Answer:
Infinite series equals 4/5
Step-by-step explanation:
Notice that the series can be written as a combination of two geometric series, that can be found independently:
The first one: 
is a geometric sequence of first term (
) "1" and common ratio (r) " 
", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: 
The second one: 
is a geometric sequence of first term "1", and common ratio (r) " 
". Again, since the common ratio is smaller than one, we can find its infinite sum:
now we simply combine the results making sure we do the indicated difference: Infinite total sum= 
C(x) = 80000 + 100x is the total cost as function of number of cycles produced
C(90) = 89000 and it costs $ 89000 to produce 90 bicycles
<em><u>Solution:</u></em>
Given that, company that manufactures bicycles has a fixed cost of $80,000
Fixed cost = $ 80,000
Let x be the number of cycles produced
Let C(x) be the total cost as function of number of cycles produced
It costs $100 to produce each bicycle
Variable cost = 100 x number of cycles produced
variable cost = 100x
The total cost for the company is the sum of its fixed cost and variable costs
total cost = fixed cost + variable cost
C(x) = 80000 + 100x
Thus total cost as function of "x" is found
<em><u>Find and interpret C(90)</u></em>
Substitute x = 90 in C(x)
C(90) = 80000 + 100(90)
C(90) = 80000 + 9000
C(90) = 89000
Thus it costs $ 89000 to produce 90 bicycles
Answer:
4 units
Step-by-step explanation:
Answer:
c = 24.34
Step-by-step explanation:
Here, we can use the cosine rule
Generally, we have this as:
a^2 = b^2 + c^2 - 2bcCos A
12^2 = 14^2 + c^2 - 2(14)Cos 19
144 = 196 + c^2 - 26.5c
c^2 - 26.5c + 196-144 = 0
c^2 - 26.5c + 52 = 0
We can use the quadratic formula here
and that is;
{-(-26.5) ± √(-26.5)^2 -4(1)(52)}/2
(26.5 + 22.23)/2 or (26.5 - 22.23)/2
24.37 or 2.135
By approximation c = 24.34 will be correct
Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
