Answer:
x = 2 /3
Step-by-step explanation:
x^3 = 8/27
Take the cube root of each side
(x^3)^1/3 = (8/27)^1/3
We know that (a/b) ^c = a^c / b^c
x = (8 ) ^1/3 / (27)^1/3
x = 2 /3
Option A. y = 1.15 + 0.95x
1.15 is a fixed cost and 0.95 is a variable cost that has to be multiplied by the number of ounces of shrimp, x.
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:
2d≤24
Step-by-step explanation:
Total number of bottled juice bought = 24 bottles
Amount she drank each day = 2 bottles
To get the inequality to represent greatest number of days she can continue before she has to replenish her stock, we will say;
1 day = 2 bottles
d days = 24 bottles
Cross multiply
2 * d = 1 * 24
2d = 24
Since we want to know the greatest number of days she can continue before she has to replenish her stock, the <u>equal to </u>to sign will be replaced with<u> less than or equal to</u> sign as shown;
2d≤24
<em>This shows that the maximum number of days she can continue before replenishing is 12days. It cannot exceed</em>
Kelso / jones = 84.5/33.8 = 5/2 = 2 1/2
==> c