Answer:
63%
Step-by-step explanation:
12/19=0.63157895
0.63157895*100=63.1578947
Answer:
32.66 units
Step-by-step explanation:
We are given that
Point A=(-2,-4) and point B=(1,20)
Differentiate w.r. t x
We know that length of curve
We have a=-2 and b=1
Using the formula
Length of curve=
Using substitution method
Substitute t=12x+14
Differentiate w.r t. x
Length of curve=
We know that
By using the formula
Length of curve=![s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7Bt%7D%7B2%7D%5Csqrt%7B1%2Bt%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%28t%2B%5Csqrt%7B1%2Bt%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=![s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7B12x%2B14%7D%7B2%7D%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%2812x%2B14%2B%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=
Length of curve=
Length of curve=
We know that
2π/3 radians-------> convert to degrees-----> 2*180/3---> 120°
120°=90°+30°
Part a) Find <span>sin(2π/3)
</span>sin(2π/3)=sin (90°+30°)
we know that
sin (A+B)=sin A*cos B+cos A*sin B
so
sin (90°+30°)=sin 90*cos 30+cos 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
sin (90°+30°)=1*√3/2+0*1/2-----> √3/2
the answer part a) is
sin(2π/3)=√3/2
Part b) Find cos (2π/3)
cos (2π/3)=cos (90°+30°)
we know that
cos (A+B)=cos A*cos B-sin A*sin B
so
cos (90°+30°)=cos 90*cos 30-sin 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
cos (90°+30°)=0*√3/2-1*1/2----> -1/2
the answer part b) is
cos (2π/3)=-1/2
So, if we look at the number pattern, we can see the numbers go up by 4.
The rule is Add 4.
So, to find the next two terms, we would add 4 to the last number shown, which is 15.
15 + 4 = 19
19 + 4 = 23
So, the next two terms are →19← and →23←.
Glad I could help, and good luck!
AnonymousGiantsFan
