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:
GF = 16.25
Step-by-step explanation:
If G is the circumcenter of triangle ABC, AG = 6x + 1, GC = 9x – 11, and BC = 38, find GF.
Step 1
We find x
AG = GC
6x + 1 =9x - 11
Collect like terms
1 + 11 = 9x - 6x
12 = 3x
x = 12/3
x = 4
Step 2
We solve for AG
GC = 9x + 11
GC = 9(4) + 11
GC = 36 + 11
GC = 25
Step 3
Solving for GF, using Pythagoras Theorem
GF² + BG² = GC²
GF² = GC² - BG²
GF = √GC² - BG²
GF = √25² - 19²
GF = √264
GF = 16.248076809
GF = 16.25
<span>2
— = 0.66667
3 hello
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Firstly the equation would be y=7.7x+59
(A)The slope is 7.7 (B) and shows that there is a 7.7 charge per week the person attends.
(A)The y intercept is 59 (B) and is the initial fee that the gym charges.
