Using the given values from the problem and the illustration, three points are known which are (0,0), (6.5,-31), (-6.5,-31). The first step in solving this problem is to determine the equation of the parabola.
y = ax²
-31 = a(6.5)²
-31 = 42.25a
a = -31/42.25
a = -124/169
Therefore, the equation of the parabola is y = (-124/169)x². The value 4.5 is then substituted in the equation as x to get the answer which is 16.14 meters.
Answer:
A ≈ 119.7°, b ≈ 25.7, C ≈ 24.3°
Step-by-step explanation:
A suitable app or calculator does this easily. (Since you're asking here, you're obviously not unwilling to use technology to help.)
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Given two sides and the included angle, the Law of Cosines can help you find the third side.
... b² = a² + c² - 2ac·cos(B)
... b² = 38² + 18² -2·38·18·cos(36°) ≈ 661.26475
... b ≈ 25.715
Then the Law of Sines can help you find the other angles. It can work well to find the smaller angle first (the one opposite the shortest side). That way, you can tell if the larger angle is obtuse or acute.
... sin(C)/c = sin(B)/b
... C = arcsin(c/b·sin(B)) ≈ 24.29515°
This angle and angle B add to less than 90°, so the remaining angle is obtuse. (∠A can also be found as 180° - ∠B - ∠C.)
... A = arcsin(a/b·sin(B)) ≈ 119.70485°
The fucntion is an exponential function. The correct option is D; P(x) = 100,000(0.9)^x.
<h3>What are exponential functions?</h3>
When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
For example, y^x, where a is a constant is an exponential function.
The table below shows the population of a city for the five years following the closing of a large factory in the city.
We can see that the when we put the value of x = 0 we get p(x) is 100,000
when we put x = 1. we get p(x) = 90,000.
So, We conclude that the function is an exponential function as the value of x increases the value of p(x) decreases.
Hence, the fucntion is an exponential function. The correct option is D; P(x) = 100,000(0.9)^x.
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Answer:
Step-by-step explanation:
Denote this equivalence relation by (i.e, if and only if ), is clear that is an equivalence relation since is. Now, by definition we have that .
Answer:
16 12/5= 18 2/5
Step-by-step explanation:
you get the answer and then simplify it to become a mixed number