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>
There are 2 significant figures (sig figs) which are the two '5' digits. The zeros aren't considered sig figs because we can write the number as 5.5 * 10^8 to represent the exact same idea. The 0's are simply placeholders to tell how big the number is, not necessarily how accurate it is. If the 0s were between the decimal point and a nonzero value, then the 0s would be significant. If the 0s were to the right of the decimal, then they would be significant.
Answer: 2
Answer:
y = 2x + 5
Step-by-step explanation:
First, find the slope using rise over run, (y2 - y1) / (x2 - x1)
With this information, we can create 2 points: (2, 9) and (5, 15)
Plug in the points:
(15 - 9) / (5 - 2)
6 / 3
= 2
Plug in the slope and a point into y = mx + b, and solve for b:
y = mx + b
15 = 2(5) + b
15 = 10 + b
5 = b
Plug in the slope and b into the equation:
y = 2x + 5 is the equation of the line
Answer:
yes you flip the sign because you are diving by a negative
Answer:
Yes
Step-by-step explanation:
To determine if (1, 2 ) is a solution of the inequality, substitute the coordinates into the inequality and if satisfied then they are a solution, that is
(6 × 1) - 2 = 6 - 2 = 4 > 3
Since 4 > 3 then (1, 2 ) is a solution
