Answer:
Step-by-step explanation:
×
Answer:
3pi/4 and -pi/4
Step-by-step explanation:
We can simplify -6/6 to -1.
Therefore, this function can be simplified to arctan(-1).
Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.
Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.
If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.
If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.
Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.
Answer:
a) The y-intercept is 160. It represents the initial distance Jayden was from his home.
b) The x-intercept is 4. It represents the amount of time taken for Jayden to reach his home.
Step-by-step explanation:
The y-intercept can be found by looking at the value of y when x=0. When x=0, y= 160. Since the x-axis is the amount of time in hours, x=0 would mean the initial time. The x-axis is the number of miles from Jayden's home thus, Jayden was 160 miles away from his home when x=0 hours.
The x-intercept can be found by looking at the x value when y=0. When y=0, x=4. This means that it took Jayden 4 hours to reach home or 4 hours to travel 160miles to his house.
Answer: 49 students
Step-by-step explanation:
2 /7 of students in a school wore shorts today. The number of students to be selected in order to get 14 students who will wear shorts to school will be:
Let the number of students that will be sampled be y. This will be:
2/7 of y = 14
2/7 × y = 14
2y/7 = 14
Cross Multiply
2y = 7 × 14
2y = 98
y = 98/2
y = 49
49 students will be selected randomly.
