Yes it is greater. If you look at the first two digets in the front, it is 37 compared to 3.7 . 37 is obviously greater than 3.7 so 37.508 is greater than 3.758
Answer:
slopes are the same
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 6 ← is in slope- intercept form
with slope m = - 5
Calculate the slope between the 2 points using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, - 16)
m =
=
= - 5
The slope of the line and the slope between the 2 points are the same
Answer:
The difference between the maximum and minimum is
![\left(\displaystyle\frac{5}{63}\right)^2\left(\displaystyle\frac{625}{63}\right)^{250}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdisplaystyle%5Cfrac%7B5%7D%7B63%7D%5Cright%29%5E2%5Cleft%28%5Cdisplaystyle%5Cfrac%7B625%7D%7B63%7D%5Cright%29%5E%7B250%7D)
Step-by-step explanation:
Since p = 10-q, we can replace p in the expression and we get a single-variable function
![f(q)=(10-q)^2q^{250}](https://tex.z-dn.net/?f=f%28q%29%3D%2810-q%29%5E2q%5E%7B250%7D)
Taking the derivative with respect to q and using the rule for the derivative of a product
![f'(q)=-2(10-q)q^{250}+250(10-q)^2q^{249}](https://tex.z-dn.net/?f=f%27%28q%29%3D-2%2810-q%29q%5E%7B250%7D%2B250%2810-q%29%5E2q%5E%7B249%7D)
Critical point (where f'(q)=0)
Assuming q≠ 0 and q≠ 10
![f'(q)=0\Rightarrow -2(10-q)q^{250}+250(10-q)^2q^{249}=0\Rightarrow\\\\\Rightarrow 250(10-q)=2q\Rightarrow q=\displaystyle\frac{625}{63}](https://tex.z-dn.net/?f=f%27%28q%29%3D0%5CRightarrow%20-2%2810-q%29q%5E%7B250%7D%2B250%2810-q%29%5E2q%5E%7B249%7D%3D0%5CRightarrow%5C%5C%5C%5C%5CRightarrow%20250%2810-q%29%3D2q%5CRightarrow%20q%3D%5Cdisplaystyle%5Cfrac%7B625%7D%7B63%7D)
To check this is maximum, we take the second derivative
![f''(q)=63252q^{250}-1255000q^{249}+6225000q^{248}](https://tex.z-dn.net/?f=f%27%27%28q%29%3D63252q%5E%7B250%7D-1255000q%5E%7B249%7D%2B6225000q%5E%7B248%7D)
and
f''(625/63) < 0
so q=625/63 is a maximum. For this value of q we get p=5/63
The maximum value of
![p^2q^{250}](https://tex.z-dn.net/?f=p%5E2q%5E%7B250%7D)
is
![\left(\displaystyle\frac{5}{63}\right)^2\left(\displaystyle\frac{625}{63}\right)^{250}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdisplaystyle%5Cfrac%7B5%7D%7B63%7D%5Cright%29%5E2%5Cleft%28%5Cdisplaystyle%5Cfrac%7B625%7D%7B63%7D%5Cright%29%5E%7B250%7D)
The minimum is 0, which is obtained when q=0 and p=10 or q=10 and p=0
The difference between the maximum and minimum is then
![\left(\displaystyle\frac{5}{63}\right)^2\left(\displaystyle\frac{625}{63}\right)^{250}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdisplaystyle%5Cfrac%7B5%7D%7B63%7D%5Cright%29%5E2%5Cleft%28%5Cdisplaystyle%5Cfrac%7B625%7D%7B63%7D%5Cright%29%5E%7B250%7D)
To find (x-9)/3=2, we do
(x-9)/3=2
(x-9)/3×3=2×3
x-9=6
x-9+9=6+9
x=15
So, x is 15
Answer:
Step-by-step explanation:
Pie 3.14