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.
Find the square numbers and see which ones 54 lies between
1, 4, 9, 16, 25, 36, 49, 64.
It lies between the two square numbers 49 and 64.
But you want the square root.
So find the square root of 49 and 64.
7 and 8.
So the square root of 54 is between 7 and 8.
Hope this helps.
To find the surface area of a triangular prism , you must follow all steps necessary in order to achieve.
Step-by-step explanation:
3x(x2 + 2x – 6) + 4(x2
– 6x + 2)
Answer:
8/3
Step-by-step explanation:
keep change flip
-3 1/3 (turn the divide into multiplication) and flip the fraction- 1/2 -2/1
-4/3 times -2/1