Answer:
875cm^2
Step-by-step explanation:
since opposite sides are equal
3x-y=2x+y
x=2y
y=x/2 ....(i)
thus new length=2x+y
=2x+(x/2) [using (i)]
=(4x+x)/2
l=5x/2 .....(ii)
now,
perimeter=2(l+b)=120cm
l+b=60cm
from figure and using (ii)
[5x/2]+2x-3=60
[5x+4x-6]/2=60
9x-6=120
9x=126
x=126/9
x=14 ..........(iii)
substitute (iii) in (i)
y=14/2
y=7 ...........(iv)
From figure,
length=2x+y [using (iii) and (iv)]
=2x14+7
length=35cm
breadth=2x-3
=2x14-3 ....[using(iii)]
=28-3
breadth=25cm
now,
Area=lxb
=35x25
=875cm^2
Given function:

The minimum value of the function can be found by setting the first derivative of the function to zero.


Solving for x:


Substituting the value of x into the original function:

Hence, the minimum value in the given range is (-1, -0.368)
Answer:
"a" must be negative
Step-by-step explanation:
The slope between points (-1, 1) and (1, -1) is a minimum of (-1-1)/(1-(-1)) = -1.
The slope between points (1, -1 and (3, -4) is a maximum of (-4-(-1))/(3-1) = -3/2.
Thus, as x increases, the slope is decreasing. In order for that to be the case, the value of <em>a</em> must satisfy a < 0.
8 gallons= 128 cups
20 guests x 2 cups each= 40 cups will be gone
128-40= 88 cups left over
88 cups= 5.5 gallons of punch left at the end of the party.