Given:
Carol has 88cm of string and cuts it in the ratio 5 : 6.
To find:
How much longer is the longest piece compared to the shortest piece.
Solution:
Let the lengths of two pieces of string are 5x and 6x. Then,
Now, the lengths of pieces are:
And,
The difference between the longer piece and shorter piece is:
Therefore, the longer piece is 8 m longer than the shorter piece.
The answer is 54 square units.
let the vertex in quadrant I be (x,y)
<span>then the vertex in quadratnt II is (-x,y) </span>
<span>base of the rectangle = 2x </span>
<span>height of the rectangle = y </span>
<span>Area = xy </span>
<span>= x(27 - x</span>²<span>) </span>
<span>= -x</span>³<span> + 27x </span>
<span>d(area)/dx = 3x</span>²<span> - 27 </span><span>= 0 for a maximum of area </span>
<span>3x</span>²<span> = 3 x 3</span>² = <span>27 </span>
<span>x</span>²<span> = 9 </span>
<span>x = ±3 </span>
<span>y = 27-9 = 18 </span>
So, the largest area = 3 x 18 = 54 square units
<span>3x − x + 2 = 12
2x + 2 = 12
2x = 10
x = 5
answer
x = 5</span>
You want to isolate the x. So you can subtract both sides by 3/4 and get:
x<8-3/4
To do 8-3/4, you multiply the 8 by 4 to get a common denominator of 4.
32/4-3/4 which is 29/4 or 7 1/4
So your final answer is x<7 1/4 or any number less than 7 1/4
Hope this helps!
