solve equation g+4/g-2=g-5/g-8
another qustion
an elliptical track has a major axis that is 80 yrds long and minor axis 72 yards long find an equation for the track if its center (0,0) and the major axis is the x axis
In your equation, you must show where the parentheses go. Do you mean
(g+4)/(g-2)= (g-5)/(g-8) ?
If so, multiply out the "cross produts", combine terms and solve the resulting equation.
(g+4)(g-8) = (g-2)(g-5)
g^2 -4g -32 = g^2 -7g +14
The g^2 terms cancel out, making it easy to solve.
still don't get it
The next step is
3g = 46
To solve the equation g+4/g-2 = g-5/g-8, we can follow the steps:
Step 1: Start by multiplying both sides of the equation by (g-2)(g-8) to eliminate the denominators.
(g+4/g-2) * (g-2)(g-8) = (g-5/g-8) * (g-2)(g-8)
This simplifies to:
(g+4)(g-8) = (g-5)(g-2)
Step 2: Expand both sides of the equation.
g^2 - 4g - 32 = g^2 - 7g + 10
Step 3: Combine like terms on both sides.
-4g + 32 = -7g + 10
Step 4: Move all terms with g to one side of the equation and the constant terms to the other side.
-4g + 7g = 10 - 32
3g = -22
Step 5: Divide both sides by 3 to solve for g.
g = -22/3
Therefore, the solution to the equation is g = -22/3.
Now, let's move on to the second question.
The equation for an ellipse with a center at (0,0) and the major axis as the x-axis can be described using the equation:
x^2/a^2 + y^2/b^2 = 1
Where (a, b) represents the semi-major and semi-minor axes.
Given that the major axis is 80 yards (which means the semi-major axis is 40 yards) and the minor axis is 72 yards (which means the semi-minor axis is 36 yards), we can substitute these values into the equation:
x^2/40^2 + y^2/36^2 = 1
Simplifying this equation, we get:
x^2/1600 + y^2/1296 = 1
Therefore, the equation for the elliptical track is x^2/1600 + y^2/1296 = 1.