Answer:
Below in bold.
Step-by-step explanation:
sin θ = 4 cos θ
Note that tan θ = sin θ / cos θ so we
Divide both sides by cosθ:
tan θ = 4
θ = 75.96
= 75 degrees 58 minutes.
Answer:
-6 is the y coordinate
Step-by-step explanation:
Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
Answer: D. y = 3x − 1
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the graph,
y2 = 2
y1 = - 1
x2 = 1
x1 = 0
Slope,m = (2 - - 1)/(1 - 0) = 3/1 = 3
To determine the intercept, we would substitute x = 1, y = 2 and m= 3 into y = mx + c
y = mx + c. It becomes
2 = 3 × 1 + c = 3 + c
c = 2 - 3 = - 1
The equation becomes
y = 3x - 1
Answer:
f(2)=1/9
Step-by-step explanation:
f(x)=(1/3)^x
f(2)=(1/3)^(2)
f(2)=1/9
