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1 year ago

12

the half -life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mas

s. starting with 155 gramsbof a radioactive isotope, how much will be left after 3 half-lives?

1 answer:

SVETLANKA909090 [29]1 year ago

7 0

Answer:

after 3 half lives the amount should be reduced to 19.375g

Step-by-step explanation:

after the first half life , amount left =

155÷2

= 77.5g

2nd half life

77.5÷2

=38.75g

3rd Half life

38.75÷2

=19.375g

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56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

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

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

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2 years ago

What is the first step in solving this equation?<br><br> 10d - 4 = 91

Vikentia [17]

Answer:

Step-by-step explanation:

the first step in solving this equation is adding 4 on both sides

10d = 95

d = 95/10 = 9.5

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2 years ago

These are the means and standard deviations for samples of prices from two

marysya [2.9K]

Its Letter B!!!!!!!!!!!!

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1 year ago

Rewrite in simplest terms: 5(0.9m+0.5)-3(0.4m+0.7)

hram777 [196]

Answer:

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Step-by-step explanation:

Multiply 5 and 0.9m

Multiply 5 and 0.5

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Hope this helps!

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2 years ago

HELP ASP Lucy has a jewelry business. To make a certain necklace, she spends $3.38 on materials and $5.57 on labor. She then sel

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2 years ago