Given two positive even integers, it turns out that the square of the largest minus 10 times the smaller is 76. what is the sum of the integers?

  26

Step-by-step explanation:

Even integers will only have a square ending in 6 if they end in 4 or 6.

The square will only have a value greater than 76 if the number is greater than 8, that is, 14 or 16, 24 or 26, and so on.

The "smaller" integer will only be smaller if the "larger" integer is less than 16.

So, the two integers are ...

  14 and (14^2 -76)/10 = 12

The sum of 14 and 12 is 26.

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In the graph, we let x represent the "larger" integer and y the "smaller". The shaded area is where x > y, and the curve is the constraint on their values. The two vertical lines are the even numbers whose squares end in 6, resulting in integer values for y.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)