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aivan3 [116]
3 years ago
6

Find the slope between: (1, -4) (-6, -1)

Mathematics
2 answers:
miv72 [106K]3 years ago
6 0
Slope = -3/7

use the slope formula: y2-y1 over x2-x1

-1-(-4) over -6-(-1) = -3/7
alexdok [17]3 years ago
4 0
Use gradient formula
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Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
HELP I’ll give you brainliest <br> This is timed I have 5 minutes
DiKsa [7]
Pretty sure it’s y=(x-5)^2+7
4 0
3 years ago
Name the<br> L corresponding<br> angle with<br> angle 2.
olchik [2.2K]

Answer:

D  angle 6

Step-by-step explanation:

Corresponding angles are in the same place if the line were on top of each other.  For example, ang1e 1  and angle 5, are corresponding;  angle 3 and angle 7 are corresponding.

6 0
2 years ago
Please help me with 7 and 10!! i’ll mark you brainliest:)
Irina-Kira [14]

Answer:

7. 18,480 feet

10. (a.) 1.5     (b.) 150%     Sorry I don't know the answers to c & d.

Step-by-step explanation:

7. \frac{3.5 miles}{1 ft.} × \frac{5,280 ft.}{1 mile} = 18,480ft.

Hope this helps!

7 0
3 years ago
What is the measure of
Art [367]
I believe it’s the bottom option since both triangles are the same and a triangle is 180° and if you subtract 60° you’ll get 120°
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2 years ago
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