Answer:
276 4/7 ft
Step-by-step explanation:
Let r1 represent the radius of the inner circle. Then its circumference in feet is ...
C = 2πr
66 = 2π(r1)
If the radius of the outer circle is (r1 +44), then its circumference is ...
C = 2π(r1 +44) = 2π(r1) +2π(44)
C = 66 +88π
Then the difference in the circumferences is ...
(66 +88π) - (66) = 88π
Using the given value of π, the difference in circumferences is ...
(88 ft)(22/7) = 1936/7 ft = 276 4/7 ft
The answer can be readily calculated using a single variable, x:
Let x = the amount being invested at an annual rate of 10%
Let (8000 - x) = the amount being invested at an annual rate of 12%
The problem is then stated as:
(x * 0.10) + ((8000 - x) * 0.12) = 900
0.10(x) + ((8000 * 0.12) - 0.12(x)) = 900
0.10(x) + 960 - 0.12(x) = 900
0.10(x) - 0.12(x) = 900 - 960
-0.02(x) = -60
-0.02(x) * -100/2 = -60 * -100/2
x = 6000 / 2
x = 3000
Thus, $3,000 is invested at 10% = $300 annually; and $8,000 - $3,000 = $5,000 invested at 12% = $600 annually, which sum to $900 annual investment.
Step-by-step explanation:
5x−4=5
1 Add 44 to both sides.
5x=5+4
5x=5+4
2 Simplify 5+45+4 to 99.
5x=9
5x=9
3 Divide both sides by 55.
x=\frac{9}{5}
x=
5
9
