Answer:
Part a) 
Part b) 
Step-by-step explanation:
Part a) Write an equation for T (d)
Let
d ----> the number of days
T ---> the time in minutes of the treadmill
we know that
The linear equation in slope intercept form is equal to

where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem we have
The slope or unit rate is

The y-intercept or initial value is

substitute

Part b) Find T (6), the minutes he will spend on the treadmill on day 6
For d=6
substitute in the equation and solve for T


Discriminant = b^2 - 4ac
a = 4
b = 16
c = 16
16^2 - 4(4 x 16)
256 - (4x64)
256 - 256 = 0
Therefore it only has one root
The formula to find the Height of a triangle when you have the Area and the base is H = 2 * A/b
if the Area is 36.8 then divide it by 4.6. You get 8. put 36.8 in calculator first, then 4.6 = 8
2 x 8 = 16...so the answer should be 16 inches.
2 is in the formula to multiply to the number you get after dividing the base into the Area.
16 Answer
1. Let a and b be coefficients such that

Combining the fractions on the right gives



so that

2. a. The given ODE is separable as

Using the result of part (1), integrating both sides gives

Given that y = 1 when x = 1, we find

so the particular solution to the ODE is

We can solve this explicitly for y :


![\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|](https://tex.z-dn.net/?f=%5Cln%7Cy%7C%20%3D%20%5Cln%5Cleft%7C%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%5Cright%7C)
![\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%7D)
2. b. When x = 9, we get
![y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B45%7D%7B21%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B15%7D7%7D%20%5Capprox%20%5Cboxed%7B1.29%7D)
(1/8) / 6 =
1/8 * 1/6 =
1/48 of a lb per fish tank <==