Answer:
-4/5
Step-by-step explanation:
To find the slope of the tangent to the equation at any point we must differentiate the equation.
x^3y+y^2-x^2=5
3x^2y+x^3y'+2yy'-2x=0
Gather terms with y' on one side and terms without on opposing side.
x^3y'+2yy'=2x-3x^2y
Factor left side
y'(x^3+2y)=2x-3x^2y
Divide both sides by (x^3+2y)
y'=(2x-3x^2y)/(x^3+2y)
y' is the slope any tangent to the given equation at point (x,y).
Plug in (2,1):
y'=(2(2)-3(2)^2(1))/((2)^3+2(1))
Simplify:
y'=(4-12)/(8+2)
y'=-8/10
y'=-4/5
Answer:
A
Step-by-step explanation:
The Tangent-Secant Exterior Angle Measure Theorem states that if a tangent and a secant or two tangents/secants intersect outside of a circle, then the measure of the angle formed by them is half of the difference of the measures of its intercepted arcs. Basically, what that means here is that 
equals half of the difference of 
and the measure of the unlabeled arc.
First, we need to find the measure of the unlabeled arc, since we can't find without it. We know that the measure of the full arc formed by the circle is 
, so the measure of the unlabeled arc must be 
by the Arc Addition Postulate.
Now, we can find . Using all of the information known, we can solve for like this:
Hope this helps!
Answer:
b = 6.928
Step-by-step explanation:
Looks like a job for the Pythagorean Theorem.
a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
b^2 = 48
b = 6.928
Hope it helps!!
Answer: Assume c = 0
Step-by-step explanation:
Step-by-step explanation:
Assume c = 0
Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:
B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:
AND
Substituting into the quadratic equation:
Because a is negative, the parabola opens up.
