Number 16- 216
number 17- 180
number 18- 252
Answer:
it is the 3 one
Step-by-step explanation:
Answer: c = 1.05p
Step-by-step explanation:
Price of the hat = p
Percentage increase in the price of the hat = 5%
The equation to calculate the increase of the total cost, c, of the hat will be:
c = p + (5% × p)
= p + (5/100 × p)
= p + (0.05 × p)
= p + 0.05p
c = 1.05p
![\displaystyle\int_{x=1}^{x=14}\frac{1-\cos4x}{4x-\sin4x}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7Bx%3D1%7D%5E%7Bx%3D14%7D%5Cfrac%7B1-%5Ccos4x%7D%7B4x-%5Csin4x%7D%5C%2C%5Cmathrm%20dx)
First, replace
![y=4x](https://tex.z-dn.net/?f=y%3D4x)
and
![\mathrm du=4\,\mathrm dx](https://tex.z-dn.net/?f=%5Cmathrm%20du%3D4%5C%2C%5Cmathrm%20dx)
. Then you have
![\displaystyle\frac14\int_{y=4}^{y=56}\frac{1-\cos y}{y-\sin y}\,\mathrm dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac14%5Cint_%7By%3D4%7D%5E%7By%3D56%7D%5Cfrac%7B1-%5Ccos%20y%7D%7By-%5Csin%20y%7D%5C%2C%5Cmathrm%20dy)
If we take
![z=y-\sin y](https://tex.z-dn.net/?f=z%3Dy-%5Csin%20y)
, then immediately we see a differential in the numerator in the form of
![\mathrm dz=(1-\cos y)\,\mathrm dy](https://tex.z-dn.net/?f=%5Cmathrm%20dz%3D%281-%5Ccos%20y%29%5C%2C%5Cmathrm%20dy)
. So the integral becomes
![\displaystyle\frac14\int_{z=4-\sin4}^{z=56-\sin56}\frac{\mathrm dz}z](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac14%5Cint_%7Bz%3D4-%5Csin4%7D%5E%7Bz%3D56-%5Csin56%7D%5Cfrac%7B%5Cmathrm%20dz%7Dz)
and evaluates to
![\dfrac14\ln|z|\bigg|_{z=4-\sin4}^{z=56-\sin56}=\dfrac14\left(\ln|56-\sin56|-\ln|4-\sin4|\right)=\dfrac14\ln\left|\dfrac{56-\sin56}{4-\sin4}\right|](https://tex.z-dn.net/?f=%5Cdfrac14%5Cln%7Cz%7C%5Cbigg%7C_%7Bz%3D4-%5Csin4%7D%5E%7Bz%3D56-%5Csin56%7D%3D%5Cdfrac14%5Cleft%28%5Cln%7C56-%5Csin56%7C-%5Cln%7C4-%5Csin4%7C%5Cright%29%3D%5Cdfrac14%5Cln%5Cleft%7C%5Cdfrac%7B56-%5Csin56%7D%7B4-%5Csin4%7D%5Cright%7C)
making (A) the correct answer.
Answer:
234
Step-by-step explanation:
i honestly don't know but i just added them all up together