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dimulka [17.4K]
3 years ago
12

PLEASE HELP MEEEE WITH THIS !!!!!

Mathematics
1 answer:
Annette [7]3 years ago
4 0
To find the length of the arc AB, we can use the following equation:

a= \frac{1}{2} (y-x)

where a is the exterior angle, y is the arc furthest from the angle, and x is the arc nearest to the angle.

We know the value of a, but now x or y. However, we do know that x = 360 - y. We can use this information to find x (arc AB):

50 =  \frac{1}{2} (y - (360 - y))

50 =  \frac{1}{2} (2y - 360)

50 = y - 180

y = 230

If y = 230, then AB = 360 - 230:

360 - 230 = 130

The correct answer is 130.
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3 years ago
Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of
Setler [38]

Answer:

  • 12 gallons 84%
  • 8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

  48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

  • 12 gallons of 84% acid solution
  • 8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

<em>Check</em>

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

_____

<em>Usual Solution</em>

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

  0.84x + 0.04(20 -x) = 0.52(20)

  0.80x + 0.8 = 10.4 . . . . simplify

  0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

  x = 9.6/0.8 = 12 . . . . gallons of 84% acid

  20-x = 8 . . . . . . . . . . gallons of 4% acid

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