Answer:
Side of 22 and height of 11
Step-by-step explanation:
Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:


As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank
Base area with open top 
Side area 4sh
Total surface area 
We can substitute 


To find the minimum of this function, we can take the first derivative, and set it to 0



![s = \sqrt[3]{10648} = 22](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%5B3%5D%7B10648%7D%20%3D%2022)

Answer:
8 hours
Step-by-step explanation:
$1,300/$32.50 = 40
$1,040/$32.50 = 32
40-32=8
Answer:
477
Step-by-step explanation:
Given that:
Number of trials (n) = 500
Mean (m) = 0
Standard deviation (s) = 1
how many readings fall within +/- 2.000 deg F of the mean value
Mean of 0 and standard deviation of 1
P(-2 ≤ x ≤ 2)
Using the Z probability calculator :
P(x ≤ 2) = 0.97725 ;
P(x ≤ - 2) = 0.02275
Hence :
P(x ≤ 2) - P(x ≤ - 2) = 0.97725 - 0.02275 = 0.9545
Hence, number of readings in 500 trials:
0.9545 * 500 = 477.25
= 477 values
Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in
,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is

where
is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with
. For convenience write
. This gives the factor
. Hence,

Notice that
. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type
will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.