How many terms in the arithmetic sequence(2,4,6, will give sum of 600

  24 terms

Step-by-step explanation:

The sum of an arithmetic sequence is the average of the first and last terms, multiplied by the number of terms. The last term is given by ...

  an = a1 + (n-1)d

We have a sequence with first term a1 = 2 and common difference d = 2. So the last term is ...

  an = 2+ 2(n -1) = 2n

Then the average of first and last terms times the number of terms is ...

  Sn = 600 = n(2 + 2n)/2 = n(n+1) . . . . . . close to n²

We can solve the quadratic in n, or we can estimate the value of n as the integer just below the square root of 600.

  √600 ≈ 24.5

so we believe n = 24.

Check

  S24 = 24·25 = 600 . . . . . . as required.

p> q if you calculate p is100 q is 79

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)