He difference of 1/2 of one number and 2/3 of another number is equal to 2. if the first number were to decrease by 5/6 of it, and the second number were to increase by 1/6 of it, their sum would be equal to 59. find the two numbers.

Step-by-step explanation:

If we let x and y represent the first and second numbers, respectively, then the first sentence of the problem statement tells us ...

  (1/2)x - (2/3)y = 2

The second sentence of the problem statement tells us ...

  (1 -5/6)x +(1 +1/6)y = 59

Solution

Multiplying the first equation by 6 gives ...

  3x -4y = 12

Multiplying the second equation by 6 gives ...

  x + 7y = 354

Solving the second equation for x gives ...

  x = 354 -7y

Substituting that into the first equation gives ...

  3(354 -7y) -4y = 12

  1050 = 25y . . . . . . . . subtract 12-25y

  42 = y . . . . . . . . . . . .  divide by 25

Then we can find x using its equation ...

  x = 354 -7·42 = 60

The first number is 60; the second number is 42.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

ιт ιѕ (9χ^5+10)(81χ^10-90χ^5+100)

step-by-step explanation:

нσρє ι ¢συℓ∂ нєℓρ уσυ συт тσ∂α