Answer:
-1 -9i, where a = -1 and b = -9
Step-by-step explanation:
1st step is to open up the brackets. Since there's a (-) in front of the second bracket, we have to multiply every term by -1, so positive becomes negative, negative becomes positive etc.
4-i-5-8i
Then we collect like terms.
-1 -9i
This is the answer. It looks wrong since the variables are 'positive' in a +bi, but you have to remember that a variable can be represented as a, but its actual value could be negative, in this case -1. This is the same with b, as b could be the same as -9.
This is an expression, so we can't multiply everything by -1 to make it 'look right'. You can only multiply by -1 or 'alter' the terms when the expression equates to something.
Answer:
11.8 feet
Step-by-step explanation:
The given situation is represented in the figure attached below. Note that a Right Angled Triangle is being formed.
We have an angle which measures 28 degrees, a side opposite to the angle which measure 6.3 feet and we need to calculate the side adjacent to the angle. Tan ratio establishes the relation between opposite and adjacent by following formula:
![tan(\theta)=\frac{Opposite}{Adjacent}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%3D%5Cfrac%7BOpposite%7D%7BAdjacent%7D)
Using the given values, we get:
![tan(28)=\frac{6.3}{x}\\\\ x=\frac{6.3}{28}\\\\x=11.8](https://tex.z-dn.net/?f=tan%2828%29%3D%5Cfrac%7B6.3%7D%7Bx%7D%5C%5C%5C%5C%20x%3D%5Cfrac%7B6.3%7D%7B28%7D%5C%5C%5C%5Cx%3D11.8)
Thus, the distance from the pole is 11.8 feet
3. Odd numbers take the form
for
. So the sum of the first
(positive) odd integers is
![\displaystyle\sum_{k=1}^n(2k-1)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5En%282k-1%29)
Recall that
![\displaystyle\sum_{k=1}^n1=n](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5En1%3Dn)
![\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5Enk%3D%5Cfrac%7Bn%28n%2B1%29%7D2)
![\implies\displaystyle\sum_{k=1}^n(2k-1)=n(n+1)-n=n^2](https://tex.z-dn.net/?f=%5Cimplies%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5En%282k-1%29%3Dn%28n%2B1%29-n%3Dn%5E2)
4. The sequence is geometric with common ratio
:
![\dfrac89\left(-\dfrac32\right)=-\dfrac43](https://tex.z-dn.net/?f=%5Cdfrac89%5Cleft%28-%5Cdfrac32%5Cright%29%3D-%5Cdfrac43)
![-\dfrac43\left(-\dfrac32\right)=2](https://tex.z-dn.net/?f=-%5Cdfrac43%5Cleft%28-%5Cdfrac32%5Cright%29%3D2)
and so on. Then the
th term in the sequence is given by the rule
![a_n=\left(-\dfrac32\right)^{n-1}\dfrac89](https://tex.z-dn.net/?f=a_n%3D%5Cleft%28-%5Cdfrac32%5Cright%29%5E%7Bn-1%7D%5Cdfrac89)
and so the 14th term in the sequence is
![a_{14}=\left(-\dfrac32\right)^{13}\dfrac89=-\dfrac{177,147}{1024}](https://tex.z-dn.net/?f=a_%7B14%7D%3D%5Cleft%28-%5Cdfrac32%5Cright%29%5E%7B13%7D%5Cdfrac89%3D-%5Cdfrac%7B177%2C147%7D%7B1024%7D)
5. The sequence is geometric with ratio
, so that the
th term in the sequence is
![a_n=\left(\dfrac12\right)^{n-1}8](https://tex.z-dn.net/?f=a_n%3D%5Cleft%28%5Cdfrac12%5Cright%29%5E%7Bn-1%7D8)
The sum of the first 10 terms is
![S_{10}=\displaystyle\sum_{k=1}^{10}a_k=8\sum_{k=1}^{10}\frac1{2^{k-1}}](https://tex.z-dn.net/?f=S_%7B10%7D%3D%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5E%7B10%7Da_k%3D8%5Csum_%7Bk%3D1%7D%5E%7B10%7D%5Cfrac1%7B2%5E%7Bk-1%7D%7D)
We then have
![S_{10}=8+4+2+\cdots+\dfrac1{64}](https://tex.z-dn.net/?f=S_%7B10%7D%3D8%2B4%2B2%2B%5Ccdots%2B%5Cdfrac1%7B64%7D)
![2S_{10}=16+8+4+\cdots+\dfrac1{32}](https://tex.z-dn.net/?f=2S_%7B10%7D%3D16%2B8%2B4%2B%5Ccdots%2B%5Cdfrac1%7B32%7D)
![\implies S_{10}-2S_{10}=-S_{10}=\dfrac1{64}-16\implies S_{10}=16-\dfrac1{64}=\dfrac{1023}{64}](https://tex.z-dn.net/?f=%5Cimplies%20S_%7B10%7D-2S_%7B10%7D%3D-S_%7B10%7D%3D%5Cdfrac1%7B64%7D-16%5Cimplies%20S_%7B10%7D%3D16-%5Cdfrac1%7B64%7D%3D%5Cdfrac%7B1023%7D%7B64%7D)
6. The
th term of the sequence {1/2, 1/4, 1/12, ...} is given by
![a_n=\dfrac1{2n!}](https://tex.z-dn.net/?f=a_n%3D%5Cdfrac1%7B2n%21%7D)
so the given sum can be written as
![2+\dfrac12\displaystyle\sum_{n=1}^\infty\frac1{n!}](https://tex.z-dn.net/?f=2%2B%5Cdfrac12%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%5Cinfty%5Cfrac1%7Bn%21%7D)
Recall that
![e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}](https://tex.z-dn.net/?f=e%5Ex%3D%5Cdisplaystyle%5Csum_%7Bn%3D0%7D%5E%5Cinfty%5Cfrac%7Bx%5En%7D%7Bn%21%7D)
so the given sum is equal to
![2+\dfrac{e-1}2=\dfrac{3+e}2](https://tex.z-dn.net/?f=2%2B%5Cdfrac%7Be-1%7D2%3D%5Cdfrac%7B3%2Be%7D2)
<h3>
Answer: See the attached image below</h3>
It shows your screenshot, but I've filled in the blanks with the answers.
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Explanation:
Positive integers represent yards that the team gains. On the opposite side, negative integers represent yards the team loses.
For example, if a team gains 3 yards, then we write that as +3 or simply 3. If a team loses 5 yards, then we write -5. Adding 3 to -5 gets us 3+(-5) = -2 showing the overall result is a loss of 2 yards at the end of the second down.
As another example, if a team gains 7 yards on first down, but then loses those 7 yards on second down, then they gained overall 7+(-7) = 0 yards overall. They haven't gone anywhere at the end of the second down.
We could do things the other way around like this. Suppose the team loses 8 yards on first down, but has better luck on second down to gain 8 yards. They get back to the original line of scrimmage (back to the starting point) and we can say -8+8 = 0. The team hasn't gone anywhere, but it could be worse and they could be dealing with a loss of yardage.
It might help to set up a vertical number line to help try to visualize negative numbers. Each gain means you go upward. Each loss means you go downward. In a sense, it's like a skyscraper and each integer represents floors of the building. Negative integers are basement floors. Zero is the ground level.
Step-by-step explanation:
Well, you are asked for the first step, and it depends. But for this equation,
5m+4-2m=4m-9+3m+1
You have to subtract both sides by 3m, and subtract both sides by 4m. You also need to subtract both sides by 4.