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artcher [175]
3 years ago
9

Researchers have found that after 25 years of age the average size of the pupil in a

Mathematics
1 answer:
laila [671]3 years ago
8 0

Answer:

At 25 = 6.8612mm

At 50 years = 5.422mm

Step-by-step explanation:

Equation,

d = 2.115Logₑa + 13.669

d = diameter of the pupil

a = number of years

Note : Logₑa = In a (check logarithmic rule)

d = 2.115Ina + 13.669

1. At 25 years,

d = -2.115In25 + 13.669

d = -2.115 × 3.2188 + 13.669

d = -6.807762 + 13.669

d = 6.8612mm

At 25 years, the pupil shrinks by 6.86mm

2. At 50 years,

d = -2.1158In50 + 13.669

d = -2.1158 * 3.912 + 13.669

d = -8.2770 + 13.699

d = 5.422mm

At 50 years, the pupil shirks by 5.422mm

To save this question, I had to plug in the values into the equation.

Solving for Logₑa might be difficult, so instead I used Inx which is the same thing. Afterwards, i substituted in the values and solve the equation for each years.

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<span>1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

</span>a) <span>show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

</span><span>* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y =  570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words</span><span>

The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
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0.30x = 0.6

x = 0.6 / 0.3 = 2

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e) check:

x + y = 12
2 qt + 10qt = 12 qt
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vinegar:

10*0.3 = 12*0.25
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f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

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Answer:

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