Let
![f(x)=\sec^{-1}x](https://tex.z-dn.net/?f=f%28x%29%3D%5Csec%5E%7B-1%7Dx)
. Then
![\sec f(x)=x](https://tex.z-dn.net/?f=%5Csec%20f%28x%29%3Dx)
, and differentiating both sides with respect to
![x](https://tex.z-dn.net/?f=x)
gives
![(\sec f(x))'=\sec f(x)\tan f(x)\,f'(x)=1](https://tex.z-dn.net/?f=%28%5Csec%20f%28x%29%29%27%3D%5Csec%20f%28x%29%5Ctan%20f%28x%29%5C%2Cf%27%28x%29%3D1)
![f'(x)=\dfrac1{\sec f(x)\tan f(x)}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac1%7B%5Csec%20f%28x%29%5Ctan%20f%28x%29%7D)
Now, when
![x=\sqrt2](https://tex.z-dn.net/?f=x%3D%5Csqrt2)
, you get
![(\sec^{-1})'(\sqrt2)=f'(\sqrt2)=\dfrac1{\sec\left(\sec^{-1}\sqrt2\right)\tan\left(\sec^{-1}\sqrt2\right)}](https://tex.z-dn.net/?f=%28%5Csec%5E%7B-1%7D%29%27%28%5Csqrt2%29%3Df%27%28%5Csqrt2%29%3D%5Cdfrac1%7B%5Csec%5Cleft%28%5Csec%5E%7B-1%7D%5Csqrt2%5Cright%29%5Ctan%5Cleft%28%5Csec%5E%7B-1%7D%5Csqrt2%5Cright%29%7D)
You have
![\sec^{-1}\sqrt2=\dfrac\pi4](https://tex.z-dn.net/?f=%5Csec%5E%7B-1%7D%5Csqrt2%3D%5Cdfrac%5Cpi4)
, so
![\sec\left(\sec^{-1}\sqrt2\right)=\sqrt2](https://tex.z-dn.net/?f=%5Csec%5Cleft%28%5Csec%5E%7B-1%7D%5Csqrt2%5Cright%29%3D%5Csqrt2)
and
![\tan\left(\sec^{-1}\sqrt2\right)=1](https://tex.z-dn.net/?f=%5Ctan%5Cleft%28%5Csec%5E%7B-1%7D%5Csqrt2%5Cright%29%3D1)
. So
Answer:
968
Step-by-step explanation:
Current office length = 22
22 * 22 = 484
484 * 2 = 968
Answer:
404.98 m
Step-by-step explanation:
The angle of depression is 5°
The horizontal distance from the airplane to the atoll is 4629 meters.
We need to find the height of the plane.
If we consider a triangle. 4629 meters will be the base and angle is 5°. Let h is the height of the plane. Using trigonometry to find it :
![\tan\theta=\dfrac{x}{4629 }\\\\\tan(5)=\dfrac{x}{4629 }\\\\x=\tan(5)\times 4629 \\\\x=404.98\ m](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7Bx%7D%7B4629%20%7D%5C%5C%5C%5C%5Ctan%285%29%3D%5Cdfrac%7Bx%7D%7B4629%20%7D%5C%5C%5C%5Cx%3D%5Ctan%285%29%5Ctimes%204629%20%5C%5C%5C%5Cx%3D404.98%5C%20m)
So, the height of the plane is 404.98 m.
Answer:
mFG = 67r ( Where r is the radius of the circle)
∠ECF = 67°
Step-by-step explanation:
i) m FG
Join CG
∠GCF=67°
(As FG=ED and equal chords subtend equal angle at center)
Now The length of the minor arc is given by the formula
m arc FG =
![\frac {C}{2 \pi} \times 2 \pi r](https://tex.z-dn.net/?f=%5Cfrac%20%7BC%7D%7B2%20%5Cpi%7D%20%5Ctimes%202%20%5Cpi%20r)
∠C=67
m arc FG = ![\frac {67}{2 \pi} \times 2 \pi r](https://tex.z-dn.net/?f=%5Cfrac%20%7B67%7D%7B2%20%5Cpi%7D%20%5Ctimes%202%20%5Cpi%20r)
m arc FG = 67r
Where r is the radius of the circle.
2. ∠ECF = 67°
It is because of the rule which says that equal chords subtend equal angle at center
DE = EF
Hence ∠DCE = ∠ECF
Answer:
2 loaves of blueberry bread
Step-by-step explanation:
for 1 loaf of bread she uses 1 cup
for 2 loaves she will use 2 cupa