Mathematics, 03.02.2021 14:00 kmcpig

.A tank contains seven liters of 10% alcohol solution. How many liters of 6% alcohol solution should be added to have 8% alcohol solution?

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The amount of 6% alcohol solution should be added to 7 liters of 10% alcohol solution to have 8% alcohol solution is 7 liters.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 6% mixed in the 10% alcohol be x.

We know that the total solution is 7 liter of 10% alcohol, and x liters of 6% alcohol. And we need to make 8% alcohol solution, therefore, the total alcohol in the mixed solution can be written as,

$(10\%\ of\ 7\ liters) + (6\%\ of\ x\ liters) = (8\%\ of\ Total\ solution)\\\\(0.10 \times 7)+(0.06 \times x) = 0.80(7+x)\\\\0.7 + 0.06x = 0.56 +0.08x\\\\0.14 = 0.02x\\\\x = 7$

Hence, the amount of 6% alcohol solution should be added to 7 liters of 10% alcohol solution to have 8% alcohol solution is 7 liters.

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Answer from: zahid79

7 liters of 6% alcohol solution.

Step-by-step explanation:

We have 7 liters of 10% alcohol solution, and in this the total amount of alcohol is

A = (10%/100%)*7 L = 0.1*7L = 0.7L

Now, suppose that we add N liters of 6% alcohol solution, then we have a total of:

(N + 7) Liters

And the total amount of alcohol would be:

(6%/100%)*N + 0.7L

0.06*N + 0.7L

The quotient between the total volume of alcohol and the total volume of liquid needs to be 0.08 (because we want a percentage of 8% of alcohol, and the decimal form of 8% is 0.08)

Then:

(0.06*N + 0.7L)/(N + 7L) = 0.08

We want to sove this for N

(0.06*N + 0.7L) = 0.08*(N + 7L)

0.06*N + 0.7L = 0.08*N + 0.56L

0.7L - 0.56L = 0.08*N - 0.06*N

0.14 L = 0.02*N

0.14L/0.02 = N = 7L

Then we need to add 7 liters of 6% alcohol solution.

Answer from: Quest

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Answer from: Quest

answer: $\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

$\frac{sin40^{\circ}}{x} = \frac{sin60^{\circ}}{12}$

which is the required equation for finding the value of x,

$\frac{x}{sin40^{\circ}}= \frac{12}{sin60^{\circ}}$

$x= 12\times \frac{sin40^{\circ}}{sin60^{\circ}}$

$x= 12\times 0.74222719896$

$x= 8.90672638762\approx 8.967$

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