<h2>Steps:</h2>
So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:
y = x² + bx + c
Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:
Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:
Now that the c variable has been eliminated we can solve for b. For this, divide both sides by -8 and your first part of your answer is b = 6.
Now that we know the value of b, plug it into either equation to solve for c:
<h2>Answer:</h2>
<u>Putting it together, your final answer is x² + 6x - 7 = 0.</u>
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
For more information about differential equation, visit
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Answer:
- 3/4
Step-by-step explanation:
m = difference of y / difference of x = (3 - (-3)) / (-5 -3) = 6 / -8 = - 3 / 4
The fraction that has been given illustrates that the person who ran further is Jane.
<h3>How to solve fraction</h3>
Your information isn't complete. Therefore, an overview of the fraction will given.
Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/4 of a mile. In order to know who ran more, you can convert the fraction to percentage.
This will be:
Lisa = 1/2 × 100 = 50%
Jane = 3/4 × 100 = 75%
Therefore, Jane ran more.
Learn more about fractions on:
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Area of Parallelogram= base * height
A= (12 3/4)(2 1/2)
A= (51/4)(5/2)
A= 255/8
A= 31 7/8
OR
A= (12.75)(2.5)
A= 31.875
Hope this helps! :)
