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andreev551 [17]
3 years ago
5

13. Find the measure of ZABC. Show your work.​

Mathematics
1 answer:
ale4655 [162]3 years ago
6 0

Answer:

47°

Step-by-step explanation:

In the picture attached, the problem is shown.

When two secants intersect at a point, the angle made is one-half of the difference between the greater arc and the minor arc formed. In this case:

∠ABC = 1/2*(arc DE - arc AC)

Replacing with data from the picture:

∠ABC = 1/2*(142° - 48°)

∠ABC = 47°

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Angela wants to estimate the mean number of siblings for each student in her school. She records the number of siblings for each
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Answer:

the number of siblings for each of student that Angela selected

Step-by-step explanation:

The data that you are interested is the number of siblings for each student in Angela´s school, so the data is centered in the number of siblings for the 200 randomly selected students.

Its like Angela will survey each student and ask for the number of siblings and she will record the answer of her companions of school.

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3 years ago
Here are 100 seats on an airplane, and each of 100 passengers has a ticket for a different seat. The passengers line up to board
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Answer:

There are 1% probability that the last person gets to sit in their assigned seat

Step-by-step explanation:

The probability that the last person gets to sit in their assigned seat, is the same that the probability that not one sit in this seat.

If we use the Combinatorics theory, we know that are 100! possibilities to order the first 99 passenger in the 100 seats.

LIke we one the probability that not one sit in one of the seats, we need the fraction from the total number of possible combinations, of combination that exclude the assigned seat of the last passenger. In other words the amount of combination of 99 passengers in 99 seats: 99!

Now this number of combination of the 99 passenger in the 99 sets, divide for the total number of combination in the 100 setas, is the probability that not one sit in the assigned seat of the last passenger.

P = 99!/100! = 99!/ (100 * 99!) = 1/100

There are 1% probability that the last person gets to sit in their assigned seat

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3 years ago
Round 3160.9903 to the nearest tenths place
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The tenths place is right after the decimal point. So, 3160.9903 can be 3160.9.
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Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.
jarptica [38.1K]
  • y''-y'+y=\sin x

The corresponding homogeneous ODE has characteristic equation r^2-r+1=0 with roots at r=\dfrac{1\pm\sqrt3}2, thus admitting the characteristic solution

y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x

For the particular solution, assume one of the form

y_p=a\sin x+b\cos x

{y_p}'=a\cos x-b\sin x

{y_p}''=-a\sin x-b\cos x

Substituting into the ODE gives

(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x

-b\cos x+a\sin x=\sin x

\implies a=1,b=0

Then the general solution to this ODE is

\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}

  • y''-3y'+2y=e^x\sin x

\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2

\implies y_c=C_1e^x+C_2e^{2x}

Assume a solution of the form

y_p=e^x(a\sin x+b\cos x)

{y_p}'=e^x((a+b)\cos x+(a-b)\sin x)

{y_p}''=2e^x(a\cos x-b\sin x)

Substituting into the ODE gives

2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x

-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x

\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12

so the solution is

\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}

  • y''+y=x\cos(2x)

r^2+1=0\implies r=\pm i

\implies y_c=C_1\cos x+C_2\sin x

Assume a solution of the form

y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)

{y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)

Substituting into the ODE gives

(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)

-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)

\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49

so the solution is

\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}

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