Answer:
![\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}](https://tex.z-dn.net/?f=%5Cbf%20cos%28x%29%5Capprox1-%5Cdisplaystyle%5Cfrac%7Bx%5E2%7D%7B2%7D%2B%5Cdisplaystyle%5Cfrac%7Bx%5E4%7D%7B4%21%7D%3D%5C%5C%5C%5C%3D1-%5Cdisplaystyle%5Cfrac%7Bx%5E2%7D%7B2%7D%2B%5Cdisplaystyle%5Cfrac%7Bx%5E4%7D%7B24%7D)
The polynomial is an approximation with an error less than or equals to <em>0.002652</em> for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
According to Taylor's theorem
with
for some c in the interval (-x, x)
In the particular case f
<em>f(x)=cos(x)
</em>
<em>
</em>
we have
therefore
and the polynomial approximation of T5(x) of cos(x) would be
In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that
for some c in (-x,x). So
and we must find the values of x for which
Working this inequality out, we find
Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval
[-1.113826815, 1.113826815]
500/7 = 71.43 gallons per hour
950-500 = 450
450/71.43 = 6.3 more hours.
The student has to pay back $1240
Further explanation:
Simple interest is calculated on the principal amount. It can be applied only one or over a period of time. For example, if the interest is to be applied annually then it will be calculated each year on the starting principal amount.
Given
Amount = Principal amount = P_0 = $1000
Interest rate = r = 8%
time = t = 3 years
The formula for calculating interest is:
![I=P_0rt\\= 1000*0.08*3\\=240](https://tex.z-dn.net/?f=I%3DP_0rt%5C%5C%3D%201000%2A0.08%2A3%5C%5C%3D240)
The interest for three years will be $240.
The amount to be paid back by the student is:
![A=P_0+I\\=1000+240\\=1240](https://tex.z-dn.net/?f=A%3DP_0%2BI%5C%5C%3D1000%2B240%5C%5C%3D1240)
The student has to pay back $1240
Keywords: Simple interest, yearly interest
Learn more about simple interest at:
#LearnwithBrainly
Answer:
and
are two such planes.
Step-by-step explanation:
To find the two planes whose intersection is the line
![x=6+3t\\ y=-8-3t\\ z=-1-t](https://tex.z-dn.net/?f=x%3D6%2B3t%5C%5C%20y%3D-8-3t%5C%5C%20z%3D-1-t)
You can say that <em>t</em> is equal to this expression
![t=\frac{x-6}{3} =\frac{y+8}{-3}=-z-1](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bx-6%7D%7B3%7D%20%3D%5Cfrac%7By%2B8%7D%7B-3%7D%3D-z-1)
Next,
![\frac{x-6}{3} =\frac{y+8}{-3}\\ \frac{y+8}{-3}=-z-1](https://tex.z-dn.net/?f=%5Cfrac%7Bx-6%7D%7B3%7D%20%3D%5Cfrac%7By%2B8%7D%7B-3%7D%5C%5C%20%5Cfrac%7By%2B8%7D%7B-3%7D%3D-z-1)
Then,
and
are two such planes.
You can see in the image attached that the intersection of this planes is the line
![x=6+3t\\ y=-8-3t\\ z=-1-t](https://tex.z-dn.net/?f=x%3D6%2B3t%5C%5C%20y%3D-8-3t%5C%5C%20z%3D-1-t)
Answer:
Step-by-step explanation:
This time we use the sin identity.
I am too lazy to write it out again but the answer is 6.97