Answer: 68/67.8 toothpicks
Step-by-step explanation
first convert how many inches 11.3 feet is
11.3 = 135.6 inches
so after you get your number you get your calculator and divide it by how many inches the toothpicks are
135.6 ÷ 2= 67.8
then to get a solid answer you would round it to a whole number
67.8--> 68
so you ether say the rounded number or you cut .2 inches off the last toothpick
(also im not sure if its 11.3ft or 113ft so if so then take away the decimal and do the same math, you'll end up with 678 toothpicks)
We can write an equation of this, with p representing the unknown population. We know that 90% of the population owns cars:
90% * p
We also know that 4761 people own cars, which is the same as the above expression, so we write:
90% * p = 4761.
From there, you just divide both sides by 90%, or 0.9
p = 4761/0.9 = 5290
The population is 5290 people.
Answer:
A = √29
Step-by-step explanation:
The short of it is that ...
A² = 2² + 5² = 29
A = √29
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<u>Amplitude</u>
If you expand the second form using the sum-of-angles formula, you get ...
Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Comparing this to the first form, you find ...
c₂ = 2 = Acos(φ)
c₁ = 5 = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
(Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²
In terms of c₁ and c₂, this is ...
(c₁)² +(c₂)² = A²
A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude
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<u>Phase Shift</u>
We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...
φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*
φ = arctan(5/2) ≈ 1.19029 radians
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* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.
Answer:
Step-by-step explanation:
