For each, you'll use the slope formula
m = (y2-y1)/(x2-x1)
For function f, you'll use the two points (1,6) and (2,12) since x ranges from x = 1 to x = 2 for function f
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (12-6)/(2-1)
m = 6/1
m = 6
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For function g, you'll use (2,4) and (3,20)
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (20-4)/(3-2)
m = 16/1
m = 16
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For function h, you'll use (0,-6) and (2,-18). The y coordinates can be found by plugging in x = 0 and x = 2 respectively into h(x)
The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (-18-(-6))/(2-0)
m = (-18+6)/(2-0)
m = (-12)/(2)
m = -6
-------------------------------------------
The order from left to right is: h, f, g
Answer:
44 swimmers
Step-by-step explanation:
<h2>
Answer: 0.85 radians</h2>
Step-by-step explanation:
We have the following trigonometric expression:
The result of this calculation is:
where the angle is in degrees
If
then:
Therefore the answer is 0.85 radians
We can parameterize this part of a cone by
![\mathbf s(u,v)=\left\langle u\cos v,u\sin v,\dfrac hau\right\rangle](https://tex.z-dn.net/?f=%5Cmathbf%20s%28u%2Cv%29%3D%5Cleft%5Clangle%20u%5Ccos%20v%2Cu%5Csin%20v%2C%5Cdfrac%20hau%5Cright%5Crangle)
with
![0\le u\le a](https://tex.z-dn.net/?f=0%5Cle%20u%5Cle%20a)
and
![0\le v\le2\pi](https://tex.z-dn.net/?f=0%5Cle%20v%5Cle2%5Cpi)
. Then
![\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=\sqrt{1+\dfrac{h^2}{a^2}}u\,\mathrm du\,\mathrm dv](https://tex.z-dn.net/?f=%5Cmathrm%20dS%3D%5C%7C%5Cmathbf%20s_u%5Ctimes%5Cmathbf%20s_v%5C%7C%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv%3D%5Csqrt%7B1%2B%5Cdfrac%7Bh%5E2%7D%7Ba%5E2%7D%7Du%5C%2C%5Cmathrm%20du%5C%2C%5Cmathrm%20dv)
The area of this surface (call it
![\mathcal S](https://tex.z-dn.net/?f=%5Cmathcal%20S)
) is then