A square has side length 6x+2. A rectangle with width 3x+1 has the same area as a square. What is the length of the rectangle
2 answers:
Answer:
L = 12x + 4
Step-by-step explanation:
(see diagram for reference)
the area of the square
= (6x+2) (6x+2) (factor out 2 from each parentheses)
= (2)(3x+1)(2)(3x+1) (group like terms and simplify)
= 4(3x + 1)²
the area of the rectangle,
= (3x+1) (L)
It is given that the square and the circle have the same area, hence we equate the areas of square and rectangle:
4(3x + 1)² = (3x+1) (L) (divide both sides by 3x+1)
4(3x + 1) = (L) (rearranging and expanding the parentheses)
L = 12x + 4
Hope this helps
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Answer:
18 years
Step-by-step explanation:
The formula for computing accrued amount A for a principal of P at an interest rate of r(in decimal) compounded n times in a year for t years is given by
Note that r is percentage converted to decimal. So 3% = 3/100 = 0.03
We can rearrange the above equation to:
Taking logs on both sides
This gives
In this particular problem, n = 4, , A= 9600, P = 5600, r =0.03, so r/n = 0.03/4 = 0.0075
1 + r/n = 1+0.0075 = 1.0075
4t = log(9600/5600)/log(1.0075) = log(1.714) / log(1.0075) = 0.234 /0.00325 = 72
t = 72/4 = 18 years