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3 years ago

Scientist needs 10 liters of a 20% acid solution for an experiment, but she has

Mathematics

1 answer:

grin007 [14]3 years ago

4 0

Answer:

40/7 liters of 5% acid, 30/7 liters of 40% acid

Step-by-step explanation:

We need to find a value so that the amount of acid is 20% = 1/5 of the total amount of liquid. Therefore, if x represents the total amount of liquid, we can say that

1/5 (x) = amount of acid at the end

We know that we need 10 liters of solution, so

1/5 (10) = amount of acid at the end = 2 liters

If we have y amount of 5% = 0.05 acid solution and z amount of 40% =0.4 acid solution, the total amount of acid will be equal to

0.05 * y (amount of acid from 0.05 acid solution) + 0.4 * z = 2

Next, we know that the total amount of liters is 10, and the liters come from the 5% and 40% acid solutions, so

y + z = 10

We therefore have

0.05 * y + 0.4 * z = 2

y + z = 10

One way to solve this is to solve for z in the second equation and plug that into the first.

subtract y from both sides in the second equation to isolate z

10 -y = z

plug 10-y in for z in the second equation

0.05 * y + 0.4 * (10-y) = 2

0.05 * y + 4 -0.4 * y = 2

-0.35 * y + 4 = 2

subtract 4 from both sides to isolate the y and its coefficient

-0.35y = -2

divide both sides by -0.35 to isolate y

y = -2/-0.35 = 40/7 * (-0.05/-0.05) = 40/7 liters

z = 10 - y = 10-40/7 = 70/7 - 40/7 = 30/7 liters

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3 years ago

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denis-greek [22]

Hello there!

Your answer is 180 units²

Step-by-step explanation:

$\large \boxed{ \mathsf{ \frac{1}{2} \times sum \: of \: two \: parallel \: \times height}}$

The formula in the box is an area of trapezoid formula. We know the sum of two parallel lines which is 15 because 7+4 = 11 + 4 = 15

another 4 comes from parallel side. If both sides are parallel, they have same length.

The only thing that is missing is the height. The height can be found by using Pythagorean Theorem as you notice a right-angle triangle when splitting in half.

$\large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }$

The formula in the box is Pythagorean Theorem for finding a length of right-angle triangle.

Given where a is opposite, b is adjacent and c is hypotenuse. (Note that c must be hypotenuse.)

Our a is missing

Our b is 7

Our c is 25.

From the formula and given lengths:

$\large{ {a}^{2} + {7}^{2} = {25}^{2} } \\ \large{ {a}^{2} + 49 = 625} \\ \large{ {a}^{2} = 625 - 49} \\ \large{ {a}^{2} = 576} \\ \large{a = 24}$

Therefore, our opposite is 24. Since our opposite equals the height of a trapezoid. We can proceed with the trapezoid formula.

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Our rectangle formula is length × width. We know width which is 4 and our length is 24 from opposite side of triangle which equal to the length of rectangle.

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Next, we find the area of triangle which is 1/2 × base × height.

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If we add the area of triangle and rectangle up each other, we will get the area of trapezoid for this problem which is 96 from rectangle and 84 from triangle. Therefore, 96+84 = 180 units²

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