Answer:
The vertex of this parabola, 
, can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where 
, 
, and 
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at 
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for 
, and the coefficient for 
should all match accordingly. That is:
.
The first equation implies that is equal to 
. Hence, replace the "
" in the second equation with 
to eliminate 
:
.
.
Similarly, replace the "" and the "" in the third equation with and 
, respectively:
.
.
Therefore, 
would be equivalent to 
. The vertex of this parabola would thus be:
.
Answer:
C. 26°
Step-by-step explanation:
We have to subtract m∠GOH ( 24° ) from m∠FOH ( 50°)
50° - 24° = 26°
C. 26°
There are 16 lines between 1 and 2, so each line would be 1/16. The arrow is pointing to the 3rd line so it would be 3/16
Answer:
a. 20,579.52 cubic inches
b.10,289.76 cubic inches.
c. 13.49 inches
Step-by-step explanation:
Hi, to answer this question we have to calculate the volume of a sphere:
Volume of a sphere: 4/3 π r³
Since diameter (d) = 2 radius (r)
Replacing with the value given:
34 =2r
34/2=r
r= 17 in
Back with the volume formula:
V = 4/3 π r³
V =4/3 π (17)³
V = 20,579.52 cubic inches
The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.
20,579.52/2 = 10,289.76 cubic inches.
To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76
10,289.76= 4/3 π r³
Solving for r
10,289.76/ (4/3 π)= r³
2,456.5 = r³
∛2,456.5 = r
r = 13.49 inches
