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inna [77]
1 year ago
9

Differential equations dy/dx = e^x-y

Mathematics
1 answer:
MA_775_DIABLO [31]1 year ago
5 0

\frac{dy}{dx}=e^{x-y} \\ \\ \frac{dy}{dx}=\frac{e^{x}}{e^{y}} \\ \\ e^{y} \text{ } dy=e^{x} \text{ } dx \\ \\ \int e^{y} \text{ } dy=\int e^{x} \text{ } dx \\ \\ e^{y}=e^{x}+C \\ \\ \boxed{y=\ln \left(e^{x}+C \right)}

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Would the function ƒ(x) = 4 be considered a step function? Explain your reasoning.
lana66690 [7]

Hey there! I'm happy to help!

A step function is a function that looks like stairs when you graph it. Normally the end of one line will be graphed as an open circle (less or greater than, not equal to) while the other end would be a closed circle. This allows for a new line of the function to start directly above it without it not being a function (an input cannot have two outputs)

The function f(x)=4 is just a horizontal line as it has a slope of 0 (there is no x on the right side of the equation), so this doesn't resemble a step function.

Have a wonderful day and keep learning! :D

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3 years ago
Tim count his friends fingers by fives. he counts the fingers on six hands. what number does he say?
Fudgin [204]
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6 0
3 years ago
Add 5 gal 2qt + 4gal 3qt​
loris [4]
It’s 9 gal and 3 qt.
6 0
3 years ago
Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material
Contact [7]
<span>(a) What is the capacity of the container?
Volume = length * width * height
V = 4ft * 2ft * 3ft
V = 24 ft</span>³
<span>
(b) How much material was used to make the container?
Surface area = sum of 6 faces of the prism
4 ft x 3 ft = 12 ft</span>² → 12 ft² x 2 = 24 ft²
<span>4 ft x 2 ft = 8 ft</span>² → 8 ft² x 2 = 16 ft²
<span>2 ft x 3 ft = 6 ft</span>² → 6 ft² x 2 = 12 ft²
<span>
Surface area = 24 ft</span>² + 16 ft² + 12 ft² = 52 ft²<span>

</span>
4 0
3 years ago
Read 2 more answers
Oil prices are projected to increase by 50% by next March. A quart of oil currently costs $1.85. What is the projected cost of a
Zolol [24]

Answer:

$11.10 per gallon.

Step-by-step explanation:

There are 4 quarts in a gallon so the cost of a gallon of oil currently is 1.85×4=$7.40

If the gallon price of oil goes up 50% then our answer is: 7.40×\frac{3}{2}=\frac{22.2}{2}=11.1

The price of oil in March will be $11.10 per gallon.

6 0
3 years ago
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