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3 years ago

How many liters of a 90% acid solution must be added to 6 liters of a 15% acid solution to obtain a 40% acid solution?

Mathematics

1 answer:

tatiyna3 years ago

4 0

3 liters must be added

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A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

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4 years ago

The expression x4 + 6x3 – 11x2 – 60x + 100 is equivalent to (x – 2)(x – 2)(x + 5)(x + 5). At what points does the graph of the f

nikdorinn [45]

Since y equals the product of the factors, any value for x which makes any factor equal to zero is a point where the graph touches the x-axis.

x=-5 and 2 (technically the points (-5,0) and (2,0))

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4 years ago

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What is 170% of 97 tons???

Ede4ka [16]

$x=170\% * 97 \\ \\ x= \frac{170}{100} *97 \\ \\ x= \frac{17}{10}*97 \\ \\ x= \frac{1649}{10}=164.9$

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3 years ago

Can someone help me with this please?

Ksivusya [100]

The equation is y=3x-2

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3 years ago

The height of males approximates a normal distribution. The average height of the players on an NBA team is 6.6 feet with a stan

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D) 4.5 Standard Deviations Above the Mean

All you have to do is add .2 to 6.6 until you reach 7.5

6.8
7.0
7.2
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3 years ago