Answer:
The expression is 10t = 65
Step-by-step explanation:
At the point where the local train and the express train meet, both trains would have travelled an equal distance.
A local train leaves the station in Springfield traveling toward New York City at a constant rate of 55 mph.
Let t represent the time it spent in travelling a given distance.
Distance = speed × time
Therefore,
Distance travelled by the local train is 55 × t = 55t
The express train headed for New York City on the same route leaves the station 1 hour later. The rate of the express train is 65 mph. It means that total time spent travelling the same distance as the local train is t - 1
Therefore, distance travelled is
65(t - 1)
Since the distance travelled is the same, therefore,
55t = 65t - 65
65t - 55t = 65
10t = 65
Answer:
Euler's method is a numerical method used in calculus to approximate a particular solution of a differential equation. As a numerical method, we have to apply the same procedure many times, until get the desired result.
In first place, we need to know all the values the problem is giving:
- The step size is 0.2; h = 0.2. This step size is a periodical increase of the x-variable, which will allow us to calculate each y-value to each x.
- The problem is asking the solution y(1), which means that we have to find the y-value assigned for x = 1, through the numerical method.
- The initial condition is y(0) = 9. In other words,
.
So, if the initial x-value is 0, and the step size is 0.2, the following x-value would be: 
; then 
; 
; and so on.
Now, we have to apply the formula to find each y-value until get the match of 
, because the problem asks the solution y(1).
According to the Euler's method:
Where 
, and 
; 
.
Replacing all values we calculate the y-value assigned to 
:
.
Now, 
, 
. We repeat the process with the new values:
Then, we repeat the same process until get the y-value for 
, which is 
, round to four decimal places.
Therefore, 
.
Answer:
To solve an exponential equation, take the log of both sides, and solve for the variable.
Step-by-step explanation:
Example 1: Solve for x in the equation tex2html_wrap_inline119 .
Solution:
Step 1: Take the natural log of both sides:
displaymath121
Step 2: Simplify the left side of the above equation using Logarithmic Rule 3:
displaymath123
Step 3: Simplify the left side of the above equation: Since Ln(e)=1, the equation reads
displaymath127
Ln(80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln(80)..
Check: Check your answer in the original equation.
displaymath131
Answer:
Step-by-step explanation:
2n² + 9n - 35 = (2n-5)(n+7)
n = 2.5, -7
