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Alla [95]
3 years ago
8

Bronze is an alloy or mixture of the metals copper and tin. The properties of bronze depends on the percentage of copper in the

mix. A chemist decides to study the properties of a given alloy of bronze as the proportion of copper is varied. She starts with 7 kg of bronze that contain 3.5 kg of copper and 3.5 kg of tin and either adds or removes copper. Let f(x) be the percentage of copper in the mix if x kg of copper are add (x>0) or removed (x<0).
(
a. State the domain and range of f (assume that the chemist wants a non-negative amount of both copper and tin).
Domain: Range: What do each of the answers mean in the context of bronze?
The domain tells us The range tells us (
b. Write a formula in terms of x for f(x). (
c. If the formula you found in part (
b. was not intended to represent the percentage of copper in an alloy of bronze, but instead simply defined an abstract mathematical function, what would be the domain and range of this function?
Domain: Range:
Mathematics
2 answers:
bija089 [108]3 years ago
7 0

(a)

Because there is 3.5 kg of copper in the original mix, then the maximum amount of copper that can be removed is 3.5 kg, in that case, x would be equal to -3.5 and the percentage of copper would be 0%. Then, (-3.5, infinity) interval is the domain. When 3.5 kg of copper are removed, f(x) = 0%, and in the limit when x tends to infinity, f(x) = 100%. So, the range is 0% to 100%.      

(b)

The percentage of copper in the mix, f(x) = 100*(3.5 + x)/(7 + x)

where x is kg of copper that are add (x>0) or removed (x<0)

(c)

In this case, the domain of the function is every real number except -7, i. e., (-infinity, -7) U (-7, infinity) interval.  

The range of a rational function where the grade of the polynomial in the numerator is less or equal than the grade of the polynomial in the denominator is all real numbers, i. e., (-infinity, infinity) interval.

olchik [2.2K]3 years ago
5 0
A. The domain is any real number.
The range is f(x) ≥ 0.5 (or 50%)

b. The formula is
f(x) = (3.5 + x) / (7 + x)

c. The domain is any number except -7. The range is any real number greater than 0.
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What is 246 : 7 in long division​
Mars2501 [29]

Here we will show you step-by-step with detailed explanation how to calculate 246 divided by 7 using long division.

Before you continue, note that in the problem 246 divided by 7, the numbers are defined as follows:

246 = dividend

7 = divisor

Step 1:

Start by setting it up with the divisor 7 on the left side and the dividend 246 on the right side like this:

7 ⟌ 2 4 6

Step 2:

The divisor (7) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:

0

7 ⟌ 2 4 6

Step 3:

Multiply the divisor by the result in the previous step (7 x 0 = 0) and write that answer below the dividend.

0

7 ⟌ 2 4 6

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.

0

7 ⟌ 2 4 6

- 0

2

Step 5:

Move down the 2nd digit of the dividend (4) like this:

0

7 ⟌ 2 4 6

- 0

2 4

Step 6:

The divisor (7) goes into the bottom number (24), 3 time(s). Therefore, put 3 on top:

0 3

7 ⟌ 2 4 6

- 0

2 4

Step 7:

Multiply the divisor by the result in the previous step (7 x 3 = 21) and write that answer at the bottom:

0 3

7 ⟌ 2 4 6

- 0

2 4

2 1

Step 8:

Subtract the result in the previous step from the number written above it. (24 - 21 = 3) and write the answer at the bottom.

0 3

7 ⟌ 2 4 6

- 0

2 4

- 2 1

3

Step 9:

Move down the last digit of the dividend (6) like this:

0 3

7 ⟌ 2 4 6

- 0

2 4

- 2 1

3 6

Step 10:

The divisor (7) goes into the bottom number (36), 5 time(s). Therefore put 5 on top:

0 3 5

7 ⟌ 2 4 6

- 0

2 4

- 2 1

3 6

Step 11:

Multiply the divisor by the result in the previous step (7 x 5 = 35) and write the answer at the bottom:

0 3 5

7 ⟌ 2 4 6

- 0

2 4

- 2 1

3 6

3 5

Step 12:

Subtract the result in the previous step from the number written above it. (36 - 35 = 1) and write the answer at the bottom.

0 3 5

7 ⟌ 2 4 6

- 0

2 4

- 2 1

3 6

- 3 5

1

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 246 divided by 7 calculated using Long Division is:

35

1 Remainder

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