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irga5000 [103]
3 years ago
13

1. Carbon-14 is used to determine the age of artifacts in carbon dating. Carbon-14 has a half-life of 5730 years. Write an expon

ential decay function for a 52-mg sample

Mathematics
1 answer:
masha68 [24]3 years ago
3 0
See the attached graphic.  (I'm rewording the attached formula)
Ending amount = Beginning Amount * e ^(k * t)
where "e" is the mathematical constant 2.718281828
and k = natural log (.5) / half-life
k = -.693147 / 5,730 = <span><span><span>-0.000120968062827225 </span> </span> </span>
Ending amount = 52 * e ^(-0.000120968062827225* t)

As a test, let's see how much remains after <span> <span> <span> 11,460 </span> years.</span>
</span>Ending amount = 52 * e ^(-0.000120968062827225 * 11,460)
Ending amount = 52 * e ^ ( <span> <span> <span> -1.386294 </span> </span> </span> )
Ending amount = 52 * <span> <span> <span> 0.250000
</span></span></span>Ending amount = 13
(which is correct because that is one quarter of the amount after two half-lives).

Source:
http://www.1728.org/halflif2.htm


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Solve each compound inequality. Graph your solutions.<br> 5 + m &gt; 4 or 7m&lt; -35
Yuliya22 [10]

Answer:

Solving the inequality 5 + m > 4\: or\: 7m< -35 we get \mathbf{m>-1\:or\: \:m

The graph of the inequality is shown in figure attached.

Step-by-step explanation:

We need to Solve each compound inequality 5 + m > 4\: or\: 7m< -35

Solving the inequalities

For solving compound inequalities we solve both inequalities simultaneously and find the value of m.

For solving 5+m > 4, we subtract 5 from both sides.

While solving 7m < -35, we divide both sides by 7 to get value of m

Applying these functions we get:

5 + m > 4\: or\: 7m< -35\\m>4-5\:or\:m-1\:or\:m

So, solving the inequality 5 + m > 4\: or\: 7m< -35 we get \mathbf{m>-1\:or\: \:m

The graph of the inequality is shown in figure attached.

5 0
2 years ago
Help- ASAP please (25 points)
Alina [70]

Answer:

(t^2 -4) (t^2 +4)

(t-2)(t+2)(t^2+4)

Step-by-step explanation:

t^4 - 16

We can write this as the difference of squares

We know the dfference of squares is

(a^2 - b^2) = (a-b) (a+b)

( t^2 ^2 - 4^2) = (t^2 -4) (t^2 +4)

We can write t^2 -4 as the difference of squares

t^2 -4 = t^2 -2^2 = (t-2)(t+2)

Replacing this in

( t^2 ^2 - 4^2) = (t^2 -4) (t^2 +4) =  (t-2)(t+2)(t^2+4)

8 0
3 years ago
Read 2 more answers
With full explanation from the internet like before<br> 3x2-6x+5=0
Elodia [21]

Answer:

\sf x=1+i\sqrt{\dfrac{2}{3}}   \ \quad and  \quad \:x=1-i\sqrt{\dfrac{2}{3}}

Explanation:

<u>Given Expression</u>:

  • 3x² - 6x + 5 = 0

Use the Quadratic Formula:

\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a}  \  \ when   \ \  ax^2 + bx + c = 0

<u>insert coefficients</u>

\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}

\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}

\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}

\Longrightarrow \sf x =1 \pm   i\dfrac{\sqrt{6} }{3}

\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}},  \quad 1-i\sqrt{\dfrac{2}{3}}

6 0
2 years ago
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PLEASE HELP WORTH 99 POINTS AND CORRECT ANSWER WILL GET BRAINLIEST
Soloha48 [4]

Hello!

I believe the answers are:

A) The vertex is (1, −6)

C) The graph has a minimum.

I hope it helps!

7 0
2 years ago
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