Which one is bigger 2/3 or 7/8
2 answers:
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Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
Answer:
The given sequence 6, 7, 13, 20, ... is a recursive sequence
Step-by-step explanation:
As the given sequence is
- It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.
As
,
As d is not same. Hence, it cannot be an arithmetic sequence.
- It also cannot be a geometrical sequence and exponential sequence.
It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.
As
,
,
As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.
So, if we carefully observe, we can determine that:
- The given sequence 6, 7, 13, 20, ... is a recursive sequence.
Please have a close look that each term is being created by adding the preceding two terms.
For example, the sequence is generated by starting from 1.
and
for n > 1.
<em>Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence</em>
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