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2 years ago

12

Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 86 boards,how long are they altoge

ther

1 answer:

BlackZzzverrR [31]2 years ago

4 0

You multiply 86 by 42.5 because each board is 42.5 and there are 86 boards.

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Which values of a, b, and c correctly represent the answer in simplest form? 6 al- o a=1,0-5,0-9 a= 10,5= 18.0= 1 a=9,0-5,0- 1 a

kumpel [21]

Answer:

The question is not explained well, Please explain it better or take a screenshot or something

Step-by-step explanation:

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2 years ago

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:

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

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2 years ago

A large bottle of juice contains 500 milliliters. A smaller size bottle has 70% as much juice. How many milliliters or juice are

marishachu [46]

350 millimeters hope this helps

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2 years ago

Read 2 more answers

What is the value of x? Enter your answer in the box

g100num [7]

x = 180° - 67° - 52°

x = 61°

So, the value of x is 61°

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3 years ago

What is the greatest possible product of a 2-digit number and a 1-digit number.Explain how you know

Elodia [21]

The answer is 891. 99 is the greatest 2 digit number and 9 is the greatest 1 digit number. So the product of the two (multiply them) gives you your answer of 891 (99 x 9 = 891).

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2 years ago