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Maslowich
1 year ago
6

Questions attached as screenshot below:Please help me I need good explanations before final testI pay attention

Mathematics
1 answer:
Nikitich [7]1 year ago
8 0

The acceleration of the particle is given by the formula mentioned below:

a=\frac{d^2s}{dt^2}

Differentiate the position vector with respect to t.

\begin{gathered} \frac{ds(t)}{dt}=\frac{d}{dt}\sqrt[]{\mleft(t^3+1\mright)} \\ =-\frac{1}{2}(t^3+1)^{-\frac{1}{2}}\times3t^2 \\ =\frac{3}{2}\frac{t^2}{\sqrt{(t^3+1)}} \end{gathered}

Differentiate both sides of the obtained equation with respect to t.

\begin{gathered} \frac{d^2s(t)}{dx^2}=\frac{3}{2}(\frac{2t}{\sqrt[]{(t^3+1)}}+t^2(-\frac{3}{2})\times\frac{1}{(t^3+1)^{\frac{3}{2}}}) \\ =\frac{3t}{\sqrt[]{(t^3+1)}}-\frac{9}{4}\frac{t^2}{(t^3+1)^{\frac{3}{2}}} \end{gathered}

Substitute t=2 in the above equation to obtain the acceleration of the particle at 2 seconds.

\begin{gathered} a(t=1)=\frac{3}{\sqrt[]{2}}-\frac{9}{4\times2^{\frac{3}{2}}} \\ =1.32ft/sec^2 \end{gathered}

The initial position is obtained at t=0. Substitute t=0 in the given position function.

\begin{gathered} s(0)=-23\times0+65 \\ =65 \end{gathered}

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Bacteria triples every hour. How much bacteria will there be after two days if they started with 13,000 bacteria.
timofeeve [1]
13,000 • 3 = 1 hour = 39,000
Now we take the one hours worth 39,000 • 48 (hours in two days) = 1,872,000
Hope this helps!
6 0
3 years ago
The temperature fell 5°C each hour for 3h. a. Write an integer multiplication to represent the temperature change, b. What was t
MakcuM [25]

Answer:

Step-by-step explanation:

a) 3 x 5

b) 15 Celcius

8 0
3 years ago
HELP PLS
Neko [114]
Expansions and compressions are transformations that change the length or width of the graph of a function.


 To graph y = a*f (x)
 if a> 1, the graph of y = f (x) is expanded vertically by a factor a. 
 We have then:
 f (x) = 2/5 x ^ 2-2
 The function g (x) is a vertical stretch of f (x) by a factor of 2:
 g (x) = 2f (x)
 g (x) = 2 (2/5 x ^ 2-2)
 g (x) = 4/5 x ^ 2-4

 Answer:
 The equation of g (x) is: 
 g (x) = 4/5 x ^ 2-4
8 0
2 years ago
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of
iris [78.8K]

Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is \\ P(z>0.48) = P(x>533.2) = 0.3156

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> with mean \\ \mu and standard deviation \\ \frac{\sigma}{\sqrt{n}}. Mathematically

\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})

For values of the sample \\ n \ge 30, no matter the distribution the data come from.

And the variable <em>z</em> follows a <em>standard normal distribution</em>, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}} [1]

That is

\\ z \sim N(0, 1)

We have a variance of 3364. That is, a <em>standard deviation</em> of

\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58

The population mean is

\\ \mu = 530

The sample size is \\ n = 75

The sample mean is \\ \overline{x} = 533.2

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}

\\ z = \frac{3.2}{\frac{58}{8.66025}}

\\ z = \frac{3.2}{6.69726}

\\ z = 0.47780

With this value of z we can consult a <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

\\ P(z

However, in the question we are asked for \\ P(z>0.48) = P(x>533.2). As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

\\ P(z>0.48) = 1 - P(z

Thus

\\ P(z>0.48) = 1 - 0.68439

\\ P(z>0.48) = 0.31561

Rounding to four decimal places, we have

\\ P(z>0.48) = 0.3156

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) \\ P(z>0.48) = P(x>533.2) = 0.3156.

5 0
3 years ago
The audience thinks 30\%30%30, percent of Brandon's jokes are funny.
Kisachek [45]

Answer:

3/10

Step-by-step explanation:

Brandon's jokes does the audience think are funny = 30%

What fraction of Brandon's jokes does the audience think are funny?

Express the percentage as a fraction

= 30%

= 30 / 100

= 3/10

The fraction of Brandon's jokes that the audience think are funny is 3/10

6 0
2 years ago
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