the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.
The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.
In terms of hyperbola, F1F2=2c, c=20.
The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.
Use formula c^2=a^2+b^2c
2
=a
2
+b
2
to find b:
\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}
(20)
2
=(18)
2
+b
2
,
b
2
=400−324=76
.
The branches of hyperbola go in y-direction, so the equation of hyperbola is
\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1
b
2
y
2
−
a
2
x
2
=1 .
Substitute a and b:
\dfrac{y^2}{76}- \dfrac{x^2}{324}=1
76
y
2
−
324
x
2
=1 .
Answer: 300x200
Step-by-step explanation: First of all...Your perimeter equals 2x+3y. X=length, y=width.
2x+3y=1200
3y=1200-2x
y=400-(2/3)x
y=400-(2/3)x
Your Area = xy=x(400-2x/3)=400x-2^2/3
dA/dx=400-4x/3=0
4x/3=400
4x=1200
x=300ft length
y=400-(2/3)(300)=200ft
I hope this helps you!
Answer: Use order of operations (PEMDAS). Answer is 45.72.
Step-by-step explanation:
First, solve inside parenthesis:
(5.25*1 1/5 - 4.5*4/5)
Convert 1 1/5 into decimal. It will be easier. 1 1/5 is the same as 1.2
Do multiplication and division first.
5.25*1.2 = 6.3
Now it looks like: (6.3 - 4.5*4/5)
Convert 4/5 to a decimal: 4/5 = 0.8
(6.3 - 4.5*0.8)
Multiply 4.5*0.8 = 3.7
Subtract (6.3 - 3.7) = 2.6
Now the full equation is: 19.6*2 1/5 + (2.6)
2 1/5 as a decimal: 2.2
Multiply 19.6*2.2 = 43.12
Now the equation is: 43.12 + 2.6
Add 43.12 + 2.6 = 45.72
The answer is A.
D= 6<=x<=11
Answer: possible values of Range will be values that are >=91 or <=998
Step-by-step explanation:
Given that :
Set Q contains 20 positive integer values. The smallest value in Set Q is a single digit value and the largest value in Set Q is a three digit value.
Therefore,
given that the smallest value in set Q is a one digit number :
Then lower unit = 1, upper unit = 9( this represents the lowest and highest one digit number)
Also, the largest value in Set Q is a three digit value:
Then lower unit = 100, upper unit = 999 ( this represents the lowest and highest 3 digit numbers).
Therefore, the possible values of the range in SET Q:
The maximum possible range of the values in set Q = (Highest possible three digit value - lowest possible one digit) = (999 - 1) = 998
The least possible range of values in set Q = (lowest possible three digit value - highest possible one digit value) = (100 - 9) = 91
