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Vladimir79 [104]
3 years ago
7

Write an equation in slope-intercept form for the line with slope −6 and y - intercept 6 .

Mathematics
1 answer:
valkas [14]3 years ago
7 0

Answer:y=-6x+6

Step-by-step explanation:

The format is y=mx+c

m=slope c=y-intercept

Slope given=-6

y-intercept=6

Therefore they equation will be

y=-6x+6

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4 years ago
The diagonals in a kite __________.
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Three equal-sized cardboard boxes are stacked on top of each other. Each box is 56.4 cm in height. What is the combined height o
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Answer:

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Solve Using Dirac Deltla/discontinuous forcing
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Let A(t) denote the amount of salt in the tank at time t. We're told that A(0)=0.

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\text{rate in}=u(t)-u(t-15)+20\delta(t-15)

(in lb/min)

The salt from the mixed solution flows out at a rate of

\text{rate out}=\left(\dfrac{A(t)\,\mathrm{lb}}{50+(5-5)t\,\mathrm{gal}}\right)\left(5\dfrac{\rm gal}{\rm min}\right)=\dfrac A{10}\dfrac{\rm lb}{\rm min}

Then the amount of salt in the tank at time t changes according to

\dfrac{\mathrm dA}{\mathrm dt}=u(t)-u(t-15)+20\delta(t-15)-\dfrac A{10}

Let \hat A(s) denote the Laplace transform of A(t), \hat A(s)=\mathcal L_s\{A(t)\}. Take the transform of both sides to get

s\hat A(s)-A(0)=\dfrac1s-\dfrac{e^{-15s}}s+20e^{-15s}-\dfrac1{10}\hat A(s)

Solve for \hat A(s), then take the inverse of both sides.

\hat A(s)=\dfrac{\frac{10-10e^{-15s}}{s^2}+\frac{200e^{-15s}}s}{10s+1}

\implies\boxed{A(t)=10-10e^{-t/10}+\left(30e^{3/2-t/10}-10\right)u(t-15)}

7 0
4 years ago
Help I got too much homework today help me please
DiKsa [7]

Solution:

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