What is the length of MN?<br> 8x

Find an equation for the tangent to the curve at P and the horizontal tangent to the curve at Q. y = 5 + cot x - 2 csc x 0 1 2 3

oksian1 [2.3K]

Answer with explanation:

The given function in x and y is,

y= 5 +cot x-2 Cosec x

To find the equation of tangent, we will differentiate the function with respect to x

$y'= -\csc^2 x+2 \csc x\times \cot x$

Slope of tangent at (π/2,3)

$y'_{(\frac{\pi}{2},3)}= -\csc^2\frac{\pi}{2} +2 \csc \frac{\pi}{2}\times \cot \frac{\pi}{2}\\\\=-1+2\times 1 \times 0\\\\= -1$

Equation of tangent passing through (π/2,3) can be obtained by

$\rightarrow \frac{y-y_{1}}{x-x_{1}}=m(\text{Slope})\\\\ \rightarrow \frac{y-3}{x-\frac{\pi}{2}}=-1\\\\\rightarrow 3-y=x-\frac{\pi}{2}\\\\\rightarrow x+y-3-\frac{\pi}{2}=0$

⇒There will be no Horizontal tangent from the point (π/2,3).

5 0

4 years ago

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?

klio [65]

A=(απr^2)/360=(απd^2)/1440 (r^2=d^2/4)

α=1440A/(πd^2)

s=απd/360 (where s=arc length) so

s=(1440Aπd)/(360πd^2)

s=4A/d and since A=10mi^2 and d=20mi

s=(4*10)/20

s=2 miles

8 0

3 years ago

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a red card

joja [24]

Answer: $\dfrac{3}{51}$