8 is the first.
Reasoning:
So we know what the Fibonacci sequence is. To get the next number, you add the number behind it, by the number behind that.
For example, these are the first 5 Fibonacci numbers.
1, 1, 2, 3, 5.
1 + 0 = 1.
So 1 is the second number.
1 + 1 is 2.
So 2 is the third number.
2 + 1 = 3.
So 3 is the fourth number.
3 + 2 = 5.
So 5 is the fourth number.
The problem:
If the fifth term is 49, and the fourth term is 30. We can subtract 49 by 30, to find the third number, and so on.
49 - 30 = 19.
So 19 is the third number.
30 - 19 = 11.
11 is the second.
19 - 11 = 8.
8 is the first.
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.
The time of takeoff of this hovercraft would be 0 seconds, as if you were starting a timer. So, if you plug in 0 for x (unit for seconds) in your equation, it will look like this:
h(0) = -3(0 - 3)² + 108
Parenthesis first
h(0) = -3(-3)² + 108
Exponents next
h(0) = -3(9) + 108
Multiplication
h(0) = -27 + 108
Combine like terms
h(0) = 81: The height of the hovercraft at the time of takeoff is 81 meters!
Hope this helps :)
Answer:
41 units cubic
Step-by-step explanation:
