Answer:
There is a vertical change of 3 units down.
Hi there!
If Andrea bought 12 bagels and 2/3 were multigrain we can determine what the total amount of bagels that are multigrain by finding a common denominator. We can do this by multiplying 2/3 * 4 which gets us the common denominator we need.
2/3 * 4 <--- Equation
8/12 <--- Simplified from step 1.
Therefore 8 out of the 12 bagels Andrea bought were multigrain!
By the chain rule,
which follows from 
.
is then a function of 
; denote this function by 
. Then by the product rule,
![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dt}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm df}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%2B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20df%7D%7B%5Cmathrm%20dx%7D)
and by the chain rule,
so that
Then the ODE in terms of 
is
The characteristic equation
has two roots at 
and 
, so the characteristic solution is
Solving in terms of gives
Answer:
x=11
Step-by-step explanation:
3x+28+5x+52+12=180
8x+92=180
-92 on both sides
8x=88
/8 on both sides
x=11
The tank WILL overflow.
60*30*40= 72000cm^3
<em>The max volume the fish tank can hold: 72000cm^3</em>
amount of L * 1000= cm^3
70L * 1000= 70000cm^3
<em>There is already 70000cm^3 of water in the tank</em>
70000cm^3 + 3000cm^3 = 73000cm^3
The tank can only hold 72000cm^3 and the water and rocks are 73000cm^3, so the tank will overflow.
