The Saginaw Bay tides vary between two feet and eight feet. The tide is at its lowest point when time (t) is 0 and completes a f
ull cycle in 16 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
2 answers:
Answer: Amplitude = 3, period = 16 hours and midline is y=5.
Step-by-step explanation: Given that the Saginaw Bay tides has minimum point at 2 feet and maximum point is at 8 feet.
To find the amplitude, period and midline of the function that would model this periodic phenomenon.
See the attached graph of the periodic function. The minimum point is A(4.5,2) and the maximum point is B(1.5,8).
The midline of the function is
The amplitude is the perpendicular distance between the midline and one of its extreme point. So, amplitude is given by
Also, period is the time taken by the waves to travel from one maximum point to another i.e., between two consecutive maximum points or minimum points.
So, period of the function is 16 hours.
Thus, amplitude = 3, midline is y=5 and period of the function is 16 hours.
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Answer:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
,
and
:
The following system of linear equations is obtained:
Whose solution is , which means that the set of vectors is linearly independent.
,
and
The following system of linear equations is obtained:
Since the number of variables is greater than the number of equations, let suppose that , where
. Then, the following relationships are consequently found:
It is evident that and
are multiples of
, which means that the set of vector are linearly dependent.
,
and
The following system of linear equations is obtained:
Whose solution is , which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
Ans: Option A
Explanation:
Let's solve it smartly!
Given expression:
--- (A)
Factors: (x+p)(x+q)
Condition: c<0
Now let us expand (x+p)(x+q):
=>
--- (B)
By comparing (B) with (A), we can say that:
pq = c --- (C)
Now, as the condition says, c<0, it means either p or q is negative. Both cannot be positive or both cannot be negative.
1) If p>0, q>0, it means c>0 since (+p)(+q) = (+c)(according to equation (C)). Condition is not met.
Hence, option B and D are wrong.
2) If p<0, q<0 it means c>=0 since (-p)(-q) = (+c)(according to equation (C)). Condition is not met.
Hence option C is out as well.
We are left with Option A:p<0, q>0 it means c<0 since (-p)(+q) = (-c)(according to equation (C)).
Condition is MET!
Hence,
Ans: Option A: p= -3, q= 7
Explanation:
Let's solve it smartly!
Given expression:
Factors: (x+p)(x+q)
Condition: c<0
Now let us expand (x+p)(x+q):
=>
By comparing (B) with (A), we can say that:
pq = c --- (C)
Now, as the condition says, c<0, it means either p or q is negative. Both cannot be positive or both cannot be negative.
1) If p>0, q>0, it means c>0 since (+p)(+q) = (+c)(according to equation (C)). Condition is not met.
Hence, option B and D are wrong.
2) If p<0, q<0 it means c>=0 since (-p)(-q) = (+c)(according to equation (C)). Condition is not met.
Hence option C is out as well.
We are left with Option A:p<0, q>0 it means c<0 since (-p)(+q) = (-c)(according to equation (C)).
Condition is MET!
Hence,
Ans: Option A: p= -3, q= 7