Answer:
![a_{n} = 32(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2032%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Step-by-step explanation:
The nth term of a geometric sequence is given by the following equation.
![a_{n+1} = ra_{n}](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20ra_%7Bn%7D)
In which r is the common ratio.
This can be expanded for the nth term in the following way:
![a_{n} = a_{1}r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7Dr%5E%7Bn-1%7D)
In which
is the first term.
This means that for example:
![a_{3} = a_{1}r^{3-1}](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%20a_%7B1%7Dr%5E%7B3-1%7D)
So
![a_{3} = a_{1}r^{2}](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%20a_%7B1%7Dr%5E%7B2%7D)
![2 = a_{1}(\frac{1}{4})^{2}](https://tex.z-dn.net/?f=2%20%3D%20a_%7B1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D)
![2 = \frac{a_{1}}{16}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7Ba_%7B1%7D%7D%7B16%7D)
![a_{1} = 32](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2032)
Then
![a_{n} = 32(\frac{1}{4})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2032%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7Bn-1%7D)
Answer:
Step-by-step explanation:
J is a tangent to the circle and it is at right angle,
So applying Pythagorean theorem
HK² = KJ² + HJ²
HK² = 8²+ 15²
HK² = 64 + 225
HK² = 289
HK = √289
HK = 17 mi
Answer:
The sign would be 784 ft. long.
Step-by-step explanation:
The sign would be painted across the total perimeter of the building.
- the distance across the front of the store is 294 feet
- the distance from the front to the back is one third of this distance = (1/3) × 294 = 98 ft.
The perimeter of a rectangular = 2(L + B)
L = length of the building = 294 ft.
B = Breadth of the building = 98 ft.
Perimeter of the chocolate factory that the Sign would be painted across = 2(294 + 98) = 784 ft.
Hope this Helps!!!
Answer:
1598.2
Step-by-step explanation:
I used a calculator on this one.
Answer:
A 100 lb person will weight 40 lb on Mars
Step-by-step explanation:
Given:
Weight on Mars directly varies as its weight on earth.
Let weight on Mars be = ![M](https://tex.z-dn.net/?f=M)
Let weight on Earth be = ![E](https://tex.z-dn.net/?f=E)
Its known that:
∝ ![E](https://tex.z-dn.net/?f=E)
Thus
where
is constant of proportionality.
when
, then ![M=38\ lb](https://tex.z-dn.net/?f=M%3D38%5C%20lb)
thus, we have
dividing both sides by 95.
∴ ![k=\frac{38}{95}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B38%7D%7B95%7D)
Thus when
,
would be calculated as
![M=\frac{38}{95}\times 100](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B38%7D%7B95%7D%5Ctimes%20100)
![M=\frac{3800}{95}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B3800%7D%7B95%7D)
∴
(Answer)
∴ A 100 lb person will weight 40 lb on Mars.