4 because doubled it equals eight, add four it equals twelve, subtract four it equals eight, subtract three and it equals five.
It looks like
![y(x)=\displaystyle\int_{\cos x}^{\sin x}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cint_%7B%5Ccos%20x%7D%5E%7B%5Csin%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
(If the limits are in the wrong order, just multiply the result by -1)
Split the integral at an arbitrary value between
![\cos x](https://tex.z-dn.net/?f=%5Ccos%20x)
and
![\sin x](https://tex.z-dn.net/?f=%5Csin%20x)
, and write
![y(x)](https://tex.z-dn.net/?f=y%28x%29)
as
![y(x)=\displaystyle\left\{\int_{\cos x}^c+\int_c^{\sin x}\right\}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cleft%5C%7B%5Cint_%7B%5Ccos%20x%7D%5Ec%2B%5Cint_c%5E%7B%5Csin%20x%7D%5Cright%5C%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
![y(x)=\displaystyle\int_c^{\sin x}(3+v^5)^8\,\mathrm dv-\int_c^{\cos x}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cint_c%5E%7B%5Csin%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv-%5Cint_c%5E%7B%5Ccos%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
Then by the FTC,
![\dfrac{\mathrm dy}{\mathrm dx}=(3+\sin^5x)^8\cdot\dfrac{\mathrm d\sin x}{\mathrm dx}-(3+\cos^5x)^8\cdot\dfrac{\mathrm d\cos x}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%283%2B%5Csin%5E5x%29%5E8%5Ccdot%5Cdfrac%7B%5Cmathrm%20d%5Csin%20x%7D%7B%5Cmathrm%20dx%7D-%283%2B%5Ccos%5E5x%29%5E8%5Ccdot%5Cdfrac%7B%5Cmathrm%20d%5Ccos%20x%7D%7B%5Cmathrm%20dx%7D)
<h3>
Answer: 5.5 which is choice B</h3>
Have a look at the diagram I posted below. I marked on your image to add in another angle. This angle is also 20 degrees because of congruent alternate interior angles (horizontal lines are parallel). This angle I add in is the reference angle of the triangle
opposite the reference angle is the vertical side x
adjacent to the reference angle is the horizontal side 15
We'll use the tangent rule. Make sure your calculator is in degree mode.
tan(angle) = opposite/adjacent
tan(20) = x/15
15*tan(20) = x <<-- multiply both sides by 15
x = 15*tan(20)
x = 5.45955 <<--- use calculator; this is approximate
x = 5.5 <<--- round to one decimal place
Answer:
4*5+6 = 26
6*5-2= 28
Nancy has the shortest ribbon