Answer:
y = -2
Step-by-step explanation:
To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx
The equation is

implicit differentiation give us
![\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5By%5E2%28y%5E2-4%29%3Dx%5E2%28x%5E2-5%29%5D%5C%5C%5C%5C2y%5Cfrac%7Bdy%7D%7Bdx%7D%28y%5E2-4%29%2By%5E2%282y%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D2x%28x%5E2-5%29%2Bx%5E2%282x%29%5C%5C%5C%5C4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D-8y%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x%5E3-10x%2B2x%5E3%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B4x%5E3-10x%7D%7B4y%5E3-8y%7D)
But we know that

Hence, for the point (0,-2) and by replacing for dy/dx

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:
y=(0)x+b = -2
HOPE THIS HELPS!!
Answer:
25,000
Step-by-step explanation:
If the number after it is under 5 change the number to 0
if it’s grater then 5 round the number up one
Total outcomes = 6*6 = 36
favourable outcomes = (1,3), (2,2), (3,1)
Probability = 3/36 = 1/12
Hope it helps!
Answer:
$130
Step-by-step explanation:
Renting the dvd for one day costs $10.
$15 is charged for every late day .
Timmy rented the DVD player for 4 days and returned it 10 days later.
For 4 days , the amount
= $10 x 4
= $40
For the remaining six days he’ll pay
$15 x 6= $90 because he was charged the late fee .
Therefore, total amount paid by Trimmy
= $40 + $90
= $130
Trimmy paid $130