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inn [45]
2 years ago
13

Separating variable in the equation gives you the following equation:​

Mathematics
2 answers:
zlopas [31]2 years ago
7 0

Answer:

\textsf{E.} \quad y\:dy=xe^x\:dx

Step-by-step explanation:

Given equation:

ye^{-x}\dfrac{dy}{dx}=x

Divide both sides by e^{-x}:

\implies \dfrac{ye^{-x}}{e^{-x}}\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}

\implies y\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}

Multiply both sides by dx :

\implies y\:\dfrac{dy}{dx}\cdot dx=\dfrac{x}{e^{-x}}\cdot dx

\implies y\:dy=\dfrac{x}{e^{-x}}\:dx

\textsf{Apply exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:

\implies y\:dy=xe^x\:dx

vova2212 [387]2 years ago
4 0

Answer: E

Step-by-step explanation:

ye^{-x} \frac{dy}{dx}=x\\\\y \frac{dy}{dx}=xe^{x} \\ \\ \boxed{y dy=xe^{x} dx}

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Sherrie's biology class is studying the ability of a certain microbe to dissipate oil spilled in seawater. to be effective the p
choli [55]

The exponential equation for the growth is f(x)=57e^{0.51x} where x is the number of days and the population on 21st march is 2069983.5 of microbes.

Given:

Days                   population

0                                57

1                                 95

5                               700

10                               8525

We have to form exponential equation which shows the growth of microbes.

We know that exponential equation which shows the sum is as under:

f(x)=Pe^{rt} where r is the rate of growth and x is the number of days, months or years depending on how things grows.

In the question when x=0 population is 57.

f(0)=57

Pe^{0}=57

P=57

When x=1, population is 95.

f(1)=95

Pe^{r}=95

57 e^{r}=95

57=95/e^{r}----1

when x=5,population is 700.

f(5)=700

Pe^{5r}=700

57e^{5r}=700

57=700/e^{5r}-----2

Equating 1&2

95/e^{r}=700/e^{5r}

e^{5x} /e^{x} =700/95

e^{5r-r}=7.36

e^{4r}=7.36

(2.7182)^{4r}=(2.7182)^{2}

equating both sides

4r=2

r=0.5

put the value of t=21 in the exponential equation

f(21)=57e^{0.5*21}

=57e^{10.5}

=57*36315.5

=2069983.5

Hence the population on 21st march is 2069983.5.

Learn more about equation at brainly.com/question/2972832

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8 0
2 years ago
Is 21/48 greater or less than 1/2
Vlada [557]

Answer:

Less

Step-by-step explanation:

1/2=.5

21/48=.4

6 0
4 years ago
Read 2 more answers
What property is this?(n+13) + 4 = n + (13+4) Associative Property Commutative Property Additive Identity O Distributive Propert
navik [9.2K]

Answer:associative property?

Step-by-step explanation: because you adding

7 0
3 years ago
5x−4≥12 OR 12x+5≤−4 please answer asap and right and explain like im 5 how to solve OR problems ill give brainliest and a lot of
weeeeeb [17]

Answer: x>_3.2 OR x<_ -0.75

Step-by-step explanation: first break down your compound inequality. 5x-4>_12

You first cancel out your constants by adding 4 to both sides. Now you’re left with 5x>_16 then to cancel five you have to divide on both sides by five which equals to 3.2. Then, x>_ 3.2.

Next you do your second part, 12x+5<_-4

So first cancel out the constant of 5 by subtracting 5 on both sides, making the equation 12x<_-9. Now, you divide by 12 on both sides, making it -9/12. Which effectively is -0.75. Therefor, the answer being x<_ -0.75. Add the two together x>_3.2 OR x<_0.75

4 0
3 years ago
Which rock is mainly made up of quartz, feldspar, mica, and usually hornblende?
vazorg [7]

Answer:

What Minerals Form Rocks?

The list of minerals that commonly form rocks is short. With a little practice you will recognize most of them when you see them. Descriptions of some of the minerals, as they look in rocks, follow: Quartz: Quartz is the last mineral to crystallize, so in igneous rocks it never has any definite shape. In rocks, it does not show flat faces. It is usually gray in igneous rocks; gray, white, yellow, or red in sedimentary rocks; and gray or white in metamorphic rocks. It has a glassy, or sometimes waxy, look to it.

Potassic Feldspars*: (microcline, orthoclase) Potassic feldspars are pink or tan, sometimes white. They show flat, shiny faces in igneous rocks. The crystal grains are usually blocky and nearly rectangular. They look like good china.

Plagioclase Feldspars*: (albite, labradorite) Look like the potassic feldspars, except they are white to dark gray, sometimes black. They may show flashes of blue or green.

Micas*: (muscovite, biotite, phlogopite) Micas have very thin layers that peel off (or cleave) very easily. In rocks they are usually flakes or layers of flakes. Muscovite is silvery to brown; biotite is black; phlogopite is a reddish brown. Phlogopite may be found in marble.

Chlorite*: Like mica, but the flakes are usually not as thin and do not peel apart as easily. The color is medium to dark green, sometimes almost black but with a greenish tint.

Hornblende: Hornblende is dark green to black. It shows nearly flat, shiny faces in almost rectangular or long thin needle like crystals in rock. Hornblende is usually found in dark colored metamorphic rocks; sometimes in igneous rocks.

Actinolite and Tremolite: Actinolite and tremolite are usually in long thin blades or needle like crystals. Actinolite is dark green; tremolite is white to gray. The crystals may be parallel to each other, or spread from a point. Actinolite is usually found in schists or gneisses. Tremolite may be found in marble.

Olivine*: Olivine in rocks is an olive green to greenish yellow. In rocks it is in rounded grains. If there is much of it, it is almost sugary. It is found mostly in dark colored igneous rocks.

Calcite and Dolomite: The color is usually white, but can be other colors when impure. Crystal grains show flat shiny faces, often shaped like parallelograms. Calcite and dolomite are both soft. They are easily scratched with a steel point. Powdered calcite will fizz in white vinegar; dolomite will not. The minerals are found in limestone or dolostone ( the rock is dolostone, the mineral is dolomite) and marble.

4 0
3 years ago
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