Answer:
1/6 has been vacummed.
Step-by-step explanation:
Answer:
we have
when
base=8cm
height=11cm
area of parallelogram is :base×height
=8*11=88cm³
Now for
base=15cm
height=h
we have
the area of parallelogram=88cm²
base ×height=88cm²
15*h=88
h=88/15
h=88/15 or 5 13/15 or 5.86 cm in approximately
Answer:Answer:

Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as ![S_n = \frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
![S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70](https://tex.z-dn.net/?f=S_7%20%3D%20%5Cfrac%7B7%7D%7B2%7D%5B2%28-4%29%2B%287-1%29%28-2%29%5D%5C%5C%5C%5CS_7%20%3D%20%20%5Cfrac%7B7%7D%7B2%7D%5B-8%2B%286%29%28-2%29%5D%5C%5C%5C%5CS_7%20%3D%20%20%5Cfrac%7B7%7D%7B2%7D%5B-8-12%5D%5C%5C%5C%5C%5C%5CS_7%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20-20%5C%5C%5C%5CS_7%20%3D%20-70)
The sum of the nth term of the sequence will be;
![S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2%28-4%29%2B%28n-1%29%28-2%29%5D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B-8%2B%28-2n%2B2%29%5D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B-6-2n%5D%5C%5C%5C%5CS_n%20%3D%20%20%5Cfrac%7B-6n%7D%7B2%7D%20-%20%20%5Cfrac%7B2n%5E2%7D%7B2%7D%5C%5CS_n%20%3D%20-3n-n%5E2%5C%5C%5C%5CS_n%20%3D%20-n%283%2Bn%29)
The sigma notation will be expressed as
. <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>
Answer:
Step-by-step explanation:
Domain : [-9,-3]
Range: [2,6]