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kirill [66]
3 years ago
8

What is the minimum number of base-ten pieces needed to replace each set?

Mathematics
1 answer:
andreev551 [17]3 years ago
3 0

Answer:

The answer is .B

Step-by-step explanation:

Hope this can help you !

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umka2103 [35]
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5 0
3 years ago
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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
Write an expression with five different terms that is equivalent to 8x^2 + 3x^2 + 3y
Misha Larkins [42]

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

An expression having five terms which is equivalent to above term is :

  • 5x {}^{2}  + 3 {x}^{2}  + 3{x}^{2}  +4y - y

3 0
3 years ago
How do you solve this?? Please help!
Aleks04 [339]

f = (f1 f2) / (f1 + f2)

f(f1 + f2) =  f1 f2

f f 1 + f  f 2 = f1 f 2

f1 f2 - f f2 = f f1

f2 (f1 - f)  = f f1

f2 = (f f1) / (f1 - f) <==== solution


5 0
4 years ago
30 random samples of high school students were asked if they played a sport for their high school. Each sample was 20 students.
Ludmilka [50]

Answer:

<em>a. This option is correct</em>

<em>b. This will be true only if we take the </em><em>mode</em><em> as the best representative value </em>

c. <em>This is a correct choice</em>

<em>d. This is not a correct choice</em>

Step-by-step explanation:

<u>Statistics</u>

We are given a dot plot representing 30 random sample proportions of high school students about their sports activities. Based on the data extracted from the plot, we can make some basic conclusions and, less accurately, some predictions.

From the data plot we can see that the following proportions were obtained, along with their absolute frequencies:

0.05 -> 3

0.10 -> 8

0.15 -> 7

0.20 -> 5

0.25 -> 4

0.30 -> 2

Let's select which of the following options are correct

a. A sample proportion of 0.20 means that 4 of 20 high school students responded that they play a sport.

The ratio between the sport playing students to the total of high school students is

\displaystyle \frac{4}{20}=\frac{1}{5}=0.20

Thus, this statement is correct.

b. The best prediction for the proportion of all high school students that play a sport is 0.10.

This will be true only if we take the mode as the best representative value for the whole dataset. Personally, I don't like to trust the mode as a good central tendency result, I'd prefer the mean instead.

c. The mean of the 30 sample proportions calculated to the nearest hundredth is 0.16

Computing the mean of the sample proportions

\displaystyle \bar x=\frac{\sum x_i.f_i}{\sum f_i}

\displaystyle \bar x=\frac{0.00\cdot 1+0.05\cdot 3+0.10\cdot 8+0.15\cdot 7+0.20\cdot 5+0.25\cdot 4+0.30\cdot 2}{1+3+8+7+5+4+2}

\bar x\approx 0.16

<em>This is a correct choice</em>

d. The shape of the sample distribution is fairly symmetrical

We can see the distribution if left-skewed because its peak value is not at the mean value. The mode and the mean are fairly different, thus this choice is not correct

5 0
3 years ago
Read 2 more answers
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