Answer:
Step-by-step explanation:
Given function l:
h= -16t² + 26t
where h represents height and t represents time.
The time for dolphin atbthe height 5 feet is given by putting the value of h as 5 in the function,
5 = -16t² + 26t
16t² - 26t + 5 = 0
For this equation: a=16, b=-26, c=5
Use quadratic formula with a=16, b=-26, c=5.
x=(−b±√b2−4ac)/2a
x=−(−26)±√(−26)2−4(16)(5)/2(16)
x=13/16 + 1/16√89 or x=13/16+ −1/16√89
x=1.40 or 0.22
Answer:
The road width is x = 10 m.
Step-by-step explanation:
A formula for the area of the horizontal rectangle is A1 = (x)(20 m).
A formula for the small rectangle on top of that is A2 = (x)(18 - x).
The total area of the new roadway is 280 m^2.
Summing up A1 and A2 and equating the result to 280 m^2, we get:
20x + 18x - x^2 = 280
Rewriting this in the standard quadratic form:
-x^2 + 38x - 280 = 0
Here the coefficients are a = -1, b = 38 and c = -280.
The discriminant is thus b^2 - 4ac, or:
38^2 - 4(-1)(-280) = 1444 - 4(280) = 324, or 18^2.
Thus, the roots (x-values) are:
-38 ± 18
-------------- = 28 and 10
-2
Only the value x = 10 makes sense here, so we omit the other value (28).
The road width is x = 10 m.
x = ----------------------
The two angles are supplementary angles which means they need to equal 180 degrees when added together.
4x + x = 180
5x = 180
Divide both sides by 5:
x = 180/5
x = 36
