1. 2,359,412; 2,937,158; 3,356,000; 3,368,742
2. 2,009,604; 2,009,832; 2,103,425; 2,112,300
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)]
Answer:
$462.7
Step-by-step explanation:
15% commission on $54
= $8.1
he sell 27 boards so
8.1 × 27=$218.7
so
$245.00+$218.7=$463.7
The inequality which represents the missing dimension x is x≥1.6 or x≥8 / 5.
Given that the area is greater than or equal to 8 square feet and image is attached below.
We want to find the missing inequality x in the form of inequality.
The figure is assumed to be a right triangle with Root = x and perpendicular = 10ft.
As we know the area of a triangle is half the product of the base and the height.
First of all, we will find the area of the triangle by substituting the given values we get
Area=(1/2)×Base×height
Area=(1/2)×x×10
Area=5x ......(1)
Assume that this area is greater than or equal to 8 square feet.
That means Area≥8ft² ......(2)
Now we will balance equation (1) and equation (2), we get
5x≥8ft²
Furthermore, they we will divide both sides by 5 we get
(5x)/5≥8/5
x≥8/5
x≥1.6
Therefore, the inequality represents the missing size x when the area is larger or equal to 8 square feet is x ≥1.6ft².
Learn more about the dimension from here brainly.com/question/13271352
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Six million, seven thousand and two hundred.
