Answer:
Step-by-step explanation:
3n = 3² × 8 3² = 3 × 3
n × 3 = 3 × 3 × 8 notice a times 3 on both sides of the equation
divide both sides by 3
n = 3 × 8
n = 24 <---------------- FINAL ANSWER
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)
Answer:
A
Step-by-step explanation:
f = 1/2s
Let s = 2 that means f = 1 That means for 2 cups of sugar there is 1 cup of flour.
This point must be on the graph
It is on A, not on B, not on C
Answer:
Linear
Step-by-step explanation:
x values increase by one
y values increase by 5
exponential doesn't follow linear patterns
Answer:
No
If the fraction is an improper fraction, the product would be higher
if the numerator of the fraction is smaller than the denominator, the product would be lower
2 x 3/4 = 3/2 = 1 1/2
2 x 4/3 = 8/3 = 2 2/3
Step-by-step explanation:
an improper fraction is a fraction in which the numerator is greater than the denominator
The numerator is the number above. While the denominator is the number below
an example of a fraction =
4 is the numerator while 5 is the denominator