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White raven [17]
2 years ago
7

A bag contains ten tiles labeled b c d e f g h I j and k of picking a letter that is not a vowel

Mathematics
1 answer:
Lunna [17]2 years ago
3 0

Answer:

The probability of picking a non-vowel  = 9/10

Step-by-step explanation:

Each letter has an equal probability of being picked.

Vowels; e

Number of vowels =1

Non-vowels; b,c,d,f,g,h,l,j,k

Number of non-vowels= 9

Probability of picking a non-vowel = 9/(1+9) = 9/10

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Solve the formula for the perimeter of a rectangle, P = 21 + 2w for l
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2(w+l)=21+2w

w+l=10.5+w

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Solve this problem. 4|3x+4|=4x+8
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Can someone please help me
Umnica [9.8K]

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Answer:

  • central: XWR, VWU
  • inscribed: VST

Step-by-step explanation:

Point W is the center of the circle. Any angle with W as its vertex is a central angle:

  angles XWR and VWU are central angles

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2 years ago
4 sisters share 3 muffins equally how much does each get
Allushta [10]
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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
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