A rectangular swimming pool has a length of l yards and a width 5 yards less than its length. How much does it cost to border th
1 answer:
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Answer:
see below
Step-by-step explanation:
The terms being summed are of the form ...
a1(r)^(i-1)
which is the form of the general term of a geometric sequence. The summation symbol tells you the values of i range from 1 to 6, so this is the sum of 6 terms of the series. (n=6)
Comparing the form of the general term to the one shown, you can see that the leading coefficient (a1) is -4, and the common ratio (r) is 1/2. With these values in mind, the first and third answer choices are possibilities. However, the sum must be negative, since all of its terms are negative. Thus the only viable answer choice is the third one.
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<em>Check</em>
The sum of n terms of a geometric series is ...
Sn = a1(1 -r^n)/(1 -r)
For the given values, this is ...
S6 = -4(1 -(1/2)^6)/(1 -1/2) = -4(63/64)/(1/2) = -63/8
Answer:
Step-by-step explanation:
STEP 1:
2/3 + 7/10 = ?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(2/3, 7/10) = 30
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
*
+
= ?
Complete the multiplication and the equation becomes
The two fractions now have like denominators so you can add the numerators.
Then:
This fraction cannot be reduced.
The fraction 41/30
is the same as
41 divided by 30
Convert to a mixed number using
long division for 41 ÷ 30 = 1R11, so
41/30 = 1 11/30
Therefore:
2/3+7/10= 1 11/30
STEP 2:
41/30 + -2/3
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(41/30, -2/3) = 30
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
The two fractions now have like denominators so you can add the numerators.
Then:
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 21 and 30 using
GCF(21,30) = 3
Therefore:
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