6+(9-1)^2/4 = 22
______________[
Answer:
Option H, π/3 and 2π/3
Step-by-step explanation:
sin x = sqrt(3) / 2
<em>It happens at 60 degrees and 120 degrees. In radians, it is π/3 and 2π/3</em>
<em />
Answer: Option H, π/3 and 2π/3
If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
A general circle's equation is (x-h)^2+(y-k)^2= r^2
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)
Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0).
The formula for slope is <u>Y1-Y2</u>
X1-X2
We can break this down with our two points (center and tangent)
(0,0) and (-4,-5)
(X1,Y1) and (X2,Y2)
therefore, we will put the equation as such
<u>0-(-5)= 5</u> = <em> </em><u><em>5</em></u>
0-(-4)= 4 <em> 4</em>
<em>this is our slope from the center to the point of tangency.</em>
We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to.
Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> = <u>-5</u> = <u>-4</u><u>
</u>4 4 5
Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.
Slope-int y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept ( the point where x=0, or where its on the y axis)
now we plug things in
(-4,-5) is our point,
<u>-4</u> is our slope
5
-5=<u>-4</u>(-4)+b After we plug things in, solve for b
5
-5= 3.2+b
-1.8= b or b= <u />1 <u>4</u>
5
Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u> = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u> 5
<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em> This is the equation of the tangent line</em><u>
</u><em> 5 5</em>
Hope that helped
Answer:
We would advise her to choose Country Route because in this route time consistent between 15 and 18 minutes.
Step-by-step explanation:
We are given that Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can take to the school, one through the city and one through the countryside.
Jean sets up a randomized experiment where each day she tosses a coin to decide which route to take that day. She records the following data for 5 days of travel on each route.
Country Route - 17, 15, 17, 16, 18 (in minutes)
City Route - 18, 13, 20, 10, 16 (in minutes)
Now, we have to decide which route is better for Jean to go to college.
As we can see from the data that the Country route timings is consistent between 15 to 18 minutes which means most of the times she will reach college between these minutes only.
While on the other hand, we can observe that City route timings are very much consistent as it has a low value of 10 minutes and high value of 20 minutes which means Jean can't be sure that at which time she will reach college.
Hence, we would advise her to choose Country route.
