Given:
The nth term of a number sequence is 
.
To find:
The first 3 terms and the 10th term.
Solution:
We have, nth term of a number sequence.
For n=1,
For n=2,
For n=3,
For n=10,
Therefore, the first three terms are 3, 8 and 15 respectively. The 10th term is 120.
QR = 4, RP = 2. Remember that fraction is also known as ratio. So use steps/formulas as per necessary. U can also use algebra ☺
72 ponytail holders ÷ 8 girls = 9
Each girl will get 9 ponytail holders each.
The slope of the tangent line to a curve is the first derivative, dy/dx, of the curve at the point of tangency.
<span>In this problem the point of tangency has theta = pi/6, so the corresponding r = 5 sin[(3)(pi/6)] = 5. </span>
<span>Converting these (r, theta) coordinates to (x, y) coordinates you use the polar to cartesian coordinate conversion eqns.: </span>
<span>x = r cos(theta) and y = r sin(theta). </span>
<span>So x = 5 cos(pi/6) = 4.33; y = 5 sin(pi/6) = 2.5 </span>
<span>So the point of tangency where the tangent line intersects the curve is (x,y) = (4.33, 2,5) </span>
<span>Using the formula from the attached website, which I assume your teacher derived in class: </span>
<span>dy/dx = [[dr/d(theta)] sin(theta) + r cos(theta)] / [[dr/d(theta)] cos(theta) - r sin(theta)] </span>
<span>From r = 5sin(3 theta) , dr/d(theta) = 15 cos(3 theta) </span>
<span>dy/dx = [ [15 cos(3 theta)] sin(theta) + r cos(theta)] / [ [15 cos(3 theta)] cos(theta) - r sin(theta)] </span>
<span>dy/dx evaluated at theta = pi/6 and r = 5 is: </span>
<span>dy/dx = [ [15 cos(3 pi/6] sin(pi/6) + 5 cos(pi/6)] / [ [15 cos(3 pi/6)] cos(pi/6) - 5 sin(pi/6)] </span>
<span>dy/dx = - cot(pi/6) = -1.732 </span>
<span>So we have the tangent line of the form y = (-1.732)x + b where the point (x,y) = (4.33, 2.5) is on the line. </span>
<span>b = 2.5 + (1.732)(4.33) = 10 </span>
<span>So the tangent line is y = -1.732 x + 10</span>
24 is a common denominator.
