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oee [108]
3 years ago
11

10m^2 of tiles cover a pool, the pool is shaped as a square, so all four edges are the same, and the depth is constant but not e

qual to the size of the side. what is the maximum volume?
Mathematics
1 answer:
nignag [31]3 years ago
3 0
Assume:

Size of sides = x m
Depth of the pool = y m

Therefore, surface area = x^2+4xy =10 m^2

Then, y = (10-x^2)/(4x)

Now,
Volume (V) = x^2*y = x^2*y =x^2(10-x^2)/4x = (10x-x^3)/4 = 1/4(10x-x^3)
For maximum volume, first derivative of volume function is equal to zero.
That is,
dV/dx =0 = 1/4(10-3x^2)
Then,
1/4(10-3x^2) = 0
10-3x^2 = 0
3x^2=10
x= sqrt (10/3) = 1.826 m
And
y= (10-1.826^2)/(4*1.826) = 0.913 m

Therefore,
V= 1.826^2*0.913 = 3.044 m^3
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Santos went on a bike ride of 90 miles. He realized that if he had gone 24 mph faster, he would have
Gnoma [55]
<h3>Answer:  6 mph</h3>

========================================

Explanation:

distance = rate*time

90 = r*t

where r is the slower speed and t is the time it takes when going that slower speed.

If r is bumped up 24 mph faster, to r+24, then Santos takes t-12 hours to get there. The second equation is

90 = (r+24)(t-12)

-------------------------------------

We can solve the first equation for r to get r = 90/t

Then plug this into the second equation and do a bit of algebra

90 = (r+24)(t-12)

90 = (90/t+24)*(t-12)

90 = 90 - 1080/t + 24t - 288

90t = 90t - 1080 + 24t^2 - 288t

0 = 90t - 1080 + 24t^2 - 288t-90t

0 = 24t^2 - 288t - 1080

24t^2 - 288t - 1080 = 0

If you apply the quadratic formula, then you should get the two solutions t = -3 and t = 15. Due to time constraints, I'll skip these steps.

We'll ignore the negative t value. It makes no sense to have a negative time.

So we focus on t = 15 as the only solution.

-------------------------------------

If t = 15, then,

r = 90/t

r = 90/15

r = 6

Santos rode his bike at <u>6 mph</u> at first. Going this speed means he takes 15 hours.

If he rode 24 mph faster, at 6+24 = 30 mph, then he would ride for 15-12 = 3 hours instead. Note that 90/30 = 3.

5 0
3 years ago
Which lines are perpendicular to 7x-3y=18
inna [77]
The answer is going to be   3y=7x-15. hope that helped
8 0
3 years ago
Hi, a recipe calls for 1/2 cups of flour. How much flour should be used if only half of the recipe is to be made. Thank You.
Luden [163]

Answer:

¼ cup of flour

Step-by-step explanation:

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4 0
3 years ago
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Natali [406]
Amount of potatoes that Zoe has = 5 pounds
Quantity of potatoes that Zoe need for each recipe = 5/(3/4) 
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                                                                                 = 20/3 
                                                                                 = 6 2/3 
From the above deduction, we can conclude that only 6 recipes can be made. The remaining amount of 2/3 will remain unused. I hope the procedure is clear enough for you to understand.
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3 years ago
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The quotient of a number and three, increased by one <br><br><br> Using the variable N
solniwko [45]
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