Answer:
Step-by-step explanation:
Step-by-step explanation:
By Pythagoras' theorem,
12^2 = 11^2 + height^2
height = ±√12^2 - 11^2 (rej -ve value since height > 0)
height = 16.279 (5sf) = 16.3 (nearest tenth place)
Topic: Pythagoras theorem
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ANSWER: 7.53
Step-by-step explanation:
To convert a percent to decimal you need to divide the percent by 1,
753% ÷ 1 = 7.53
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 equivalent expressions of 22c + 33d are (a), (c) and (e)
<h3>How to determine the equivalent expressions?</h3>
The expression is given as:
22c + 33d
Factor out 11 from the expression
11(2c + 3d)
Multiply by 1
1 * 11(2c + 3d)
Express 1 as -1 * -1
-1 * -1 * 11(2c + 3d)
Evaluate the product
(-11) * (-2c - 3d)
Also, we have:
22c + 33d
Multiply by 1
(22c + 33d) * 1
Express 1 as 3/3
(22c + 33d) * 3/3
Evaluate the product
(66c + 99d) * 1/3
Hence, the equivalent expressions are (a), (c) and (e)
Read more about equivalent expressions at:
brainly.com/question/27911936
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