Answer:
x = 4
Step-by-step explanation:
After you simplify the left side by eliminating parentheses and collecting terms, you have a 2-step linear equation.
-3(4x +3) +4(6x +1) = 43 . . . . . . given
-12x -9 +24x +4 = 43 . . . . . eliminate parentheses
12x-5 = 43 . . . . . . . . . . . collect terms (now a 2-step equation)
12x = 48 . . . . . . . . . . step 1, add the opposite of the unwanted constant
x = 4 . . . . . . . . . . . step 2, divide by the coefficient of x
The solution is x = 4.
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<em>Check</em>
-3(4·4 +3) +4(6·4 +1) = 43 . . . . substitute for x
-3(16 +3) +4(24 +1) = 43
-3(19) +4(25) = 43
-57 +100 = 43 . . . . . true
Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0
=> For general solution of equation,
Solve D4 - 5D3 + 5D2 + 5D - 6 = 0
=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0
=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0
=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)
Now
D2 - 1 = (D - 1)(D + 1) and
Factors of D2 - 5D + 6
D2 - 5D + 6 = D2 - 2D - 3D + 6
= D(D - 2) - 3(D - 2)
= (D - 3)(D - 2)
Therefore, equation (1) implies
(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0
=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3
=> General solution of differential equation is,<span>
=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
Hope it helps
</span>
Answer:
probably A
Step-by-step explanation:
Brainliest pls
Answer:
A
Step-by-step explanation:
Start with the 3.
You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing. The members of the sequence are going up.
n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.
The answer is an = a1 + (n-1)*d
d = 3
a1 = - 7
So let's try the formula out.
a4 = -7 + (4 - 1)*3
a4 = -7 + 3 * 3
a4 = -7 + 9
a4 = 2
Is 2 the 4th term in the series? Yes it is!
