The numbers for the first eight beads that r white is 2 white beads. The rule of the pattern is 1,3,1,3,1,3 (its an A,B,A,B pattern) the rule is a b pattern
There would be 203,759 total registered doctors that year.
M= (-2 - -10)/(-7 - 1) = -1
y= -1x + b
y= -x+ b
b = y+x
= -10+1
-9
y = -x - 9
a. By the fundamental theorem of calculus, the velocity function is
![v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du](https://tex.z-dn.net/?f=v%28t%29%3Dv%280%29%2B%5Cdisplaystyle%5Cint_0%5Eta%28u%29%5C%2C%5Cmathrm%20du)
The particle starts at rest, so
, and we have
![v(t)=\displaystyle\int_0^t6\cos u\,\mathrm du=6\sin u\bigg|_0^t=6\sin t](https://tex.z-dn.net/?f=v%28t%29%3D%5Cdisplaystyle%5Cint_0%5Et6%5Ccos%20u%5C%2C%5Cmathrm%20du%3D6%5Csin%20u%5Cbigg%7C_0%5Et%3D6%5Csin%20t)
Then the position function is
![x(t)=\displaystyle x(0)+\int_0^tv(u)\,\mathrm du](https://tex.z-dn.net/?f=x%28t%29%3D%5Cdisplaystyle%20x%280%29%2B%5Cint_0%5Etv%28u%29%5C%2C%5Cmathrm%20du)
with
, so
![x(t)=6+\displaystyle\int_0^t6\sin u\,\mathrm du=6-6\cos u\bigg|_0^t=12-6\cos t](https://tex.z-dn.net/?f=x%28t%29%3D6%2B%5Cdisplaystyle%5Cint_0%5Et6%5Csin%20u%5C%2C%5Cmathrm%20du%3D6-6%5Ccos%20u%5Cbigg%7C_0%5Et%3D12-6%5Ccos%20t)
b. The particle is at rest whenever
; this happens for
![6\sin t=0\implies \sin t=0\implies t=n\pi](https://tex.z-dn.net/?f=6%5Csin%20t%3D0%5Cimplies%20%5Csin%20t%3D0%5Cimplies%20t%3Dn%5Cpi)
where
is any integer.
Answer:
ln 15 must be greater (larger than) if log 15 is common.
Step-by-step explanation:
log 15 [assumed to be a common logarithm]
‹–› 15 = 10 ^ log(15)
ln 15 [natural log which has a base of e] ‹–› 15 = e ^ ln(15).
10 > e
e ≈ 2.7218.
e is approximately 3 rounded to the nearest whole number.
Logically you would need to raise 3 to a greater power for 3ⁿ = 15. Than 10ⁿ = 15.
For example 3² < 10² → 3³ < 10³ → 3⁴ < 10⁴ → ... Thus 3ⁿ < 10ⁿ for n > 0.