Formula for curvature for a well behaved curve y=f(x) is
K(x)= ![\frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%7C%7By%7D%27%27%7C%7D%7B%5B1%2B%7By%7D%27%5E2%5D%5E%5Cfrac%7B3%7D%7B2%7D%7D)
The given curve is y=7
k(x)=![\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B7e%5E%7Bx%7D%7D%7B%5B%7B1%2B%287e%5E%7Bx%7D%29%5E2%7D%5D%5E%5Cfrac%7B3%7D%7B2%7D%7D)
![{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}](https://tex.z-dn.net/?f=%7Bk%28x%29%7D%27%3D%5Cfrac%7B7%28e%5Ex%29%281%2B49e%5E%7B2x%7D%29%2849e%5E%7B2x%7D-%5Cfrac%7B1%7D%7B2%7D%29%7D%7B%5B1%2B49e%5E%7B2x%7D%5D%5E%7B3%7D%7D)
For Maxima or Minima
→
[not possible ∵there exists no value of x satisfying these equation]
→
Solving this we get
x= 
As you will evaluate 
<0 at x=
So this is the point of Maxima. we get y=7×1/√98=1/√2
(x,y)=[,1/√2]
k(x)=![\lim_{x\to\infty } \frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%5Cinfty%20%7D%20%5Cfrac%7B7e%5E%7Bx%7D%7D%7B%5B%7B1%2B%287e%5E%7Bx%7D%29%5E2%7D%5D%5E%5Cfrac%7B3%7D%7B2%7D%7D)
k(x)=
k(x)=0
Answer:
Step-by-step explanation:
3x3
6 feet:10 hours
multiply by 1.5 on both sides
9 feet:15 hours
answer: 9 ft
6) x= 2, angle = 90 degrees obviously
7) Im not sure on this one
8) x = 5
9) x = 1
Answer:
Y = 12
Step-by-step explanation:
x + 1/3y = 4
Multiply both sides of the equation by 3.
3 ⋅ 1
3 ⋅ y = 3 ⋅ 4
Simplify both sides of the equation:
1. Simplify both sides of the equation.
2. Multiply 3 by 4
How to simplify:
Cancel the common factor of 3
Rewrite the expression.
Multiply by 1
y = 3 ⋅ 4
Multiply 3 by 4
(12)
