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Sladkaya [172]
4 years ago
15

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∘.
Mathematics
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)}

8 0
3 years ago
I need help with my math homework
OLEGan [10]
You need help answering all of them right ??
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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
irina [24]

Answer:

2\frac{5}{8}\ gal

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

so

5\frac{1}{4}\ gal=\frac{5*4+1}{4}=\frac{21}{4}\ gal

step 2

Divide the total gallons of paint by two

\frac{(21/4)}{2}=\frac{21}{8}\ gal

step 3

Convert improper fraction to mixed number

\frac{21}{8}\ gal=\frac{16}{8}+\frac{5}{8}=2+\frac{5}{8}=2\frac{5}{8}\ gal

7 0
3 years ago
Find the area of polygon​
Mumz [18]

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

area of triangle formula:

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

1) area of triangle AED

base = 12 cm

height = 4.5 cm

area:

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

area of rectangle formula:

length \times height

2) area of rectangle ABCD

length = 12cm

height = 5 cm

area:

12 \times 5 = 60 \: cm {}^{2}

3) area of whole polygon

= area of triangle AED + area of rectangle ABCD

= 27 cm² + 60 cm²

= 87 cm²

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3 years ago
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Answer:

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