The equation:
models the amount of money in your wallet. Where:
x: Represents the number of weeks from today
y: Represents the total in dollars
This graph is indicated in the figure bellow. The slope of this graph is 10, that is, the term accompanying the variable x. The slope of a line is the number of units the line rises (or falls) vertically for each unit of horizontal change from left to right. So, in this problem, this represents how much your adding to your wallet each week. You are adding $10 dollars for x weeks.
First integral:
Use the rational exponent to represent roots. You have
And from here you can use the rule
to derive
Second integral:
Simply split the fraction:
So, the integral of the sum becomes the sum of three immediate integrals:
So, the answer is the sum of the three pieces:
Third integral:
Again, you can split the integral of the sum in the sum of the integrals. The antiderivative of the cosine is the sine, because . So, you have
Answer: 371697
Step-by-step explanation:
For continuously compounded values, we use the formula Pe^rt, or Pert. P is our principal/initial value, 230000. e is the constant e, r is our rate, 4% or .04, t is our time, 12. So, 230000*e^(.04*12)=371697.112504, rounding down, 371697.
The sample space of an event is the list of possible elements of the event.
The set elements are:
- Ac = {x : 0, 5 ≤ x ≤ 10}
- A n B = {x : 3 ≤ x ≤ 4}
- A ∪ B = {x : 0 < x ≤ 7}
- A∩Bc = {x : 1 ≤ x ≤ 2}
- A^c ∪ B = {x : 0, 3 ≤ x ≤ 10}
<h3>How to determine the intervals of the subsets</h3>
The given parameters are:
S = {x : 0 ≤ x ≤ 10}
A = {x : 0 < x < 5}
B = {x : 3 ≤ x ≤ 7}
<u>(a) Ac </u>
This represents the list of elements in the universal set not in set A.
So, we have:
Ac = {x : 0, 5 ≤ x ≤ 10}
<u>(b) A ∩ B </u>
This represents the list of common elements in sets A and set B.
So, we have:
A n B = {x : 3 ≤ x ≤ 4}
<u>(c) A ∪ B </u>
This represents the list of all elements in sets A and set B, without repetition.
So, we have:
A ∪ B = {x : 0 < x ≤ 7}
<u>d) A∩Bc </u>
Given that:
B = {x : 3 ≤ x ≤ 7}
So, we start by calculating B^c i.e. the list of elements in the universal set not in set B.
So, we have:
Bc = {x : 1, 2, 8 ≤ x ≤ 10}
A∩Bc would then represent the list of common elements in sets A and set Bc
So, we have:
A∩Bc = {x : 1 ≤ x ≤ 2}
<u>(e) A^c ∪ B</u>
In (a), we have:
Ac = {x : 0, 5 ≤ x ≤ 10}
Given that:
B = {x : 3 ≤ x ≤ 7}
A^c ∪ B would then represent the list of all elements in sets Ac and set B
So, we have:
A^c ∪ B = {x : 0, 3 ≤ x ≤ 10}
Read more about sets are:
brainly.com/question/2193811
Answer:
- A
Step-by-step explanation: