a Use y=17 to develop a quadratic in standard form to solve. Recall that we cannot get a real value if we take the square root of a negative number.
B
b Use y=14 and the given equation to develop a quadratic in standard form to solve.
A
a No.
B
b Yes, about 137 days.
Practice makes perfect
a In this exercise, we are given an equation with two variables. One variable, y represents the hours of daylight and x is the number of days since April 1. For this part, we need to determine if any of those days have 17 hours of daylight. Let's substitute y=17 into the equation and solve for x.
Recall that sqrt(-0.001548), has no real solution. Therefore, Seattle will not get 17 hours of daylight between April and September.
b For this question, like in Part A, we need to determine if any of those days have 14 hours of daylight. Let's substitute y=14 into the equation and solve for x.
The solutions for this equation are x ≈ -0.076 ± 0.06274-0.00092. Let's separate the two cases.
x ≈ -0.076 ± 0.06274/-0.00092
x_1 ≈
x_2 ≈
-0.076 + 0.06274/-0.00092
-0.076 - 0.06274/-0.00092
-0.01326/-0.00092
-0.13874/-0.00092
14.41
150.80
From this, we can say that at 14 and 151 days after April 1 the days were 14 hours long. We can also conclude that all the days in between those ones had more than 14 hours of daylight. Therefore, since 151-14=137, we can say Seattle has about 137 days with more than 14 hours of daylight.
