The mass of Saturn is approximately 6 × 10^26 kg, while the mass of Mercury is approximately 3 × 10^23 kg. Which of the followin
1 answer:
The right answer is:
C. The mass of Saturn is approximately two thousand times the mass of Mercury.
Step-by-step explanation:
We will find the ratio of both masses to compare them.
Given
Mass of Saturn = S =
Mass of Mercury = M =
The ratio of larger mass to smaller is:
Hence,
The right answer is:
C. The mass of Saturn is approximately two thousand times the mass of Mercury.
Keywords: Mass, Ratio
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Answer:
The equation of the graph below is y = 0.5 csc[0.5(x + π/2)] - 1 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise the trigonometry transformation
- If the equation is y = A csc(B(x + C)) + D
# Amplitude is A
- The Amplitude is the height from the center line to the peak .
Or we can measure the height from highest to lowest points and
divide that by 2
# period is 2π/B
- The Period goes from one peak to the next
# phase shift is C (positive is to the left)
- The Phase Shift is how far the function is shifted horizontally
from the usual position.
# vertical shift is D
- The Vertical Shift is how far the function is shifted vertically from
the usual position.
- If y = csc(x)
∴ A = 1 , B = 1 , C = 0 , D = 0
- That means the amplitude is 1, the period is 2π, no phase shift
or vertical shift
* Now lets solve the problem
- From the graph
# The amplitude = (-0.5 - -1.5)/2 = 0.5
∴ A = 0.5
# The period is from 2.5π to -1.5π
∴ The period is 4π
∵ The period = 2π/B
∴ 4π = 2π/B ⇒ by cross multiplication
∴ B = 2π/4π = 1/2 = 0.5
* There is only one answer has A = 0.5 and B = 0.5
∴ y = 0.5 csc[0.5(x + π/2)] - 1
* The equation of the graph below is 0.5 csc[0.5(x + π/2)] - 1
* For more understand look to the color graph
- The blue graph is y = csc(x)
- The green graph is y = 0.5 csc[0.5(x + π/2)] - 1
Given:
The quadratic equation is
To find:
The vertex of the given quadratic equation.
Solution:
If a quadratic function is , then
We have,
It can be written as
...(i)
Here, .
Putting in (i), we get
On further simplification, we get
So, the vertex of the given quadratic equation is .
Therefore, the correct option is A.