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:
"Susanna starts out slower than Anita but still wins the race."
Step-by-step explanation:
The distance of the race is "5 miles". We can see the "endpoint" of each race's graph and corresponding y value. That is 5 miles.
Now, we look at corresponding "x" value, that is the time it took.
For Susannah, it is 5.5 minutes
For Anita, it is 7 minutes.
So, clearly, Susanna wins the race.
Now, we look at the "slopiness" of each person's line graph. This is the speed at which they were going.
The red line (Susanna) is quite sharper than anita, so her speed (rate) is more. But initially, we can see that the blue line (Anita) was sharper than Susanna but later gradually fell. So we can say:
Susanna started out slower than Anita, but ultimately won.
From the answer choices, last one is right -- "Susanna starts out slower than Anita but still wins the race."
429.99 + 0.34m or in slope intercept format y = 0.34x + 429.99
For question 7, if we add all votes for tiger and eagle, we get
tiger = 14 + 13 + 8 + 5 = 40
eagle = 6 + 7 + 12 + 15 = 40
so choices A and B are wrong.
C is also wrong because fifth and sixth grade votes for eagle are 6 + 7 = 13 and the 5th and 6th grade votes for tiger are 14 + 13 = 27. clearly 5th + 6th like tiger more.
D is the answer for question 7
question 8
rolling a cube does not affect the other cube so it is all independent probability.
cube: 1 2 3 4 5 6
3 even numbers and 3 odd numbers
so probability of rolling an even number is
1/6 + 1/6 + 1/6 = 3/6 = 1/2
multiplying by total number of rolls, she will get even numberss
300 * 1/2 = 150
about 150 time.
so half of the time, Cassie will roll and even number about half the number of rolls. never exactly since this is all probability. more likely for it to be around 150 times than exactly 150 time.
choice C is answer for question 8
Answer: x = -4, x = 5
Step-by-step explanation:
You can use the substitution method for this problem.
y = 
+ 2x, but y also = 3x +20.
Because of this, you can determine that +2x = 3x + 20 because they are both equal to the same thing, y.
Solve the quadratic equation you got from substitution:
+ 2x = 3x + 20
-x = 20
-x -20 = 0
You can factor this equation:
(x+4)(x-5) = 0
x = -4, x = 5
