Answer:
a.
Period = π
Amplitude = 4
b.
Maximum at: x = 0, π and 2π
Minimum at: x = π/2 and 3π/2
Zeros at: x = π/4, 3π/4, 5π/4 and 7π/4
Step-by-step explanation:
Part a:
Amplitude represents the half of the distance between the maximum point and the minimum point of the function. So the easy way to find the amplitude is: Find the difference between maximum and minimum value of the function and divide the difference by 2.
So, amplitude will be: ![\frac{Maximum-Minimum}{2}=\frac{4-(-4)}{2}=\frac{8}{2}=4](https://tex.z-dn.net/?f=%5Cfrac%7BMaximum-Minimum%7D%7B2%7D%3D%5Cfrac%7B4-%28-4%29%7D%7B2%7D%3D%5Cfrac%7B8%7D%7B2%7D%3D4)
Therefore, the amplitude of the function is 4.
Period is the time in which the function completes its one cycle. From the graph we can see that cosine started at 0 and completed its cycle at π. After π the same value starts to repeat. So the period of the given cosine function is π.
Part b:
From the graph we can see that the maximum values occur at the following points: x = 0, π and 2π
The scale on x-axis between 0 and π is divided into 4 squares, so each square represents π/4
Therefore, the minimum value occurs at x = π/2 and 3π/2
Zeros occur where the graph crosses the x-axis. So the zeros occur at the following points: π/4, 3π/4, 5π/4 and 7π/4
Answer:
(a) The angle swept by the hour hand is 297⁰30′
(b) The exact angle between the minute and hour hand is 132⁰30′
Step-by-step explanation:
Given;
(a) angle swept by the hour hand between noon and 9:55 pm
between 12 pm and 9pm, there are 9 hours = 9 x 60 = 540 mins
9.55 pm = 540 mins + 55 mins = 595 mins
The hour hand moves 0.5 degree per minute
1 mins ---------------- 0.5 degrees
595 mins --------- ?
= 297⁰30′
(b) the exact angle between the minute and hour hands at 1:25 pm
for 25 mins, the hour hand had moved 12.5 degrees
Between 1 and 5, there are 20 mins moved by the minutes hand = 20 x 6°
= 120⁰
total angle = 12.5⁰ + 120⁰ = 132⁰30′
Answer: Equation relating C to S :
The total cost to transport 19 tons of sugar is $11, 250.
Step-by-step explanation:
Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.
Total cost = $6500 + $250 x (amount of sugar transported ( in tons))
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.
Then, the equation relating C to S would be :
When S= 19 , we get
Hence, the total cost to transport 19 tons of sugar would be $11, 250.
Answer:
B.{5}
Step-by-step explanation:
2-8x-42=0
(÷2), we get,
1-4x-21=0
-4x-20=0
-4x=20
x=20÷(-4)
x=(-5)
since the question asks for a positive set, the answer is [x=5]
Answer: y= root 2, - root 2
Decimal form y= 1.41421356..., -1.41421356...