Answer:
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.
_____
<em>Check</em>
S24 = 24·25 = 600 . . . . . . as required.
<span>The dimensions are 40 inches by 55 inches.
Explanation<span>:
We know that perimeter is the sum of all of the sides. Since this is rectangular, opposite sides are equal. This gives us
y+11/8y+y+11/8y=190.
Combining like terms, we have
2y+22/8y=190.
Writing 22/8 as a mixed number, we have
2y+2 3/4y=190
4 3/4y=190.
Divide both sides by 4 3/4:
(4 3/4y)</span></span>÷<span><span>(4 3/4)=190</span></span>÷<span><span>(4 3/4)
y=190</span></span>÷<span><span>(4 3/4).
Convert the mixed number to an improper fraction:
y=190</span></span>÷<span><span>(19/4).
To divide fractions, flip the second one and multiply:
y=190*(4/19)=760/19=40.
Since y=40, 11/8y=11/8(40)=440/8=55.</span></span>
To make the monomial 125 x^18 y^3 z^25 a perfect cube, the entire expression should be reduced to a rational number when the cube root is taken. For the constant 125, the cube root is 5, so it doesn't need to be changed. For the variables, the exponents should be divisible by 3. The exponent of z is not divisible by 3. It can be subtracted with 1 or added with 2 to make the expression a perfect cube.
