Answer:
The explicit formula for the geometric sequence is
.
Step-by-step explanation:
By definition of geometric sequence, we should use the following expression:
,
(1)
Where:
- First term.
- Geometric rate.
- Position of the element within the series.
If we know that
and
, then the explicit formula for the geometric sequence is:
![c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}](https://tex.z-dn.net/?f=c%28n%29%20%3D%20-40%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E%7Bn-1%7D)
The explicit formula for the geometric sequence is
.
Answer:
![(-\infty,0)\cup(\frac{16}{3},\infty)\\That \ is x\frac{16}{3}](https://tex.z-dn.net/?f=%28-%5Cinfty%2C0%29%5Ccup%28%5Cfrac%7B16%7D%7B3%7D%2C%5Cinfty%29%5C%5CThat%20%5C%20is%20x%3C0%20%5C%20or%20%5C%20x%3E%5Cfrac%7B16%7D%7B3%7D)
Step-by-step explanation:
![h(x)=\frac{1}{8}x^{3} -x^{2} \\\\Differentiate \ h(x) \ with \ respect \ to \ x\\h'(x)=\frac{3}{8}x^{2} -2x](https://tex.z-dn.net/?f=h%28x%29%3D%5Cfrac%7B1%7D%7B8%7Dx%5E%7B3%7D%20-x%5E%7B2%7D%20%5C%5C%5C%5CDifferentiate%20%5C%20h%28x%29%20%5C%20with%20%5C%20%20respect%20%5C%20to%20%5C%20x%5C%5Ch%27%28x%29%3D%5Cfrac%7B3%7D%7B8%7Dx%5E%7B2%7D%20-2x)
For positive rate of change ![h'(x)>0](https://tex.z-dn.net/?f=h%27%28x%29%3E0)
![\frac{3}{8} x^{2} -2x>0\\x(\frac{3}{8}x-2)>0\\\\ When \ x0 \ (multiplication \ of \ two \ positives \ is \ positive)\\\\h'(x)>0 \ when \ x\frac{16}{3} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D%20x%5E%7B2%7D%20-2x%3E0%5C%5Cx%28%5Cfrac%7B3%7D%7B8%7Dx-2%29%3E0%5C%5C%5C%5C%20When%20%5C%20x%3C0%20%5CRightarrow%20%28%5Cfrac%7B3%7D%7B8%7Dx-2%29%3C0%20%5CRightarrow%20h%27%28x%29%3E0%20%5C%20%28multiplication%20%5C%20of%20%5C%20two%20%5C%20negative%20%5C%20gives%20%5C%20positive%29%5C%5C%5C%5CWhen%20%28%5Cfrac%7B3%7D%7B8%7Dx-2%29%3E0%20%5CRightarrow%20x%3E%5Cfrac%7B16%7D%7B3%7D%20%5CRightarrow%20x%3E0%5C%5C%5C%5Ch%27%28x%29%3Dx%28%5Cfrac%7B3%7D%7B8%7Dx-2%29%20%3E0%20%5C%20%28multiplication%20%5C%20of%20%5C%20two%20%5C%20positives%20%5C%20is%20%5C%20positive%29%5C%5C%5C%5Ch%27%28x%29%3E0%20%5C%20when%20%5C%20x%3C0%20%5C%20or%20%5C%20x%3E%5Cfrac%7B16%7D%7B3%7D%20%5C%5C%5C%5C)
Answer:
x = 18/25
Step-by-step explanation:
(4/5)² = 2x - 4/5
16/25 = 2x - 4/5
16/25 = 2x - 20/25
36/25 = 2x
x = 18/25
1 ) f ( x ) = 3 x
He can write { 9, 12, 18, 21, 27 } comic strips.
2 ) f ( x ) = 5 x - 3
- 13 = 5 x - 3
5 x = - 10
x = -2, etc.
The domain is: { - 2 , - 1 , 0, 3, 4 }
3 ) f ( x ) = 2 x
It will take { 8, 20, 28, 32, 36 } hours.