X=10 and y=5 so it's the first option
Answer:
<h2><em>
2ft by 2ft by 1 ft</em></h2>
Step-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>
The horizontal line has an equation: y = a, where a is any real number.
We know, the line passes through the point (2, 3) → x = 2, y = 3.
<h3>Answer: y = 3</h3>
Step-by-step explanation:
are you sure you wrote the problem here correctly ?
because the distance will be 40km after less than half an hour just by the first car driving. way before the second car even starts.
to be precise, it would be after 60 minutes × 40 / 90
(= how many minutes of an hour are needed to reach 40km while going 90km/h) :
60 × 40 / 90 = 60 × 4 / 9 = 20 × 4 / 3 = 80/3 = 26.67 minutes.
but maybe the question was about 400km distance between the two cars.
so, the first car goes 90km/h for 2 hours.
at that moment it will be 2×90=180km ahead.
that would mean that 220km are still missing for the 400km assumption.
with each hour driving the first car makes 20km more than the second car.
to build up 220km that way would require
220/20 = 11 hours.
plus the 2 original head start hours this would make 13 hours as overall answer.
