Answer:
(a) 
(b) 
(c) Maximum area
square meters
Step-by-step explanation:
(a)
Given:
Total length for fencing = 160 m
Width of the rectangle = 
m.
Let the other length of the rectangle be 
m.
Then, from the figure,
Now, area of a rectangle is equal to the product of its length and width.
So, area is, 
(b)
Given:
For maximum area, derivative of area with respect to must be 0.
So, 
Therefore, for maximum area, .
(c)
Given:
Maximum area occurs at 
. Plug in 40 for in 
expression. This gives,
Maximum area is,
Therefore, maximum area is 3200 square meters.
Reflexive property
for all real numbers (x)
a number equals itself (x=x)
If you are looking at the total of just people who have just bikes that's 40 and people who have just skateboards that's 10 so 30 but if its the total of bikes that's 72 and the total of skateboards that's 42 which is also 30. My best guess seeing as i don't know what math class you are in is 30.
A=P (1+r/n)^nt
A= Total amount invested, P=principal amount, r=Interest rate, n=number of time in a year when the interest is earned (for annual, n=1; for semi-annual, n=2, ...), t = time in years
In the current scenario, case 1, n=2; case 2, n=1 and A1=A2, t1=t2
Therefore,
800(1+0.0698/2)^2t = 1000(1+0.0543/1)t
Dividing by 800 on both sides;
(1+0.0349)^2t = 1.25(1+0.02715)^t
(1.0349)^2t = 1.25(1.02715)^t
Taking ln on both sides of the above equation;
2t*ln (1.0349)= ln 1.25 + t*ln (1.02715)
2t*0.0343 = 0.2231+ t*0.0268
0.0686 t = 0.2231+0.0268 t
(0.0686-0.0268)t = 0.2231
0.0418t=0.2231
t=5.337 years
Therefore, after 5.337 years or 5 years and approximately 4 months, their value of investments will be equal.
This value will be,
A=800(1+0.0698/2)^2*5.337 = $1,153.76
