Firstly , before solving the equation , we should know about the chain rule and its formula.
<u>Formula</u><u> </u><u>For</u><u> </u><u>the</u><u> </u><u>Chain</u><u> </u><u>rule-</u>
$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$
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$\sf\huge\underline{\underline{Question:}}$
$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$
$\sf\huge\underline{\underline{Solution:}}$
$\sf{Let\:y = (3x^2 - 9x + 5)^9}$
$\space$
☆ Differentiating both the sides w.r.t.x using chain rule-
$\mapsto$
$\space$
$\space$
$\mapsto$ = $\sf\small{(3x^2-9+5)}$
$\space$
$\space$
$\mapsto$ =
$\space$
$\space$
$\mapsto$ = $\times$
$\space$
$\space$
$\mapsto$ =
$\space$
$\space$
$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$
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Hello!
I'm assuming that the values you gave are 18, 12 and 14, but there's a period before the 14, I think that's a mistake but if it's not please let me know, anyhow, the least common multiple of 12, 14 and 18 is 252.
Good luck!
If 12 = 2y, then y = 6. To solve this kind of equation, whatever you do to one side of the equation, you must do to the other, and it will remain equivalent. If you divide both sides by 2, you get 6 = y. Also, 2 * 6 = 12, a much easier way to find the answer.
62.5 mg sample will remain after 240 days
Step-by-step explanation:
Given
Half-life = T = 60 days
The formula for calculating the quantity after n half lives is given by:
Here
N is the final amount
N_0 is the initial amount
n is the number of half lives passed
The number of half lives are calculated by dividing the time for which the remaining quantity has to be found by half life
The quantity has to be calculated for 240 days so,
Given
Putting the values in the formula
Hence,
62.5 mg sample will remain after 240 days
Keywords: Half-life, sample
Learn more about half-life at:
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