Area of the parabolic region = Integral of [a^2 - x^2 ]dx | from - a to a =
(a^2)x - (x^3)/3 | from - a to a = (a^2)(a) - (a^3)/3 - (a^2)(-a) + (-a^3)/3 =
= 2a^3 - 2(a^3)/3 = [4/3](a^3)
Area of the triangle = [1/2]base*height = [1/2](2a)(a)^2 = <span>a^3
ratio area of the triangle / area of the parabolic region = a^3 / {[4/3](a^3)} =
Limit of </span><span><span>a^3 / {[4/3](a^3)} </span>as a -> 0 = 1 /(4/3) = 4/3
</span>
Answer:
It cost $8 per person to get into the carnival
Step-by-step explanation:
Let the entry cost be y
Let Cost of 1 game be x
Cost of 5 games = 5x
Cost of 12 games = 12x
Frankie played 5 games and spent $15.50 altogether.
So, 
--- A
Maria played 12 games and spent $26 altogether.
So, 
-- B
Plot the lines
--- Black color
--- Red color
Intersection point provides the solution
(x,y)=(1.5,8)
So, it cost $8 per person to get into the carnival
Answer:
73
Step-by-step explanation:
Angle JID is supplementary to Angle JIH so:
180- Angle JIH= Angle JID
180-107=73
Angle JID is opposite to Angle AJF(angle x)
Opposite angles are always equal
Angle JID=Angle AJF(x)
73=Angle AJF(x)
Answer:
1 7/8 quarts
Step-by-step explanation:
The amount Yuan has left can be found by multiplying the original amount by the fraction he has left.
__
<h3>used</h3>
After using 1/2 of the broth for soup, the fraction remaining is ...
1 -1/2 = 1/2
The amount Yuan used for gravy is 1/4 of this, or ...
(1/4)(1/2) = 1/8 . . . of the original amount of broth
The total fraction Yuan used was ...
fraction used = fraction for soup + fraction for broth = 1/2 +1/8 = 5/8
<h3>remaining</h3>
Then the fraction remaining is ...
fraction remaining = 1 - fraction used = 1 - 5/8 = 3/8.
The amount remaining is this fraction of the original amount:
(3/8)(5 quarts) = 15/8 quarts = 1 7/8 quarts . . . . remaining
Answer:
10
Step-by-step explanation:
D=
D=
D=
D=
D=10
