The taxes are figured as follows: 0.089(value of car)
Here the taxes are 0.089(value of car) = $1100.
Divide both sides of this equation by 0.089 to determine the value of the car.
value of car = $12359.55, or approx $12360.
Answer: Alberto caught up to Omar after 6 seconds, when Alberto had to run 54 meters.
Step-by-step explanation:
We can solve this by substitution method.
Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.
Therefore, 
Now replace the 7x in the first equation with 5y - 12:
(substitute in 7x = 5y - 12)
Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12
(substitute in y = 1)
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Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then
tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2) ===> sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)
We also know that
sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1 ===> sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))
Recall the double angle identities:
cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1
sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)
Then
cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)
sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)
