Hey there, Lets solve this one by one
Firstly, a<span>dd </span>11<span> to both sides
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Now, </span><span>Simplify </span><span>5+11</span><span> to </span><span>16
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Finally, d</span><span>ivide both sides by variable </span><span>y
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Let
x------> the length side of the square base of the box
y-------> the height of the box
we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1
<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>
surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x
step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm
the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm
The first part is 1325
10 x 35=350
15 x 65=975
The you add them which equals 1325
Answer:
Alecia lives farther from school
Step-by-step explanation:
<em>Georgia</em>
we know that
The distance from the school to her home is 67/100 of a mile
<em>Alecia</em>
we know that
The distance from the school to her home is
3/10 of a mile plus 4/10 of a mile
so
Compare the distances
therefore
Alecia lives farther from school
Answer:
<h2><em><u>
x = 52</u></em></h2>
Step-by-step explanation:
<em><u>Known:</u></em>
What to find = x
Exterior angle = 142
Right angle = 90
<em><u>Unknown:</u></em>
what unknown value is = ?
Interior angle = ?
<em><u>1. Find the angle of the interior angles.</u></em>
180 - 142 = 38
<em><u>2. Add the two known angles</u></em>
38 + 90 = 128
<em><u>3. Subtract from 180</u></em>
180 - 128 = 52
<h2><em><u>
x = 52 is the answer.</u></em></h2>
Hope this helped,
Kavitha Banarjee
