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3 years ago

14

2. Write the algebraic phrases that correspond to the following word phrases: (a) The sum of four times the opposite of a number

and - 5 (b) The product of 5 and the sum of 3 times a number and 4

1 answer:

Alekssandra [29.7K]3 years ago

6 0

Answer:

would not be helpful to anser nowww... sory!

Step-by-step explanation:

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Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

Someone please help me out

enyata [817]

Answer:

5/18

Step-by-step explanation:

if they r talking bout the whole pie lol

3 0

2 years ago

Read 2 more answers

The length of a concrete slab is three more than three times the width. It's area is 330 square feet. What is the length of the

marin [14]

Answer:

Width: 10.5 feet

Length: 31.5 feet

Step-by-step explanation:

Let x represent width of the concrete slab.

We have been given that the length of a concrete slab is three more than three times the width. So length of the slab would be $3x$ .

We are also told that the area of slab is 330 square feet. We can represent this information in an equation as:

$x\cdot 3x=330$

$3x^2=330$

$x^2=\frac{330}{3}$

$x^2=110$

Now, we will take square root of both sides.

$\sqrt{x^2}=\sqrt{110}$

$x=10.488\approx 10.5$

Therefore, the width of slab is approximately 10.5 feet.

The length of the slab would be $3x\Rightarrow3(10.5)=31.5$ .

Therefore, the length of slab is approximately 31.5 feet.

6 0

3 years ago

Read 2 more answers

What is absolute deviation?

zlopas [31]

The average absolute deviation (or mean absolute deviation ( MAD )) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). answer:

Step-by-step explanation:

7 0

3 years ago

Hello!! I Need HElp ASAP PLEAASSEE

MatroZZZ [7]

Answer:

a = -1

Step-by-step explanation:

The line of symmetry for the parabola given by ...

y = ax² +bx +c

is

x = -b/(2a)

Using the given values, we have ...

-2 = -(-4)/(2a)

Multiplying by -a/2, we get ...

a = (4/2)(-1/2) = -1

The value of "a" is -1.

8 0

3 years ago