Answer:
Step-by-step explanation:
We have to take the derivatives for both functions and replace in the differential equation. Hence
for y=e^{-5x}:

for y=e^{6x}:

Now we replace in the differential equation y'' − y' − 30y = 0
for y=e^{-5x}:

for y=e^{6x}:

Now, to know if both function are linearly independent we calculate the Wronskian


I hope this is useful for you
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The millers will travel 240 miles in six hours.
Answer:
$900
Step-by-step explanation:
<u>Let the fixed salary be x and the commission be y, then as per given, the earnings:</u>
- 10000y + x = 1350
- 15000y + x = 1575
<u>Subtract the first equation from the second:</u>
- 15000y - 10000y = 1575 -1350
- 5000y = 225
then
- 10000y =2*5000y = 2*225 = 450
<u>Using the first equation:</u>
<u>So the fixed salary is</u> $900
Answer:
The salesperson called 200 people this month.
Step-by-step explanation:
Let us denote the total people that the salesperson called by a variable "x".
Then,
The ratio of successful signups(success ratio) is given as=0.625
Then total no. of successful signups is the product of the success rate and the total no. of signups ,
i.e. Total successful signups = 
According to the data given in the question,
The total no. of successful signups this month =125
or , 
or, 
∴x= 200
So, the salesperson called 200 people, out of which only 125 signed up.
Answer:
3·(x - 14) + 1 = - 4·x + 5
3·x - 42 + 1 = - 4·x + 5
3·x - 41 = - 4·x + 5
7·x - 41 = 5
7·x = 46
x = 46/7