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2 years ago

15

Identify the place value of digit 9 in each given number.

1 answer:

Ostrovityanka [42]2 years ago

5 0

Step-by-step explanation:

1) Thousands

2) 100 thousands

3) tens

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in Hanley's school, 0.723 of the students participated in an event. if there are 1000 students in Hanley School, how many partic

Ugo [173]

Answer:

723 students participated in the event

Explanations:

The total number of students in Hanley's school = 1000

0.723 of the students participated in an event

Number of students that participated in the event = 0.723 x 1000

Number of students that participated in the event = 723

4 0

10 months ago

What is a non-example of a independent variable?

alexandr402 [8]

An non-example of a independent variable is how much money you make selling cookies , because it depends on the number of cookies you sell .

7 0

3 years ago

Read 2 more answers

Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

3 years ago

FRACTIONS! PLEASE HELP!!

Alenkinab [10]

1. 1/4, 2/7, 3/8
2. 12/5
3. 3/4, 7/10, 7/12
4. 1/6, 1/2, 1/4

3 0

3 years ago

The new post office has an area that is 6.5 times the area of the old post office. Let p represent the area of the old post offi

IrinaK [193]

Answer:

$Area = 6.5p$

Step-by-step explanation:

Given

$Area\ of\ Old = p$

$Area\ of\ New = 6.5 * Area\ of\ Old$

Required

Write an expression for the area of new post office

From the question, we have the following:

$Area\ of\ Old = p$

and

$Area\ of\ New = 6.5 * Area\ of\ Old$

Substitute p for Area of Old in the second equation

$Area\ of\ New = 6.5 * p$

$Area\ of\ New = 6.5 p$

Hence, the expression is:

$Area = 6.5p$

5 0

2 years ago