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3 years ago

The living room in a new house has the dimensions shown. What is the volume of the room?

Mathematics

1 answer:

irga5000 [103]3 years ago

5 0

Answer:

v = 220 yd²

Step-by-step explanation:

Small portion

v = 5 * 4 * 3

v = 60 yd²

Large portion

v = 9 * 6 * 3

v = 162 yd²

Total

v = 60 + 162

v = 220 yd²

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Exponential Growth and Decay The expressions below represent either exponential growth or exponential decay. Check all the expre

Tomtit [17]

Answer:

First one: 5x3(0.75)2t

and fourth one: 0.05x500(0.005)t

Step-by-step explanation:

In order to have an exponencial decay, the rate of the exponencial function needs to be lesser than 1.

The rate is the value between parenthesis, so in the first equation, the rate is 0.75, so this is an exponencial decay.

The second equation has rate = 2.4, so this is not an exponencial decay.

The third equation has rate = 1.04, so this is not an exponencial decay.

The fourth equation has rate = 0.005, so this is an exponencial decay.

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3 years ago

Read 2 more answers

Sqaure root99, pi^2, 9.8 repeated decimal least to greatest

Aleksandr [31]

Answer:

π^2, 9.8 repeating, square root of 99.

Step-by-step explanation:

6 0

4 years ago

(T+10.5) + 2t + 90 = 180

Masja [62]

Answer:

x = 26.5

Step-by-step explanation:

Step 1: Write equation

(t + 10.5) + 2t + 90 = 180

Step 2: Solve for t

Combine like terms: 3t + 100.5 = 180

Subtract 100.5 on both sides: 3t = 79.5

Divide both sides by 3: t = 26.5

Step 3: Check

Plug in x to verify it's a solution.

Substitute: (26.5 + 10.5) + 2(26.5) + 90 = 180

Parenthesis: 37 + 56 + 90 = 180

Add: 180 = 180

∴ x = 26.5

5 0

3 years ago

Read 2 more answers

PLEASE HELP

alexgriva [62]

Answer:

Step-by-step explanation:

90.25$

5 0

1 year 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:

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

5 0

3 years ago