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
okay the answers are
Question 1 A survey was sent to GCA students asking the question "Who is your favorite teacher?"
What type of data was collected?
Answer) Qualitative
Question 2 ) A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?"
The data collected was
Answer) Quantitative
Question 3) You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house.
47.6 miles is an example of...
Answer) Quantitative, continuous data
Question 4
) While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole.
The number of times you were able to sink the beanbag is an example of....
Answer) Quantitative, discrete data
Question 5) You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes.
57.28 minutes is an example of....
Answer) Quantitative, continuous data
Answer:
h = s / π.r²
Step-by-step explanation:
the given equation is s = π.r².h
Now if we have to calculate the value of h from the given formula then we will solve it so that h remains alone on one side of the equation.
This only possible when we divide term on both the sides by π.r²
s/π.r² = π.r².h/π.r²
h = s / π.r²
Therefore h = s / π.r² is the right option.
Answer:
11,600
Step-by-step explanation:
What is 4% of 290,000?
Y is 4% of 290,000
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 4% * 290,000
Converting percent to decimal:
p = 4%/100 = 0.04
Y = 0.04 * 290,000
Y = 11,600