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Tanzania [10]
3 years ago
8

Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. Ho

w many liters of each does he need
to make the needed 60 liters of 60% acid solution?
Mathematics
1 answer:
timofeeve [1]3 years ago
3 0

Answer:

20 liters of the 40% solution

60-20=40 liters of the 70% solution

Step-by-step explanation:

40%x+70%(60-x)=60%(60)

0.4x+0.7(60-x)=0.6(60)

0.4x+42-0.7x=36

-0.3x+42=36

-0.3x=-42+36

-0.3x=-6

0.3x=6

3x=60

x=60/3

x=20 liters of the 40% solution

60-20=40 liters of the 70% solution

check: 0.4*20=8

0.7*40=28

8+28=36 and 0.6*60=36 also

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Answer:

Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) 3\,in, c) 4.5\,in, d) 6.5\,in, e) 10\,in, f) 13.5\,in

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

y = \sqrt{l^{2}-x^{2}} (1)

Where:

l - Hypotenuse, in inches.

x - Known leg, in inches.

y - Unknown leg, in inches.

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The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

x + y > l > x-y (2)

Where:

x - Greater side, in inches.

y - Lesser side, in inches.

l - Missing side, in inches.

If we know that x = 8\,in and y = 6\,in, then we have the following range of missing sides:

14\,in > l > 2\,in

The following straws can be used to construct the triangle: b) 3\,in, c) 4.5\,in, d) 6.5\,in, e) 10\,in, f) 13.5\,in

Exercise 4:

Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

(i) x = 4\,in, y = 2\,in

6\,in>l>2\,in

Possible choices: 5 inches.

(ii) x = 5\,in, y = 2\,in

7\,in > l > 3\,in

Possible choices: 4 inches, 6 inches.

(iii) x = 6\,in, y = 2\,in

8\,in > l > 4\,in

Possible choices: 5 inches, 6 inches.

(iv) x = 10\,in, y = 2\,in

12\,in > l > 8\,in

Possible choices: None.

(v) x = 5\,in, y = 4\,in

9\,in > l > 1\,in

Possible choices: 2 inches, 6 inches.

(vi) x = 6\,in, y = 4\,in

10\,in > l > 2\,in

Possible choices: 5 inches.

(vii) x = 10\,in, y = 4\,in

14\,in > l > 6\,in

Possible choices: None.

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11\,in > l > 1\,in

Possible choices: 2 inches, 4 inches, 10 inches.

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15\,in > l > 5\,in

Possible choices: 6 inches.

(x) x = 10\,in, y = 6\,in

16\,in > l > 4\,in

Possible choices: 5 inches.

Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

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