Answer:
(3×3)+2=11
$11
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:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, <em>this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together</em>, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
