonlinear partial differential…

A: Q1: Elzaki Adomian Decomposition Method (EADM)The equation to solve is:Step 1: Apply Elzaki…

Q: Given the letters A, B, C, D, E, F, G, H, I, J: (a) How many length-5 lists can be made from these…

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Q: 12. Prove that any subgraph of a bipartite graph is bipartite.

A: Define the ProblemLet G = (V, E) be a bipartite graph where V is the set of vertices and E is the…

Q: Solve the 2-dimensional steady-state heat equation problem. J²u a²u + = 0 მე2 Jy2 u (0, y) = И 1 (1,…

A: Steps to Solve the Problem:

Q: Find I, for the curve x = tcost, y = tsint and z = t² if ♪ (density) is proportional to √(1+52) from…

A: Step 1:Given: x=tcost,y=tsint,z=t2 δ∝1+5z​Therefore, δ=K1+5z​=K1+5t2​ where K is a proportionality…

Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) * Give appropriate graphs…

A: Required code:import numpy as np import matplotlib.pyplot as plt # Define the functions f and g x =…

Q: Can you please answer the attached grade 12 advance functions math equation on paper and please make…

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Q: Let S be the part of the plane 2x + 3y + z = 3 which lies in the first octant, oriented upward. Find…

A: To find the flux of the vector field F = i + 2j + 3k across the surface S (the part of the plane 2x…

Q: does bus Exercise 3.3.5. Decide whether the following propositions are true or false. If the claim…

A: (a) The arbitrary intersection of compact sets is compact. Truth Value: True Proof: Let {Ki​}i∈I​ be…

Q: Review of complex numbers 22-R₂e 2122 R₁ R₂+82) 01+02 =Rje C32=Re(+2x/8) The complex conjugate of z…

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Q: ki ли Mi 00 f.(+) 1+x, kz M₂ → f₂(+) 00 1-7x2 A system is modeled by a pair of masses m₁, m2…

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Q: -21 4. Find the general solution of the system x' = -1 0 x. Sketch the phase plane diagram of the…

A: Nature of the Critical Point :

Q: (3) A common way to prove that two sets A and B are equal is to show that AC B and B C A. Write down…

A: Proof that A is a subset of B:We are given that:A = {x ∈ ℝ : x² - x - 2 = 0}B = {-1,…

Q: Need detailed solutions

A: Use this python code for graphs:import numpy as np import matplotlib.pyplot as plt # Create a grid…

Q: Problem 3 3.0r €2.5 Long bones have a thick layer of hard cortical bone, and a porous inner bone…

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Q: Specifying the corresponding bijection, show ̇̇e the sets $A=[0,1]$ and $B=(0,1)$ are equipotent.

A: 1.f(x)={           x/2​,  ​,​if x∈[0,0.5)           1-(1-x)/2  if x∈[0.5,1]​           }2.To prove f…

Q: Please solve and show all steps.

A: Step 1: Step 2: Step 3: Step 4:

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Q: Please solve using Linear Algebra and show all steps and work.

A: Step 1: Step 2: Step 3: Step 4:

Q: Please solve this question it has sub parts to it. Appreciate your time. Also consider what the…

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Q: CAN YOU EXPLAIN THE DIFFERENCE BETWEEN i and ii AND CAREFULLY EXPLAIN HOW YOU GO ABOUT CONSTRUCTING…

A: Part (ii): (0,1) is equivalent to [a,b]To prove this, we need to find a bijective function g: (0,1)…

Q: Can you please answer the attached grade 12 advance functions math questions on paper and please…

A: Trigonometric functions (sin or cos) are characterized by the form of:y = Asin(B(x-C))+Dwhere:|A| =…

Q: Need help with probability.

A: Step 1: GivenE[(X−1)2]=10E[(X−2)2]=6 Step 2:Expand E[(X−1)2]=10E[X2+1−2X]=10E[X2]+E[1]−2E[X]=10The…

Q: Ex 1.4: Suppose n observations X1, X2,..., Xn have mean μ, variance σ², and cor(Xi, Xi+1) = p for…

A: a)Suppose n observations X1,X2,...,Xn​ have mean μ, variance σ2, and correlation cor(Xi,Xi+1)=ρ for…

Q: One cannot fail to notice that in forming linear combinations of linear equations there is no need…

A: # Create a grid of points in R^2 x = np.linspace(-1, 1, 10) y = np.linspace(-1, 1, 10) X, Y =…

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A: It seems like there might be some typos in your question, especially with the expressions. I'll…

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Q: Instructions: *Do not Use AI. (Solve by yourself, hand written preferred) *Give appropriate graphs…

A: Let me solve this Schauder Fixed Points problem step by step.1. Understanding the Problem:- We need…

Q: cuemath Percentage Word Problem worksheet 4 Selve the following to the attached paper Show your 1.…

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Q: Please help and explain for part a b c and d Thank you

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Q: Find the solutions to the following intial value problems.

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