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2 years ago

Simplify (9y²-x² )÷ (xy+3y²)

Mathematics

1 answer:

alexdok [17]2 years ago

6 0

Step-by-step explanation:

$\cfrac{(9y²-x² )}{ (xy+3y²)}$
$\cfrac{3 {}^{2} (y) {}^{2} - x}{3(y {})^{2} + xy }$
$3 {}^{2 - 1} y {}^{2 - 2 - 1} - x {}^{2 - 1}$
$3 y { }^{ - 1} - x$

$\cfrac{3}{y} - x$

Therefore,the answer is $\cfrac{3}{y} - x$ .

[Some of the steps I didn't show,try by yourself,to find!]

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3 years ago

Jen picked 3/4 of a gallon of strawberries in half an hour.If she keeps picking strawberries at the same time, how many gallons

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Number of gallons of strawberries will she have picked in 2 hours is, 3

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Unit rate defined as the rate are expressed as a quantity of 1, such as 4 feet per second or 6 miles per hour, they are called unit rates.

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3 years ago

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

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