Answer:
144
Step-by-step explanation:
The answer is 144 because we can take any multiple of 72, the LCM of 18, 24, and 36, but 72 is not a perfect square. So, we go to the next multiple, 144, which is a perfect square, so the answer is 144. Hope it helps!
Both computers will do the job in 5 hours and 14 minutes.
Since a computer can process the payroll for Hometel in 10 hours, while an older back up computer needs 11 hours to process payroll, to determine how long would the job take if the two computers are both used to do the job, the following calculation should be performed:
- X / 10 + X / 11 = 1
- 10X + 11X = 110
- 21X = 110
- X = 110/21
- X = 5.238
- 100 = 60
- 0.238 = X
- 0.238 x 60/100 = X
- 0.14 = X
Therefore, both computers will do the job in 5 hours and 14 minutes.
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We can use the equation y=2(0.0625)+5(0.125), y being the thickness of the plywood.
I got 5(0.125) because two sheets of the 7 were already used, meaning there are 5 sheets of plywood left over.
y=0.125+0.625
y=0.75
Therefore, the plywood is 0.75 inches thick.
Answer: 0, π, 2π
Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.
If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.
Explanation:
1) The first solution, θ = 0 is trivial:
sin (0) - tan (0) = 0
0 - 0 = 0
2) For other solutions, work the expression:
sin(θ) + tan (-θ) = 0 ← given
sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)
sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)
sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)
⇒ Any of the two factors can be 0
⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,
sin(θ) = 0 ⇒ θ = 0, π, 2π
1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π
⇒ Solutions are 0, π, and 2π
In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.