I wonder what the best way of explaining this is? You could graph the results for each choice. Or you could reason it out.
The first thing you have to do it deal with y = 3. Draw a really crude graph like a set of axis. Make the y values go from -5 to + 5. x for the moment does not matter.
Draw a horizontal line through y = 3 or going through the point (0,3). Now here's the catch and you're going to have to read it very carefully.
Condition One
If a>0 then the graph opens upward and b is going to have to be less than 3. That sentence is an absolute nightmare. Think carefully about what a>0 means. Make it 2 and draw a rough graph opening upward on the crude axis you have drawn. b is the y value of the minimum, so that minimum has to be less than 3. Are there any point like that? The two points where a>0 are C and D.
C
The lowest point that C will hit is 4. That's not good enough. b = 4 is the lowest y value. C is not the answer
D
The lowest point is 3. The graph will just touch y = 3. That's not good enough either. Touching y = 3 does not produce 2 roots. It produces just one.
Condition Two
a < 0 Here the graph opens downward. It means the a<0 and b>3. You need to look at A or B. Which point does that? A has a maximum below 3. It's no good. A is wrong.
So the answer must be B. a<0 and b>3. Right on 2 solutions.
Answer:
183
Step-by-step explanation:
125+141+213+155+281=915
915 divided by 5=183
Answer:
10+37h
Step-by-step explanation:
10 is the flat fee so only happens once
37 is hourly rate so multiply by h (hours)
The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3
<h3>The sinusoidal function</h3>
The minimum and the maximum of the function are
The amplitude (A) is calculated as:
A = 0.5 * (Maximum - Minimum)
So, we have:
A = 0.5 * (-5 + 1)
A = -2
The vertical shift (d) is calculated as:
d = 0.5 * (Maximum + Minimum)
So, we have:
d = 0.5 * (-5 - 1)
d = -3
The period (P) is calculated as:
P = 2π/B
From the graph,
B = 1
So, we have:
P = 2π/1
P = 2π
So, the amplitude is -2 and the period is 2π.
<h3>The equation of the sine function</h3>
In (a), we have:
A = -2
B = 1
d = -3
A sine function is represented as:
y = A sin(Bx + C) + D
So, we have:
y = -2sin(x + C) - 3
The graph passes through the point (0, -5)
So, we have
-5 = -2sin(0 + C) - 3
Solve for C, we have
C = 1.5
So, we have:
y = -2sin(x + 1.5) - 3
Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3
Read more about sinusoidal function at
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Scientific notation is used when a number is really big (example: 11200000000) or really small (example: .000000000002). In this case three of your situations would have really big numbers. That means the answer would be the speed of a car because that would a normal sized number.
