Answer:
True
Step-by-step explanation:
A parallelogram is a quadrilateral with 4 sides and both pairs of opposite sides are equal.
Answer:
No, it is not a right triangle
Step-by-step explanation:
Let H = 14 cm
B = 3 cm
P = 13 cm
According to pythagoras theorem:
H^2 = P^2 + B^2
14^2 = 13^2 + 3^2
196 = 169 + 9
196 is not equal to 178
Hence, it is not a right triangle
Answer:
17
Step-by-step explanation:
it's sufficient to set x=7
g(7)=2×7+3=14+3=17
I suppose you mean to have the entire numerator under the square root?
![\displaystyle\int_2^4\frac{\sqrt{x^2-4}}{x^2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_2%5E4%5Cfrac%7B%5Csqrt%7Bx%5E2-4%7D%7D%7Bx%5E2%7D%5C%2C%5Cmathrm%20dx)
We can use a trigonometric substitution to start:
![x=2\sec t\implies\mathrm dx=2\sec t\tan t\,\mathrm dt](https://tex.z-dn.net/?f=x%3D2%5Csec%20t%5Cimplies%5Cmathrm%20dx%3D2%5Csec%20t%5Ctan%20t%5C%2C%5Cmathrm%20dt)
Then for
,
; for
,
. So the integral is equivalent to
![\displaystyle\int_0^{\pi/3}\frac{\sqrt{(2\sec t)^2-4}}{(2\sec t)^2}(2\sec t\tan t)\,\mathrm dt=\int_0^{\pi/3}\frac{\tan^2t}{\sec t}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B%5Cpi%2F3%7D%5Cfrac%7B%5Csqrt%7B%282%5Csec%20t%29%5E2-4%7D%7D%7B%282%5Csec%20t%29%5E2%7D%282%5Csec%20t%5Ctan%20t%29%5C%2C%5Cmathrm%20dt%3D%5Cint_0%5E%7B%5Cpi%2F3%7D%5Cfrac%7B%5Ctan%5E2t%7D%7B%5Csec%20t%7D%5C%2C%5Cmathrm%20dt)
We can write
![\dfrac{\tan^2t}{\sec t}=\dfrac{\frac{\sin^2t}{\cos^2t}}{\frac1{\cos t}}=\dfrac{\sin^2t}{\cos t}=\dfrac{1-\cos^2t}{\cos t}=\sec t-\cos t](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctan%5E2t%7D%7B%5Csec%20t%7D%3D%5Cdfrac%7B%5Cfrac%7B%5Csin%5E2t%7D%7B%5Ccos%5E2t%7D%7D%7B%5Cfrac1%7B%5Ccos%20t%7D%7D%3D%5Cdfrac%7B%5Csin%5E2t%7D%7B%5Ccos%20t%7D%3D%5Cdfrac%7B1-%5Ccos%5E2t%7D%7B%5Ccos%20t%7D%3D%5Csec%20t-%5Ccos%20t)
so the integral becomes
![\displaystyle\int_0^{\pi/3}(\sec t-\cos t)\,\mathrm dt=\boxed{\ln(2+\sqrt3)-\frac{\sqrt3}2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B%5Cpi%2F3%7D%28%5Csec%20t-%5Ccos%20t%29%5C%2C%5Cmathrm%20dt%3D%5Cboxed%7B%5Cln%282%2B%5Csqrt3%29-%5Cfrac%7B%5Csqrt3%7D2%7D)