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:
<h2><em>
D. (-7, 3)</em></h2>
Step-by-step explanation:
The standard form of a point slope equation of a line is expressed as shown;
y-y₀ = m(x-x₀) where;
m is the slope of the line
(x₀, y₀) is the coordinate of the point that lies in the line.
Comparing the standard equation given with the equation in question
y - 3 = 4(x + 7) to get the point on the line we will have;
y₀ = 3 and -x₀ = 7
for -x₀ = 7;
multiply both sides with a minus sign
-(-x₀) = -7
x₀ = -7
<em>Hence the coordinate of the point required (x₀, y₀) is (-7, 3).</em>
Convert each to decimal form
that will be 0.122... , 0.1225, 0.12 and 0.056
so from greatest to least that is 0.1225 , 0.1222...., 0.12, 0.056
that is 0.1225 , 012(with bar over the 2) , 3/25 , 7/125
Answer:idek school is very hard
Step-by-step explanation:
Three solutions:
x=0
x=7/2
x=-6
