Celia write the equation d = 8t to represent the distance in miles d that riders could travel in t hours at a speed of 8 miles p
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Answer:
Step-by-step explanation:
In order to solve this equation, let's see what we already know.
- We know two points on the graph <em>which we can use to find the slope</em>
That's about it.
However, this can come useful to find the slope between the two points, which is the slope for the entire graph (since this is linear). The slope between two points is usually defined as (change in y / change in x). Our two points are (18, 2017) and (48, 2212).
The change in y between our two points is , and the change in x is
. Our slope will then be
, which comes out to be approximately 6.5. Therefore, our slope is 6.5.
Now that we know the slope, we can substitute inside our equation in slope intercept form.
We have yet to find b, the y-intercept (how much the plane itself weighs). To find b, we can substitute a point on the graph into the equation and solve for b. We know that the point (18, 2017) is on the graph so let's use that.
Now that we know our y-intercept is 1900, we can create our equation by using the slope and the y-intercept.
Finally, to find the weight of the plane with 66 pounds of fuel, we can substitute 66 inside this equation as x.
So the plane weighed 2329 pounds with 66 gallons of fuel.
Hope this helped!
4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3. So our numerator is 1/2 and our denominator is sqrt(3)/2.
And remember tangent is just sin/cos. So what degree has sinx as 1/2 and and cosx as sqrt(3)/2? Well, 30 degrees does, but 30 degrees is not within the range we are given. That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.
And 210 degrees in radians is 7pi/6.
I hoped that made sense.
(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2? According to the unit circle, 150 degrees and 210 degrees does. They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.
5) What quadrant is radian measure 5 in?
Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.
But to be sure let's change 5 radian to degrees:
5 * 180/pi = 900/pi = 286.48 degrees
286.48 degrees is definitely in Q4, so we are correct.