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4 years ago

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Rank the vector combinations on the basis of their angle, measured counterclockwise from the positive x axis. vectors parallel t

o the positive x axis have an angle of 0∘ . all angle measures fall between 0∘ and 360∘.

1 answer:

Charra [1.4K]4 years ago

8 0

The correct answer for this question is this one:

<span>
1- have an angle of 0∘ .
</span>2- vectors parallel to the positive x axis<span>
3- all angle measures fall between 0∘ and 360∘.</span>
Hope this helps answer your question and have a nice day ahead.

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Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation:

$53a_0=15\implies a_0=\dfrac{15}{53}$

Then the general solution to the equation is

$x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}$

With $x(0)=8$ , we have

$8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}$

and with $x'(0)=-19$ ,

$-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}$

Then the particular solution to the equation is

$\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}$

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3 years ago

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3 years ago

Kristy wanted to divide her paint evenly into two-3 1/2-gallon containers. She had 5 1/4 gallons of paint. How much paint did sh

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Answer:

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Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

so

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step 2

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3 years ago

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Answer:

87 cm²

Step-by-step explanation:

there is 1 triangle and 1 rectangle in the diagram. so you have to find the area of the both polygons and sum up to find the total area of polygon

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$\frac{1}{2} \times base \times height$

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base = 12 cm

height = 4.5 cm

area:

$\frac{1}{2} \times 12 \times 4.5 = 27 {cm}^{2}$

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