Answer:
Step-by-step explanation:
Given that:
[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]
at point (0, -2)
[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]
Taking the differential from the equation above with respect to x;
[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]
Collect like terms
[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
Hence, the slope of the tangent line m can be said to be:
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
At point (0,-2)
[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]
[tex]\dfrac{dy}{dx}= 0[/tex]
m = 0
So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:
(y - y₁ = m(x - x₁))
y + 2 = 0(x - 0)
y + 2 = 0
y = -2
How many different ways may a set of 4 books be arraged side by side on a shell?
Answer:
24
Step-by-step explanation:
4 * 3 * 2 * 1 = 24
My mom is making me do prayice and i need the answer for this thanks very much
Please help me with this I need it bad
Answer:
1
Step-by-step explanation:
The average rate of change is the gradient _
Gradient = Rise / Run = (y2 - y1) / (x2 - x1)
From the table ;
x2 = 4 ; x1 = - 1 ; y2 = 5 ; y1 = 0
Gradient = (y2 - y1) / (x2 - x1) = (5-0) / (4 - - 1) = 5/5 = 1
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Answer:
30
Step-by-step explanation:
There are 14 data points on the plot
The median is the middle value, which is between the 7th and 8th data points
Since it is even, we find the average of the 7th and 8th data points
Add the 7th and 8Th data points values and divide by 2
( 30+30)/2 = 60/2 = 30
The median is 30
Answer:
30
Step-by-step explanation:
Middle numbers are 30 and 30 so you add them and then divide by two:
[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30