Answer:
The sequence is convergent and the serie is divergent.
Step-by-step explanation:
Sequence:
We calculate the limit when n tends to infinity to see if it is convergent or divergent:
then, the sequence is convergent.
Serie:
. To know if it converges we are going to use the limit test:
. If this limit is non equal to 0 the serie diverges.
, then the serie diverges.
In the question , the length of the actual rope is given as 40 foot. Also it is given that the length of one rope after cutting the original piece of rope into 2 pieces is 9 times that of the other pice.
Let us assume that the length of one piece of rope is = X
Then the length of the orther pice of rope = 9X
Now we can easily get the equation
X + 9X = 40
10X = 40
X = 40/10
X = 4
So the length of the shorter rope is 4 foot.
The length of the longer rope is 9 times that of the shorter one.
So the length of the longer rope is 36 foot.
The first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
<h3>What is a Function?</h3>
A function assigns the value of each element of one set to the other specific element of another set.
The function given in the problem is:
f(x) = x³ + x² – 3x + 4
The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.
The second function given in the problem is:
g(x) = 2x – 4
The highest degree (power) of this function is 1. Thus, this function is a type of linear function.
Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).
Thus, the first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
Learn more about Function here:
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Answer:
2x+1
Step-by-step explanation:
I did the math
Answer:
-0.05
Step-by-step explanation:
This will become much easier if we can get the ugly decimal into a nice fraction form.
Start by recognising 
. This is almost correct except the fraction is out by some number of factors of 10 (because the 125 part is correct but the number of 0s isn't).
And hence we see that 
and now the cube root becomes easy to compute:
![\sqrt[3]{-0.000125} = \sqrt[3]{\frac{-1}{8000}} = \frac{\sqrt[3]{-1}}{\sqrt[3]{8000}} = \frac{-1}{20} = -0.05](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-0.000125%7D%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B-1%7D%7B8000%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7B-1%7D%7D%7B%5Csqrt%5B3%5D%7B8000%7D%7D%20%3D%20%5Cfrac%7B-1%7D%7B20%7D%20%3D%20-0.05)
.
Advanced: You ask for <em>all </em>real cube roots. however the function ![y=\sqrt[3]{x}](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx%7D)
is described as <em>bijective</em>. This means for all x, there is only one y corresponding to it. (And also for all y there is only one x corresponding to that). This means there can only ever be one cube root of any real number.
