Answer:
∠ 5 = 40°
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and supplementary, thus
∠ 2 = 180° - ∠ 1 = 180° - 140° = 40°
∠ 5 and ∠ 2 are alternate angles and congruent , thus
∠ 5 = 40°
You need 1/4 of sugar per cup of flour. So you need 4 cups of flour for every one cup of sugar
Answer:
a.) 4 half lives have passed
b) 9.388 minutes
Step-by-step explanation:
Formula for exponential growth / decay is given as:
![A=A_0b^{\frac{t}{c}}](https://tex.z-dn.net/?f=A%3DA_0b%5E%7B%5Cfrac%7Bt%7D%7Bc%7D%7D)
Where
is the final population
is the initial population
is the growth factor
is the time taken for the growth 'b'
is the amount of time
Here, we are given that:
= 6. 9 grams
= 110.4 grams
![b = \dfrac{1}{2}](https://tex.z-dn.net/?f=b%20%3D%20%5Cdfrac%7B1%7D%7B2%7D)
min
To find:
a.) Number of half lives taken for the decay.
b.) Total time in the decay.
Solution:
a.) Number of half lives taken for the decay is nothing but equal to
.
Putting the values in the formula, we get:
![6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4](https://tex.z-dn.net/?f=6.9%3D110.4%5Ctimes%20%5Cfrac%7B1%7D2%5E%7B%5Cfrac%7Bt%7D%7Bc%7D%7D%5C%5C%5CRightarrow%206.9%3D110.4%5Ctimes%200.5%5E%7B%5Cfrac%7Bt%7D%7Bc%7D%7D%5C%5C%5CRightarrow%200.0625%3D0.5%5E%7B%5Cfrac%7Bt%7D%7Bc%7D%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bt%7D%7Bc%7D%20%3D4)
Therefore, the answer is:
<em>4 half lives </em>have passed.
b.) Total time of decay. We have to find the value of
here.
From answer of part a.):
![\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}](https://tex.z-dn.net/?f=%5Cdfrac%7Bt%7D%7Bc%7D%20%3D4%5C%5C%5CRightarrow%20%5Cdfrac%7Bt%7D%7B2.347%7D%20%3D4%5C%5C%5CRightarrow%20t%20%3D%5Cbold%7B9.388%5C%20min%7D)