The value of h is h = -1.5
Step-by-step explanation:
The quadratic equation is represented by a parabola, the vertex form of the equation is y = a(x - h)² + k, where
- (h , k) are the coordinates of its vertex point
- a is the coefficient of x²
∵ The graph is a parabola opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h , k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5
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Answer:
40
Step-by-step explanation:
5 people in the room have 5*40 = 200 years altogether
a new person is X years old.
Now 6 people have (200 + x) years altogether.
Mean age of 6 people is (200+x)/6. and it is also = 40.
So,
(200+x)/6 = 40
200 + x = 240
x = 40
The probability of the arrow will land on a section labeled with the number greater than 3 is 
Step-by-step explanation:
Given,
The spinner is divided into 8 sections say named 1, 2, 3, 4, 5, 6, 7, 8
To find the P : probability of the arrow will land on a section labeled with the number greater than 3
Formula
<u>P = (the number of possible outcomes) ÷ ( the number of total result)</u>
We will count the probability when the arrow land on either 4 or 5 or 6 or 7 or 8 = 5 times
Total number of result = 8
Hence the probability =
Answer:
1. y' = 3x² / 4y²
2. y'' = 3x/8y⁵[(4y³ – 3x³)]
Step-by-step explanation:
From the question given above, the following data were obtained:
3x³ – 4y³ = 4
y' =?
y'' =?
1. Determination of y'
To obtain y', we simply defferentiate the expression ones. This can be obtained as follow:
3x³ – 4y³ = 4
Differentiate
9x² – 12y²dy/dx = 0
Rearrange
12y²dy/dx = 9x²
Divide both side by 12y²
dy/dx = 9x² / 12y²
dy/dx = 3x² / 4y²
y' = 3x² / 4y²
2. Determination of y''
To obtain y'', we simply defferentiate above expression i.e y' = 3x² / 4y². This can be obtained as follow:
3x² / 4y²
Let:
u = 3x²
v = 4y²
Find u' and v'
u' = 6x
v' = 8ydy/dx
Applying quotient rule
y'' = [vu' – uv'] / v²
y'' = [4y²(6x) – 3x²(8ydy/dx)] / (4y²)²
y'' = [24xy² – 24x²ydy/dx] / 16y⁴
Recall:
dy/dx = 3x² / 4y²
y'' = [24xy² – 24x²y (3x² / 4y² )] / 16y⁴
y'' = [24xy² – 18x⁴/y] / 16y⁴
y'' = 1/16y⁴[24xy² – 18x⁴/y]
y'' = 1/16y⁴[(24xy³ – 18x⁴)/y]
y'' = 1/16y⁵[(24xy³ – 18x⁴)]
y'' = 6x/16y⁵[(4y³ – 3x³)]
y'' = 3x/8y⁵[(4y³ – 3x³)]
