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tiny-mole [99]
2 years ago
15

Container A has 300 grams of salt water with 13% concentration. Container B has 700 grams of salt water with 7% concentration. A

fter we take out a certain amount of solution from Container A and the same amount from container B, we pour what we take out from A into B and vice versa. Now the two containers have the same concentration. How many grams of solution did we take out from each container?
Mathematics
1 answer:
Triss [41]2 years ago
6 0

Answer:

210 grams

Step-by-step explanation:

Simply, the final amount of each container will not be changed because we add and subtract same amount of solution in the end. Therefore final mass of Container A is 300 grams and final mass of Container B is 700 grams.

However if concentration of the both containers is the same, final amont of the salt should have following relation;

\frac{m_{A}}{m_B}=\frac{3}{7}

where m_A is the amount of salt in container A, and m_B is the amount of salt in container B.

Suppose that the x is the amount that we take away from both containers and than pour into other container. For container A, finally we will have (300-x) grams with 13% concentration and x grams with 7% concentration and vice versa. Total amount of salt in container can be written as,

m_A=(300-x)*\frac{13}{100} +x*\frac{7}{100}=\frac{3900-6x}{100}

similarly for container B ,

m_B=(700-x)*\frac{7}{100} +x*\frac{13}{100}=\frac{4900+6x}{100}

if we replace these values in first equation above and solve for the x,

\frac{m_A}{m_B}=\frac{3900-6x}{4900+6x}=\frac{3}{7}

7*3900- 42x=3*4900+18x\\60x=12600\\x=210

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The Square of the sum of three and five
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3 years ago
A. Evaluate the polynomial
sdas [7]

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a) y = x³− 5x² + 6x + 0.55 at x = 1.37.

Use 3-digit arithmetic with chopping. Evaluate the percent relative round-off error.

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b. Express y as y = ((x − 5)x + 6)x + 0.55 (this is the same equation). Use again 3-digit arithmetic with chopping. Evaluate the percent relative round-off error and compare with part (a). Make the conclusion about which form of the polynomial is superior.

-0.161%

Comparing part a and b together, part b is more superior because the percent(%) error is smaller when compared to part a

Step-by-step explanation:

a) y = x³− 5x² + 6x + 0.55 at x = 1.37.

Use 3-digit arithmetic with chopping. Evaluate the percent relative round-off error.

Let's evaluate before applying the 3 digit arithmetic chopping rule

y = 1.37³ - 5 × 1.37² + 6 × 1.37 + 0.55

y = 1.956853

Let evaluate each components of the polynomial one by one

Note that: 3-digit arithmetic chopping means to approximate chop off or remove number after the 3 significant figures.

y = x³− 5x² + 6x + 0.55 at x = 1.37.

x³ = 1.37³ = 2.571353

≈ 2.57

x² = 1.37² = 1.8769

≈ 1.88

5x² = 1.87 × 5

= 9.35

x = 1.37

6x = 1.37 × 6

6x = 8.22

Evaluating the polynomial

y = 2.57 - 9.38 + 8.22 + 0.55

y = 1.98

The percent relative round-off error =

1.956853 - 1.98/1.956853 × 100

= -1.183%

b. Express y as y = ((x − 5)x + 6)x + 0.55 (this is the same equation). Use again 3-digit arithmetic with chopping. Evaluate the percent relative round-off error and compare with part (a). Make the conclusion about which form of the polynomial is superior.

y = ((x − 5)x + 6)x + 0.55

Evaluating with the 3 digit chop off rule is applied

= ((1.37 - 5)1.37 + 6)1.37 + 0.55

=( 1.8769 - 6.85) + 6) 1.37 + 0.55

= (- 4.9731 + 6 )1.37 + 0.55

= 1.0269 × 1.37 + 0.55

= 1.406853

= 1.956853.

≈ 1.96

Note in: evaluating before applying the 3 digit arithmetic chopping rule

y = 1.37³ - 5 × 1.37² + 6 × 1.37 + 0.55

y = 1.956853

The percent relative round-off error

1.956853 - 1.96/1.956853 × 100

= -0.161%

Comparing part a and b together, part b is more superior because the percent(%) error is smaller when compared to part a

3 0
3 years ago
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