If y = xⁿ
∫y dx = xⁿ⁺¹ / (n + 1) + C Provided n ≠ -1.
y = √x
y = x^(0.5)
∫y dx = x^(0.5+1) / (0.5 + 1) = x^(1.5) / 1.5 = x^(1.5) / (3/2)
∫y dx = (2/3) x^(1.5) + C.
∫y dx = (2/3) x^(3/2) + C.
∫y dx = (2/3)√x³ + C
Answer: second option y = 2(x + 7/2)^2 + 1/2
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
Answer:
.14
Step-by-step explanation:
|√2 + 3 - 4|
|√2 - 1|
|1.14 - 1|
|.14|
.14
Tell me if I am wrong.
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