Problem 3. Consider the second-order linear ODE: x"(t) + 64x(t) = where x(0) = ? and x'(0) = |3D !! 3' (a) Using the substitution x1(t) = x(t) and x2(t) = x'(t), rewrite the second order equation as a system of linear first-order differential equations. Write your final system in matrix/vector form. (b) Solve this system by finding eigenvalues and eigenvectors of the matrix, and then reexpress your solutions so that your final solution contains only real numbers. Express the general so- lution of your system in matrix form, and the particular solution using the initial conditions above. (c) Graph the phase portait of your vector solution on the x1x2 axis. (d) Interpret your solution the initial conditions to find the solution to the second-order ODE x(t) exactly. (e) Verify that your solution is correct by showing that x1 (t) = x(t) satisfies the original second- order differential equation and its initial conditions.

Q: 4x; x = 8?

A: Find 4x if x= 8?

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A: Given, 3X = 27

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A:

Q: (d) Solve you х

A: d) From Part (a), it is known that the least square equation for the pairs (x,y) is: The value for…

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A:

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A: Given: 7x = 14

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A: We use definitions of polynomial function and degree of the polynomial to answer the given question.

Q: Please solve (b)

A: Given

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Q: -4.5 x -2.5

A:

Q: X=7, Y=24 and Z=25

A: Use trigonometric ratio

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Q: Why is x=-4 not a solution for the highlighted problem?   Thanks.

A:

Q: a. Sx-14= 8r+4

A: Given  a.) 5x -14 = 8x+4 b.) -12(-4x + 3 ) -2 = 1 +12 x

Q: 3) Solve for x: 32x + 1 = 27*

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A: Straight line

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A: Given: We have to differentiate implicitly to find

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A: Solution-

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A: Consider the equation

Q: Solve for x: 7**2 = 52x-3 %3D

A: We have to simplify this expression and then take the log on both sides, then solve for x.

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Q: 6x=47 x=?

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Q: Can you solve d thru f ?

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.