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pochemuha
3 years ago
14

Solve differential equation dy(t) / dt = -2y(t) with initial condition y = 2 when t = 1

Mathematics
1 answer:
juin [17]3 years ago
6 0

Answer:

y = 2e^[2(1 - t)]

Step-by-step explanation:

1/y . dy = -2. dt

ln(y) = -2t + c

ln(2) = -2(1) + c

c = 2 + ln(2)

ln(y) = -2t + ln(2) + 2

ln(y) - ln(2) = 2 - 2t

ln(y/2) = 2 - 2t

y/2 = e^(2 - 2t)

y = 2e^[2(1 - t)]

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Given the rule: an=7(1/2)n-1 identify the first term
Shkiper50 [21]

Answer:

  • using the rule given: 2.5
  • using an exponential rule: 7

Step-by-step explanation:

Evaluating the linear rule given, for n = 1, we have ...

  a1 = 7(1/2)(1) -1 = 7/2 -1 = 5/2 = 2.5

_____

We suspect you may intend the exponential function ...

  an = 7(1/2)^(n-1)

Then, for n = 1, we have ...

  a1 = 7(1/2)^(1 -1) = 7(1) = 7 . . . . the first term is 7

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When writing an exponential expression in plain text, it requires the exponential operator, a caret (^). If the exponent contains any arithmetic, as this one does, it must be enclosed in parentheses.

3 0
3 years ago
Round 18.049 to the nearest tenth.
kirill115 [55]

Answer:

18.0

Step-by-step explanation:

Note the tenth place value (underlined and bolded): 18.<u>0</u>49

Look at the number to the direct right of the tenth place value (or the hundredth place value in this case). It is a 4.

Note the rules of rounding. If the number:

1) is 5 or greater, round up.

2) is 4 or less, round down.

In this case, it is 4, so you will round down.

18.049 rounded to the nearest tenth is 18.0

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4 0
3 years ago
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Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2? explain your answer
sertanlavr [38]
It takes 3 copies of 1/6 to show the same amount as 1 copy of 1/2 because 3 copies of 1/6 would add up to 3/6 thus making it 1/2 
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3 years ago
Find the product (x - 10) ( x - 5)​
Hatshy [7]

꙰  Hello there mohammedsaquibali45 ! My Name is ⚝Tobie⚝ and I'm glad you asked! Let me walk you step by step in order to comprehend the question better!   ꙰  

i

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x

2

−5x−10x+50

ii Collect like terms.

{x}^{2}+(-5x-10x)+50

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2

+(−5x−10x)+50

iii Simplify.

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3 years ago
A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls to a height of 8 inches on the other side o
Kisachek [45]

Answer: \frac{1}{2} inch

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