Answer:
Answer is 80.36
Step-by-step explanation:
V=πr2h=π·2.12·5.8≈80.35566
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Answer:
Step-by-step explanation:
Given that acceleration of an object is
![\frac{dv}{dt} =-2v\\\frac{dv}{v} =-2dt\\ln v = -2t+C\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D-2v%5C%5C%5Cfrac%7Bdv%7D%7Bv%7D%20%3D-2dt%5C%5Cln%20v%20%3D%20-2t%2BC%5C%5C)
is the solution to the differential equation
Since v(0) =7
we get ln 7 = C
Hence ![lnv = -2t+ln 7\\v=7e^{-2t}](https://tex.z-dn.net/?f=lnv%20%3D%20-2t%2Bln%207%5C%5Cv%3D7e%5E%7B-2t%7D)
since velocity is rate of change of distance s we have
![v=\frac{ds}{dt} =7e^{-2t}\\s= [tex]s(t) =\frac{-7}{2} (e^{-2t})+C)[](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bds%7D%7Bdt%7D%20%3D7e%5E%7B-2t%7D%5C%5Cs%3D%20%5Btex%5Ds%28t%29%20%3D%5Cfrac%7B-7%7D%7B2%7D%20%28e%5E%7B-2t%7D%29%2BC%29%5B)
substitute t=0 and s=0
![C=7/2](https://tex.z-dn.net/?f=C%3D7%2F2)
So solution for distance is
![s(t) =\frac{-7}{2} (e^{-2t}-1)](https://tex.z-dn.net/?f=s%28t%29%20%3D%5Cfrac%7B-7%7D%7B2%7D%20%28e%5E%7B-2t%7D-1%29)
A translation 2 units to the left followed by dilation by 1/2.
The correct option is (B).
<h3>What is congruency?</h3>
It states that that two triangles are said to be congruent if they are copies of each other and when superposed, they cover each other exactly.
The complete question is:
Which of the following composition of transformations would create an
image that is not congruent to its original image?
A rotation of 45° followed by a reflection across the x-axis
A translation 2 units to the left followed by dilation by 1/2
A reflection across the y-axis followed by a rotation of 60°
A rotation of 135º followed by a translation of 4 units to the right.
After a translation of 2 units to the left followed by dilation by 1/2 the image will not be congruent to its original image.
All other options are reflection and rotation, which not fit into the situation.
Learn more about congruency here:
brainly.com/question/7888063
#SPJ1
Answer:
i must be popular because my phone is blowing up- hyperbole
her smile lit up my day-metaphor
the dog continued to bark, speaking with authority-personification
he wept like a faucet-simile
Step-by-step explanation:
Answer:
Anything that does not cost more than $2,560.00
Step-by-step explanation:
Provided that Nikita is spending money that she had invested and the amount she collected over the period of 7 years. She can buy any item that costs no more than $2,560.00 but how?
It is a problem of simple interest:
Here the principal amount (P) = $2,000.00
Interest rate (r) = 4%
Time period (t) = 7 years
So, total amount that she would get by the end of 7 years is:
![A=P+SI](https://tex.z-dn.net/?f=A%3DP%2BSI)
![SI=\frac{P\times r\times t}{100}](https://tex.z-dn.net/?f=SI%3D%5Cfrac%7BP%5Ctimes%20r%5Ctimes%20t%7D%7B100%7D)
Plugging the values we get:
![SI=\frac{2000\times 4\times 7}{100}=560.00](https://tex.z-dn.net/?f=SI%3D%5Cfrac%7B2000%5Ctimes%204%5Ctimes%207%7D%7B100%7D%3D560.00)
So the interest collected over 7 years is $560.00
Therefore, the total amount after 7 years is:
![\$2000.00+\$560.00=\$2,560.00](https://tex.z-dn.net/?f=%5C%242000.00%2B%5C%24560.00%3D%5C%242%2C560.00)
If Nikita is using this money then the most expensive item that she could buy will cost no more than $2,560.00.