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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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How does the graph of the function g(x)=2^x-4 differ from the graph of f(x)=2^x
VARVARA [1.3K]

Answer:

The graph of g(x) is the graph of f(x) moved down 4 units.

Step-by-step explanation:

Subtracting a function by a constant:

Subtracting a function by a constant x is the same as moving the function down x units.

In this question:

f(x) = 2^x

g(x) = 2^x - 4

Thus, the graph of g(x) is the graph of f(x) moved down 4 units.

8 0
3 years ago
An author argued that more basketball players have birthdates in the months immediately following July​ 31, because that was the
Lady_Fox [76]

Answer:

There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

Step-by-step explanation:

In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

<em>H₀</em>: The observed frequencies are same as the expected frequencies.

<em>Hₐ</em>: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

 \chi^{2}=\sum{\frac{(O-E)^{2}}{E}}

The values are computed in the table.

The test statistic value is \chi^{2}=128.12.

The degrees of freedom of the test is:

n - 1 = 12 - 1 = 11

Compute the <em>p</em>-value of the test as follows:

p-value < 0.00001

*Use a Chi-square table.

p-value < 0.00001 < α = 0.05.

So, the null hypothesis will be rejected at any significance level.

Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

6 0
3 years ago
Multiply (5a+7)(5a-7)
vovikov84 [41]

Answer:

25a^2-49

Step-by-step explanation:

1)use FOIL

F=first

O=out

I=inside

L=last

5a*5a+5a*-7+7*5a*7*-7

25a^2-35a+35a-49

25a^2-49

Hope this helps!

5 0
3 years ago
Read 2 more answers
A sound wave travels through iron at a rate of 5120\,\dfrac{\text{m}}{\text{s}}5120
Jet001 [13]

The rate at which the sound travels in km/hr is 0.142km/hr

<h3>Conversion of m/s to km/hr</h3>

If a sound wave travels with a speed of 5120m/s, in order to convert to km/he, we will use the conversion factor below;

1hr = 3600secs

1km = 1000m

Using the conversion factor in our dimensional analysis

5120m/s = 5120m/1s * 1km/1000m * 3600s/1hr

5120m/s  = 5120m/3600000

5120m/s = 0.142km/hr

Hence the rate at which the sound travels in km/hr is 0.142km/hr

learn more on dimensional analysis here: brainly.com/question/21510595

#SPJ1

6 0
2 years ago
41-24/(4+8)-[36+{12x(10/2)}+4]
amid [387]

Answer:

-61

Step-by-step explanation:

simply put parentheses in your priority

means

1) ()

2) ^√

3) ÷×

4) +-

4 0
3 years ago
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