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Tju [1.3M]
3 years ago
5

Situation:

Mathematics
1 answer:
Rzqust [24]3 years ago
8 0
N=NOe^-kt
N=mass at time t
NO = initial mass
k= 0.1476
t= time, in days

We are asked to find the half-life, which means you want to find how long it will take for half of the substance to decay/disappear (depending on situation). 

If we are looking for half-life, we can simply set N to half of NO (which we are given a value of 40grams for)
Therefore:
N = 20
NO = 40
plugging these values and the value given for k back into the equation you get:

20 = 40e^-0.1476(t)
We are looking for t, so we have to manipulate the formula to get t by itself on one side of the equation.
We can start by dividing 40 from both sides, and you get:
0.5 = e^-0.1476(t)

We have the exponential function "e".
To get rid of e, we can use natural log (ln)
if e^y=x then ln (x) = y
look back at our equation we can set
0.5 = x
-0.1476(t) = y

Rewriting it in natural log form:
ln (0.5) = -0.1476(t)
Plug in ln (0.5) on a calculator to find its value and we get:
-0.693147 = -0.1476(t)
*Note: normally, getting a negative value would suggest that we did something wrong, because you cannot have a negative value as your t (you cannot have negative days), but because there is a negative on both sides of the equation, they will cancel out in this case. 

The last step is to simply divide both sides by -0.1476
therefore:
T = 4.696119
But it asks you for the answer to the nearest tenth (one place after decimal pt) so 
T (half life) = 4.7 days

Hope that helps :)
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Nutka1998 [239]
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2x = 0.24
x = 0.24 / 2
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so 2 factors would be 2 and 0.12.....because 2 * 0.12 = 0.24
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Step-by-step explanation:

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cinema A sells a twelve pack of moive passes for $66. Cinema B selles a five pack of moive passes for $28. Find the cost per moi
nekit [7.7K]
CINEMA A sells each movie pass for $5.50, and CINEMA B sells each movie pass for $5.60.

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2. <br> Find the area of the region bounded by the graphs of y = -x2 + 3x + 4 and y = 4. (5 points)
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Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.
Whitepunk [10]

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

<h3>What is law of cosine?</h3>

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

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We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

Learn more about law of cosines here:

brainly.com/question/17289163

#SPJ1

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