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:
1. 42
2. 6
3. 18
4. 0
5. - 2
Step-by-step explanation:
Use BIDMAS
Answer: 8 batches
Step-by-step explanation:
To get the number of batches she made, we can just use proportion to solve it. But first, we need to convert 5 1/3 to improper fraction
5 1/3 = 16/3
Then we can now use the proportion to solve
2/3 cups = 1 batch
16/3 cups = x (note:5 1/3=16/3)
cross multiply
2/3 × x = 16 /3
2x/ 3 = 16/3
we need to make x the subject of the formula, to do that we will multiply each side of the equation by 3/2
2/3 × 3/2 x = 16/3 × 3/2
6x /6 = 48 / 6
x = 8
Therefore she made 8 batches of cookies.
To figure this out, we need to use fractional proportions.
Currently, we have $120, the amount earned, and 2 days, the current rate.
Our fraction for this is: 120 / 2 = x / 6, x being the amount earned in 6 days.
Let's use a little technique to help us answer faster.
With our current money earned, 120, and our current days, 2, we can divide 120 by 2 to find out how many we earned in 1 day.
120 / 2 = 60.
We earned $60 per day.
With this formula, 60d, d being the amount of days, we can solve quicker.
We are solving for 6 days, so multiply $60 by 6 days.
60 x 6 = 360
Your proportion is :
120/2 : 360/6
I hope this helps!
Answer:
15 percent of 90 hours = 13.5 hours
What is 15% of 90?
Y is 15% of 90
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 15% * 90
Converting percent to decimal:
p = 15%/100 = 0.15
Y = 0.15 * 90
Y = 13.5
