Answer:
The time taken for the flare to hit the ground is approximately 10.7 seconds.
Step-by-step explanation:
Given : Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation
models the h height at t seconds of the flare.
To find : How long will it take for the flare to hit the ground?
Solution :
The equation
models the h height at t seconds of the flare.
The flare to hit the ground when h=0.
Substitute in the equation,
![-16t^2+ 160t + 120=0](https://tex.z-dn.net/?f=-16t%5E2%2B%20160t%20%2B%20120%3D0)
Applying quadratic formula, ![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Where, a=-16, b=160 and c=120
![x=\frac{-160\pm\sqrt{160^2-4(-16)(120)}}{2(-16)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-160%5Cpm%5Csqrt%7B160%5E2-4%28-16%29%28120%29%7D%7D%7B2%28-16%29%7D)
![x=\frac{-160\pm\sqrt{33280}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-160%5Cpm%5Csqrt%7B33280%7D%7D%7B-32%7D)
![x=\frac{-160\pm 182.42}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-160%5Cpm%20182.42%7D%7B-32%7D)
![x=\frac{-160+182.42}{-32},\frac{-160-182.42}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-160%2B182.42%7D%7B-32%7D%2C%5Cfrac%7B-160-182.42%7D%7B-32%7D)
![x=−0.70,10.70](https://tex.z-dn.net/?f=x%3D%E2%88%920.70%2C10.70)
Reject the negative value.
Therefore, the time taken for the flare to hit the ground is approximately 10.7 seconds.
1. Remove parentheses
-3x^2 + x^4 + x + 2x^4 - 7 + 4x
2. Collect like terms
-3x^2 + (x^4 + 2x^4) + (x + 4x) - 7
3. Simplify
-3x^2 + 3x^4 + 5x - 7
Answer:
$125.97
Step-by-step explanation:
To answer this question, simply plug the known values into the equation. We know that 100 is the principal (starting amount), 0.08 is the interest rate as a decimal, and t is 3 years.
Now plug in all those values to the given formula: B = p(1 + r)^t
Solve, and you end up with $125.9712, rounded to $125.97
Answer:
Step-by-step explanation:
Given
To find
- Coordinates of intersection of lines
As per the graph the intersection point has coordinates:
The point is (-3, -2)
5 root 41/41
draw a right triangle. label the sides. use the Pythagorean theorem. do sin of the angle A. rationalize denominator.