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2 years ago

What temperature is 10 degrees less than 4 degrees Celsius ?

Mathematics

2 answers:

Nataly_w [17]2 years ago

5 0

4 degrees C - 10 degrees C = negative 6 degrees C

Paraphin [41]2 years ago

3 0

It would be -6 degrees Celsius because you are subtracting 10 from 4.
4-10=-6

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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

PLEASE HELP ASAP!!! DUE IN 20 MINUTES!!

frez [133]

Answer:

6 blocks each measuring One-third times 1 times 1

Step-by-step explanation:

8 0

2 years ago

Max competed in a 50-meter freestyle swimming event. His finishing time was 31.26 seconds. What is the value 6 in Max's time (pl

miss Akunina [59]

Answer:

2.9 seconds

Step-by-step explanation:

3 0

2 years ago

Ali buys pair of shoes for $18 the price is one fourth off the original price what decimal represents the discount?

jeyben [28]

The discount is one fourth, or 1/4 as a fraction.

To convert fraction to decimal, divide the numerator by the denominator.
1/4= 0.25

You can also convert to a fraction over 100, so that you can create a decimal down to the hundredths place value.
1/4= 25/100= 0.25

Final answer: 0.25

3 0

3 years ago

According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an a

CaHeK987 [17]

Answer:

a) 0.0065 = 0.65% probability of receiving no emails during an hour.

b) 0.1212 = 12.12% probability of receiving at least three emails during an hour

c) The expected number of emails received during 15 minutes is 1.2604.

d) 0.2835 = 28.35% probability that no emails are received during 15 minutes

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

In this question.

121 emails per day.

A day has 24 hours, so per hour, 121/24 = 5.0417, which means that $\mu = 5.0417n$ , in which n is the number of hours.

A. What is the probability of receiving no emails during an hour?

n = 1, so $\mu = 5.0417$

This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065$

0.0065 = 0.65% probability of receiving no emails during an hour

B. What is the probability of receiving at least three emails during an hour?

Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So

$P(X < 3) + P(X \geq 3) = 1$

We want $P(X \geq 3)$

Then

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065$

$P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326$

$P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212$

0.1212 = 12.12% probability of receiving at least three emails during an hour

C. What is the expected number of emails received during 15 minutes?

15 minutes is a fourth of an hour, so n = 1/4 and $\mu = \frac{5.0417}{4} = 1.2604$

The expected number of emails received during 15 minutes is 1.2604.

D. What is the probability that no emails are received during 15 minutes?

$P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835$

0.2835 = 28.35% probability that no emails are received during 15 minutes

6 0

2 years ago