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dimulka [17.4K]
2 years ago
7

Find the area of the shaded region. Please help! Brainliest to who gets it right !

Mathematics
1 answer:
damaskus [11]2 years ago
7 0
0.367 centimeters squared

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Answer:

\boxed{x - y = -2\sqrt{7}}

Given:

x + y = 4 \\  \\  {x}^{2}  +  {y}^{2}  = 22 \\  \\  {x}^{4}  =  {y}^{4}  - 176 \sqrt{7}

Step-by-step explanation:

=  >  {x}^{4}  =  {y}^{4}  - 176 \sqrt{7}  \\  \\  =  >  {x}^{4}  -  {y}^{4}  =  - 176 \sqrt{7}  \\  \\  =  >  {( {x}^{2}) }^{2}  -  { ({y}^{2}) }^{2}  =  - 176 \sqrt{7}  \\  \\  =  > ( {x}^{2}  +  {y}^{2} )( {x}^{2}  -  {y}^{2} ) =  - 176 \sqrt{7}  \\  \\  =  > ( {x}^{2} +  {y}^{2})  (x + y)(x - y) =  - 176 \sqrt{?}  \\  \\  =  > 22 \times 4(x - y) =  - 176 \sqrt{7}  \\  \\  =  > 88(x - y) =  - 176 \sqrt{7}  \\  \\ =  >  x - y =  -  \frac{176 \sqrt{7} }{88}  \\  \\  =  > x - y =  - 2 \sqrt{7}

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to arrive at 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution. How many liters of eac
CaHeK987 [17]

Answer:

<u>800 liters</u> of 90% saline solution and <u>1200 liters</u> of 40% saline solution should be used.

Step-by-step explanation:

Given:

At 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution.

Now, to find the number of liters of saline solution each should be used.

<u><em>Let the liters of 90% saline solution mix be </em></u>x.<u><em /></u>

<u><em>And let the liters of 40% saline solution mix be</em></u> y.

So, the total number of liters:

x+y=2000.

y=2000-x\ \ \ ....(1)

Now, the total percentage of saline solution:

90\%\ of\ x+40\%\ of\ y=60\%\ of\ 2000

\frac{90}{100}\times x+\frac{40}{100}\times y=\frac{60}{100}\times 2000

0.9x+0.4y=1200

Substituting the value of y from equation (1) we get:

0.9x+0.4(2000-x)=1200

0.9x+800-0.4x=1200

0.5x+800=1200

Subtracting both sides by 800 we get:

0.5x=400

Dividing both sides by 0.5 we get:

x=800.

<u>The liters of 90% saline solution mix = 800.</u>

Now, substituting the value of x in equation (1) to get the liters of 40% saline solution:

y=2000-x

y=2000-800

y=1200.

<u>Thus, the liters of 40% saline solution = 1200.</u>

Therefore, 800 liters of 90% saline solution and 1200 liters of 40% saline solution should be used.

8 0
3 years ago
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