Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
Answer: 0.559192903....
Step-by-step explanation:
There are no options given, Please post the options in the comment.
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
Triangle DGH is isosceles with base angles at D and G. The external angle 134° at H is the sum of those two base angles, so we have ...
2(5x+7) = 134
5x +7 = 67 . . . . . divide by 2
5x = 60 . . . . . . . subtract 7
x = 12 . . . . . . . . divide by 5
Answer:
Both groups had prepared for the exam. Therefore music would not really affect performance. Reassurance is given in every exam so distractions are not blind generally and most certainly not in this context where the scores were compared afterwards.
Step-by-step explanation:
