Answer:49
Step-by-step explanation:
A=ab/2
98=ab/2
98/2=ab
49=ab
Take the LCM of the three numbers. Since 2 is a multiple of 4, you can ignore the two and just take the LCM of 4 and 3.5. Since 3.5 is a decimal, the LCM is just 3.5*4 which is 14. That is how many minutes after 8:00 they will flash together again.<span />
9514 1404 393
Answer:
RS = √(b² +(c -a)²)
Step-by-step explanation:
Put the given point coordinates in the given formula:
- R = (x₁, y₁) = (0, a)
- S = (x₂, y₂) = (b, c)
RS = √((b -0)² +(c -a)²)
RS = √(b² +(c -a)²)
Answer:
Hyperbola.
Step-by-step explanation:
We start from the function:
We may get the traces if we cut the surface in planes x=k. This is equivalent to replace x for k:
The last equation is the equation of an hyperbola, which varies its characteristics depending on K (the plane cut).
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>
