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3 years ago

Select all the statements that apply to the concept of a residual

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

4 0

Answer:

first and second one, and fourth one

Step-by-step explanation:

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What is the slope of a line passing through (5, 9) and (7, 15)?

LenaWriter [7]

Slope = change in y / change in x

= (15 - 9) / (7 - 5)

= 6 / 2

= 3

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3 years ago

1000 grams 1 kilogram 6,000 grams x kilograms

Dominik [7]

Answer:

6 kilograms

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Question on laplace transform... number 7

irinina [24]

Recall a few known results involving the Laplace transform. Given a function $f(t)$ , if the transform exists, then denote it by $F(s)$ . We have

$\mathcal L_s\left\{e^{ct}f(t)\right\}=\mathcal L_{s-c}\left\{f(t)\right\}=F(s-c)$

$\mathcal L_s\left\{\displaystyle\int_0^t f(u)\,\mathrm du\right\}=\dfrac{F(s)}s$

$\mathcal L_s\left\{f'(t)\right\}=sF(s)-f(0)$

Let's put all this together by taking the transform of both sides of the ODE:

$y'(t)+2e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du=e^{-t}\sin t$

$\implies \bigg(sY(s)-y(0)\bigg)+2\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\dfrac1{(s+1)^2+1}$

Here we use the third fact and immediately compute the transform of the right hand side (I'll leave that up to you).

Now we invoke the first listed fact:

$\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\mathcal L_{s+2}\left\{\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}$

Let $g(u)=e^{2u}y(u)$ . From the second fact, we get

$\mathcal L_s\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s)}s\implies\mathcal L_{s+2}\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s+2)}{s+2}$

From the first fact, we get

$G(s)=\mathcal L_s\left\{e^{2u}y(u)\right\}=Y(s-2)$

so we're left with

$\dfrac{G(s+2)}{s+2}=\dfrac{Y((s+2)-2)}{s+2}=\dfrac{Y(s)}{s+2}$

To summarize, taking the Laplace transform of both sides of the ODE yields

$sY(s)+\dfrac{2Y(s)}{s+2}=\dfrac1{(s+1)^2+1}$

Isolating $Y(s)$ gives

$Y(s)=\dfrac1{\left(s+\frac2{s+2}\right)\left((s+1)^2+1\right)}$
$Y(s)=\dfrac{s+2}{\left((s+1)^2+1\right)^2}$

All that's left is to take the inverse transform. I'll leave that to you as well. You should end up with something resembling

$y(t)=\dfrac12(t\cos t-(t+1)\sin t)(\sinh t-\cosh t)$

4 0

3 years ago

Paula spent 3/8 of her allowance on clothes and 1/6 on entertainment. What fraction of her allowance did she spent on other item

kompoz [17]

3/8 x 3 = 9/24
1/6 x 4 = 4/24
9/24 + 4/24 = 13/24

24/24 - 13/24 = 11/24

3 0

3 years ago

Artie needs to save $450 to buy the new bicycle that he wants. He currently has $300. What percent of the cost of a new bicycle

lora16 [44]

"Artie needs to save $450 to buy the new bicycle that he wants. He currently has $300. What percent of the cost of a new bicycle has he saved?"

Write and solve an equation of ratios (proportions)"

$300 x
--------- = ------- which results in x = 300/450 = 0.667 (approx.) or 20/3.
$450 1

and this works out to 67% (answer)

7 0

3 years ago