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2 years ago

Please help for another 10 points :))

Mathematics

2 answers:

MA_775_DIABLO [31]2 years ago

8 0

(-3,3)
i hope this helps :)

Nadya [2.5K]2 years ago

7 0

Answer:

(-3, 3)

Step-by-step explanation:

You need to find the median of the x value, and then the median of the y value, and that's your point. Good luck. I never liked graphing.

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Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

3 years ago

In the figure, x ǁ y and a ǁ b. What is m∠2? m∠2 = ___°

Marizza181 [45]

∠2 =∠1 which is 180° -65° =115°
So ∠2=115°

8 0

3 years ago

Read 2 more answers

Rewrite the expression, the quotient of k decreased by 4 and 9, using the division symbol and as a fraction.

AlexFokin [52]

Answer:

(k - 4) ÷ 9

(k - 4) / 9

Step-by-step explanation:

k decreased by 4 = k - 4

quotient of k decreased by 4 and 9

= (k - 4) ÷ 9 (using division sign)

= (k - 4) / 9 (as a fraction)

8 0

3 years ago

Please help due soon

Schach [20]

Answer:

You should divide (÷)

Step-by-step explanation:

4.80÷ 80/100

then u add them together and get ur answer

4 0

3 years ago

ABC and ACD are both right angled triangles. a) explain why the length of AC is 13cm.

timofeeve [1]

Answer:

In the picture attached, the question is shown.

a) Applying Pythagorean theorem to triangle ABC, and solving for AC:

CB² + BA² = AC²

5² + 12² = AC²

√169 = AC

13 cm = AC

b) Applying Pythagorean theorem to triangle ACD, and solving for AD:

CD² + AC² = AD²

5² + 13² = AD²

√194 = AD

13.9 cm = AD

Step-by-step explanation:

6 0

2 years ago

Please help for another 10 points :))​

Please help for another 10 points :))