Answer:
f'(x) = ![-\frac{9}{x^2}](https://tex.z-dn.net/?f=-%5Cfrac%7B9%7D%7Bx%5E2%7D)
Step-by-step explanation:
i) f(x) = 9 / x
ii) f'(x) = ![$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}](https://tex.z-dn.net/?f=%24%5Clim_%7Bh%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29%20-%20f%28x%29%7D%7Bh%7D%20%24%20%20%5Chspace%7B0.2cm%7D)
![= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$](https://tex.z-dn.net/?f=%3D%20%24%5Clim_%7Bh%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B9%7D%7Bx%2Bh%7D%20%20-%20%5Cfrac%7B9%7D%7Bx%7D%20%7D%7Bh%7D%20%20%3D%20%20%5Chspace%7B0.1cm%7D%20%24%5Clim_%7Bh%5Cto%200%7D%20%5Cfrac%7B9x%20-%209%28x%2Bh%29%7D%7Bhx%28x%2Bh%29%7D%20%24%20%5Chspace%7B0.1cm%7D%20%3D%20%20%5Chspace%7B0.1cm%7D%24%5Clim_%7Bh%5Cto%200%7D%20%5Cfrac%7B-9h%7D%7Bhx%28x%2Bh%29%7D%20%20%3D%20%20%24%5Clim_%7Bh%5Cto%200%7D%20%5Cfrac%7B-h%7D%7Bx%28x%2Bh%29%7D%20%3D%20%5Cfrac%7B-9%7D%7Bx%5E2%7D%24)
Answer:
The constant would be A) 9
Step-by-step explanation:
The Constant in a math expression is One number that is on its own or without a varialbe
To evaluate the probability that the lifespan will be between 1440 and 1465 hours will be given by:
P(1440<x<1465)
using the z-score formula we obtain:
z=(x-μ)/σ
where:
μ=1450
σ=8.5
hence
when x=1440
z=(1440-1450)/8.5
z=-1.18
P(z<-1.18)=0.1190
when x=1465
z=(1465-1450)/8.5
z=1.77
P(z<1.77)=0.9625
hence:
P(1440<x<1465)
=0.9625-0.1180
=0.8445
Answer:
6.3 yards
Step-by-step explanation:
mathematically, to get the circumference of the circle, we will have to use the formula for the circumference of a circle
we have this as;
C = 2 * pi * r
r is 1 yard
c = 2 * pi * 1 = 2pi yards = 6.3 yards