Answer:
dy/dt = - (1/5) ft/s = - 0.2 ft/s
Step-by-step explanation:
Given
L = 5 ft
Qin = 25 ft³/s
Qout = 30 ft³/s
h = 10 ft
dy/dt = ?
We can apply the relation
ΔQ = Qint - Qout = 25 ft³/s - 30 ft³/s
⇒ ΔQ = - 5 ft³/s
Then we use the formula
Q = v*A
where Q = ΔQ, A = L² is the area of square base and v = dy/dt is the rate of change in the depth of the solution in the tank
⇒ ΔQ = (dy/dt)*L²
⇒ dy/dt = ΔQ/L²
⇒ dy/dt = (- 5 ft³/s)/(5 ft)²
⇒ dy/dt = - (1/5) ft/s = - 0.2 ft/s
Answer:
Option C is correct.
Step-by-step explanation:
We need to find the pattern as the exponent decreases.
the first value in the table is 125.
if we divide 125 by 5 i.e 125/5 we get 25
the next value in the table is 25
if we divide 25 by 5 i.e 25/5 we get 5
the next value in the table is 5
if we divide 5 by 5 i.e 5/5 we get 1
the next value in the table is 1
if we divide 1 by 5 i.e 1/5 we get 1/5
the next value in the table is 1/5
if we divide 1/5 by 5 i.e 1/5*5 we get 1/25
the next value in the table is 1/25
So, the pattern is if we divide the previous value by 5 we get the next value in the table.
So, Option C is correct.
Answer:
The factorization of 
is 
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form 
or 
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation , and the exponent of the letter x is divided by 3.
![\sqrt[3]{729x^{15}} =9x^{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B729x%5E%7B15%7D%7D%20%3D9x%5E%7B5%7D)
then ![\sqrt[3]{10^{3}} =10](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B10%5E%7B3%7D%7D%20%3D10)
So, we got that
which has the form of which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>
with 
y 
2.) Solving the sum of cubes.
.
