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wel
3 years ago
15

PLEASE HELP!!!

Mathematics
2 answers:
ludmilkaskok [199]3 years ago
4 0

Answer:

The half life of the substance is 6.0 days.

Step-by-step explanation:

The initial equation for the initial mass and mass at time t is;

                                N = N_{0} e^{-kt}

Where N is the mass at time t, N_{0} is the initial mass, k is the constant and t is the half life. After the half life i.e t,

So that at a given time t, N_{0} = 33 grams and N = 16.5 grams

        ⇒       16.5 = 33 e^{-kt}

                  16.5 = \frac{33}{e^{kt} }

cross multiply, we have;

                e^{kt} = \frac{33}{16.5}

                  e^{kt} = 2

Find the natural logarithm of both sides,

          ln e^{kt}  = ln2

          kt = ln2

 ⇒     t = \frac{ln2}{k}

         t = \frac{0.6932}{0.1142}

         t = 6.07

The half life of the substance is 6.0 days.

 

Aneli [31]3 years ago
3 0
From the attached graphic, Half-life = ln (.5) / k

Half-life =.693147 / <span>0.1142
= </span><span><span><span>6.0695884413 </span> days

The value of "k" should be negative and should have units associated with it.
</span> </span>

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3 years ago
A brick is 5/7 of a foot tall. If you need to build a brick wall that is 10 feet tall, how many bricks tall will the wall be?
svlad2 [7]

Answer:

7 1/7

Step-by-step explanation:

For the problem:

5 /7 × 10  = ?

Convert any mixed numbers to fractions:

10 = 10

Multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:

5 × 10

7 × 1

=  

50 /7

50 ÷ 7 = 7R1, therefore:

50 /7 =  7 1/7

The result is:

5

7

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3 years ago
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3 years ago
Savvas Texas Algebra II
Elan Coil [88]

Answer:

The number of small balloons = 46

The number of large balloons = 159

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

Step-by-step explanation:

The volume of each small balloon = 300 in.³

The volume of each large balloon = 1000 in.³

The cost of one package of 50 small balloons = $2.59

The cost of one package of 24 large balloons = $1.99

The volume of one small tank of pressurized helium = 20 ft³

The volume cost of one small tank of pressurized helium = $10.49

By conversion

20 ft³ = 34,560 in.³

The volume of 30 small balloons = 30 × 300 in.³ = 9,000 in.³

The volume of 30 large balloons = 30 × 1000 in.³ = 30,000 in.³

The volume taken by 24 large balloons = 24,000 in.³,

24 large balloons cost = $1.99

The volume taken by 50 small balloons = 15,000 in.³

50 small balloons cost = $2.59

Therefore, we buy more large balloons

We have;

A×300 + B×1000 = C×34,560

Given that all the helium will be used, the volume of helium will be a multiple of 300, therefore, when 5 bottles of helium is used, we have;

A×300 + B×1000 = 5×34,560 = 172,800 in.³

Given that there will be at least 30 of each balloon, gives;

We remove the minimum possible quantity (more than 30) of small balloons from 172,800 in.³ leaving multiples of 1,000s as follows;

Using Excel, the quantities of 36 and 46 small balloons give the same cost

For 46 small balloons

The volume of 46 small balloons = 13,800 in.³

Therefore, 172,800 in.³ - 13,800 in.³ = 159,000  in.³ = The volume of the large balloons

The quantity of the large balloons = 159,000  in.³/(1,000  in.³/balloon) = 159 balloons

Therefore, we have 46 small balloons, and 159 large balloons, with 5 small bottles of helium gas

The number of package of large balloons is 159/24 = 6.625 ≈ 7 packages

The cost of the 7 packages of large balloons = 7 × $1.99 = $13.93

The number of package of small balloons is 46/50= 0.92 ≈ 1 package

The cost of the 1 packages of small balloons = 1 × $2.59 = $2.59

The cost of the five bottles of helium = 5 × $10.49 = $52.45

$68.97

The number of small balloons = 46

The number of large balloons = 159

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

At the same cost, we can also have;

The number of small balloons = 36

The number of large balloons = 162

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

Therefore, we can have 36 or 46 small balloons and 162 or 159 large balloons along with 5 bottles of helium gas with a total cost of $13.93 + $2.59 + $52.45 = $68.97.

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The point Al-2, 3) is translated using T: (x,y) → (x+4, y+2).
almond37 [142]

Answer:

The distance between A and A' is:

distance=\sqrt{20}

Step-by-step explanation:

Notice that point A' after the given translation becomes: (-2+4, 3+2) = (2, 5),

So one can calculate the distance between A (-2, 3) and A' (2, 5) using the distance formula:

distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\distance=\sqrt{(2-(-2))^2+(5-3)^2} \\distance=\sqrt{(4))^2+(2)^2} \\distance=\sqrt{(16+4} \\distance=\sqrt{20}

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