Answer:
The answer is below
Step-by-step explanation:
River racing us a company that provides inner tubes for a children and adults to float the river. The child tube has a diameter of 2 feet and the adult tube has a diameter of 3 feet. River racing owns a total of 160 tubes and the total diameter of all the tubes is 430 feet. Write a system to determine the number of child tubes , c , and number of adult tubes, a , that river racing owns.
Solution:
Let c represent the number of child tubes and let a represent the number of adult tubes owned by river racing.
Given that there are a total of 160 tubes, hence:
a + c = 160 (1)
The total diameter of all tubes is 430 feet, hence:
3a + 2c = 430 (2)
To find a and c, we have to solve equation 1 and 2 simultaneously. multiply equation 1 by 2 and subtract from 2:
a = 110
Put a = 110 in eqn 1:
110 + c = 160
c = 50
(1, 1) is the equivalent to <span>(x^2 y^-1)^2 (2x^4 y^-3)^-1</span>
The points of inflection are where the second derivative changes sign. It is the point where the concavity change from upward to downward, or vice versa.
The first derivative is
4(x+3)³
The second derivative is
12(x+3)²
This expression never changes sign. The expression (x+3)⁴ is concave upward everywhere (except x=-3, where it is flat).
There are no points of inflection.
The Geometric Mean<span> is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. Below is the solution for the above problem:
</span>First we multiply them: 10 × 1250 = 12,500
Then (as there are two numbers) take the square root: √12,500<span> = </span>111.8034
Compare to . Then in applying the LCT, we have
Because this limit is finite, both
and
behave the same way. The second series diverges, so
is divergent.