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Nitella [24]
2 years ago
11

You need a 75% alcohol solution. On hand, you have a 25 mL of a 10% alcohol mixture. You also have 80%

Mathematics
1 answer:
Ilya [14]2 years ago
8 0

Answer:

325 mL

Step-by-step explanation:

You will use all 25mL of the 10%, and you will add an amount of 80% solution that will result in a 75% solution.

We need to find the amount of 80% solution added that will produce a 75% alcohol solution.

Let the amount of 80% solution be x.

Amount of alcohol:

10% * 25 mL + 80% * x = 75% * (25 mL + x)

2.5 + 0.8x = 18.75 + 0.75x

0.05x = 16.25

x = 16.25/0.05

x = 325

Answer: 325 mL

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What is the circumference of a circular amphitheater with a diameter of 33 meters
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if alpha and beta are the roots of the equation 3x^2-9x+2=0 find the values of: (I) alpha ×beta + alpha^2 × beta. (ii) alpha^2-a
Kryger [21]

Answer:

in steps

Step-by-step explanation:

The question did not state if alpha>beta or alpha<beta, so the answer will have 2 answers  for each questions

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x = (-(-9) ± √(-9)²-4*(3)*(2)) / (2*3)

x = (9 + √57) / 6   or x = (9 - √57) / 6      (alpha and beta) or (beta and alpha)

(I) alpha (a) ×beta (b) + alpha² × beta = ab (1+a)

   = ((9 + √57) / 6) ((9 - √57) / 6) (1 + (9 ± √57))  

   = ((9² - (√57)²)/36) (10 ± √57)

   = (24/36) (10 ± √57)

   = 2/3 (10 ± √57)   or (11.7 or 1.63)

(ii) alpha²-alpha×beta+beta² = a² -2ab + b² +ab = (a - b)² + ab

if a is alpha    

=​ ((9 + √57) / 6) - ((9 - √57) / 6)) + ((9 + √57) / 6) ((9 - √57) / 6))  

    = √57/3 + 2/3

     = (√57 + 2) / 3

if a is beta

((9 - √57) / 6) - ((9 + √57) / 6)) + ((9 - √57) / 6) ((9 + √57) / 6))  

    = - √57/3 + 2/3

     = - (√57 + 2) / 3

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Answer:

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Step-by-step explanation:

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