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e-lub [12.9K]
3 years ago
7

Find the general solution of the differential equation. (use c for the constant of integration.) dr dt = 8et 1 − e2t

Mathematics
1 answer:
natulia [17]3 years ago
5 0
Try this solution:
if given dr/dt=8e^t -e^(2t), then
\frac{dr}{dt}=8e^t-e^{2t}; \   \int\ {dr} \, =\int\ (8e^t-e^{2t})dt;  \ r=8e^t- \frac{1}{2}e^{2t}+C.
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Is there a smallest decimal that is greater than the number 2? Explain your answer.
olga nikolaevna [1]

Answer:

Technically, yes. It's called epsilon, which is defined as an infinitely small number. So

 2 + epsilon is the smallest number greater than 2. But for practical purposes no there isn't.

00

Step-by-step explanation:Not without limits. You can always move the .1 one place further from the interring. For example,  

2.1>2.01

and  

2.01>2.001

So, unless there are a limited number of decimal spaces, you can continually add an infinite amount of zeros behind the decimal point, followed by a one.

If you use two or three decimal spaces as a standard in your class, then the smallest decimal greater than 2 would be 2.01 or 2.001, respectively.

8 0
3 years ago
Can someone please help
EastWind [94]
You basically just switch it around and subtract the fractions

7 0
3 years ago
Please solve the following quadratic equation and show your work: x^2 -x =30
saveliy_v [14]
Rewriting the equation as a quadratic equation equal to zero:
     x^2 - x - 30 = 0
We need two numbers whose sum is -1 and whose product is -30. In this case, it would have to be 5 and -6. Therefore we can also write our equation in the factored form
     (x + 5)(x - 6) = 0
Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x + 5) or (x - 6) zero will make their product zero.
     x + 5 = 0  => x = -5
     x - 6 = 0  => x = 6
Therefore, our solutions are x = -5 and x = 6.
8 0
3 years ago
2x 1/2 x3 2/3 im goin to be need a lot of helpppp
RSB [31]

Answer:

3.66666666667

or

3.67(rounded to the nearest tenth)

Step-by-step explanation:

2x 1/2 x3 2/3 = 3.66666666667

<em>Ace Carlos</em>

<em>Developer</em>

4 0
4 years ago
Read 2 more answers
Write the quadratic function with the following transformations: vertical shrink by 3, left 4, down 9.
xz_007 [3.2K]
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\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\&#10;\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}&#10;\\\\&#10;\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\&#10;\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\&#10;\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\

\bf \bullet \textit{ vertical shift by }{{  D}}\\&#10;\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\&#10;\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\&#10;\bullet \textit{ period of }\frac{2\pi }{{{  B}}}


with that template in mind, let's see

so, the parent equation could be
y = x²      ====>     y = A(x + C)² + D

shrink by 3, A = 3
left 4, C = +4
down 9, D  = 9
7 0
4 years ago
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