The ODE is linear:


Multiplying both sides by
gives

Notice that the left side can be condensed as the derivative of a product:

Integrating both sides with respect to
yields


Since
,

so that

Answer:

Step-by-step explanation:
we are given that A robot is expected to filter pollution out of at least 350 liters of air and water.
Also It filters air at the rate of 50 liters per minute, and it filters water at the rate of 20 liters per minute.
The inequality for number of minutes the robot should filter air (A) and water (W) to meet this expectations can be writte as follows:

Hence the required inequality has been formulated.
Answer:
<h3>The standard error of the mean is <u>15</u></h3>
Step-by-step explanation:
Given that a simple random sample of 64 observations was taken from a large population.
Hence it can be written as n=64
The population standard deviation is 120.
It can be written as 
The sample mean was determined to be 320.
It can be written as 
<h3>To find the standard error of the mean :</h3>
The formula for the standard error of the mean is given by

Now substitute the values in the formula we get




<h3>∴ The standard error of the mean is 15</h3>
Answer:
abc = - 126
Step-by-step explanation:
(2x + 3)(3x - 1) ← expand product using FOIL
= 6x² + 7x - 3 ← in standard form
with a = 6, b = 7, c = - 3
Then
abc = 6 × 7 × (- 3) = - 126
Answer:
14x+49z+7
Step-by-step explanation:
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