By converting into parametric equations,
<span>{<span><span>x<span>(θ)</span>=r<span>(θ)</span><span>cosθ</span>=<span>cos2</span>θ<span>cosθ</span></span><span>y<span>(θ)</span>=r<span>(θ)</span><span>sinθ</span>=<span>cos2</span>θ<span>sinθ</span></span></span></span>
By Product Rule,
<span>x'<span>(θ)</span>=−<span>sin2</span>θ<span>cosθ</span>−<span>cos2</span>θ<span>sinθ</span></span>
<span>x'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>−<span>cos<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>=1</span>
<span>y'<span>(θ)</span>=−<span>sin2</span>θ<span>sinθ</span>+<span>cos2</span>θ<span>cosθ</span></span>
<span>y'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>+<span>cos<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>=0</span>
So, the slope m of the curve can be found by
<span>m=<span><span>dy</span><span>dx</span></span><span>∣<span>θ=<span>π2</span></span></span>=<span><span>y'<span>(<span>π2</span>)</span></span><span>x'<span>(<span>π2</span>)</span></span></span>=<span>01</span>=0</span>
I hope that this was helpful.
Given the equation <span>-4a/a+4=12/a-11, for sure we need to the solution for a.
</span><span>-4a/a+4=12/a-11
</span>-3a + 4 = 12/a - 11
-3a -12/a = -11 - 4
3a + 12 / a = 15
(3a^2 + 12) / a = 15
3a^2 + 12 = 15a
<span>3a^2 - 15a + 12 = 0
</span>
In order to get a , we need to find the roots.
(3a - 3) (a - 4) = 0
3a - 3 = 0 --> a = 1
a - 4 = 0 -- > a = 4
So the possible solutions for a are 1 and 4.
Answer:24, 4, 8, 12
Step-by-step explanation:
It should be the first one
Answer:
The three consecutive integers are:
8, 9, 10
Step-by-step explanation:
Given:
There are three consecutive integers.
Three times the smallest is 14 more than the largest.
To find the three integers.
Solution:
Since the integers are consecutive , so each have a common difference of 1.
For example : -3,-2,-1
Let the integers be =
Three times the smallest is 14 more than the largest can be given as:
Simplifying and solving for .
Subtracting both sides by
Dividing both sides by 2.
∴
Smallest integer = 8
Next integer = 9
Largest integer = 10