If you take 1/2 of a pizza and divide it up between 6 people, will you have more than 1 whole Pizza or less than 1 whole pizza?
If you divide up a fraction into smaller pieces it will always be less than 1 because it started out less than 1 and you're making it even smaller.
v = w - 20
move -20 to the other side
sign changes from -20 to +20
to get w by itself
v+20= w-20+20
Answer:
w= v+20 or w= 20+v
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
(Image Attached)
I believe about two thirds
Answer:
x = 20
Step-by-step explanation:
→ Remember how many degrees are on a straight line
180°
→ Set up an equation
2x + 70 + 3x + 10 = 180
→ Simplify
5x + 80 = 180
→ Minus 80 from both sides
5x = 100
→ Divide both sides by 5
x = 20