Given:
The equation of ellipse is
To find:
The length of the minor axis.
Solution:
The standard form of an ellipse is
...(i)
where, (h,k) is center, if a>b, then 2a is length of major axis and 2b is length of minor axis.
We have,
...(ii)
On comparing (i) and (ii), we get
Taking square root on both sides.
Consider only positive value of b because length cannot be negative.
Now,
Length of minor axis = 
= 
= 
So, the length of minor axis is 8 units.
Therefore, the correct option is B.
The llike terms are {17xy^2, -13xy^2} {9, 3} {8y^3, -6y^3} {10x, -9x} first combine 9 and 3 now your new equation is 12 <span>+ 17xy^2 + 8y^3 + 10x –13xy^2 – 9x – 6y^3 then add 17xy^2 and -13xy^2 your new equation is 12 + 4xy^2 </span><span>+ 8y^3 + 10x – 9x – 6y^3 now combine 8y^3 and 6y^3 your new equation is 12 + 4xy^2 + 2y^3 </span><span>+ 10x – 9x now combine 10 and -9x and your answer is </span><span><span>12 + 4xy^2 + 2y^3 <span>+ x</span></span> </span>
Answer:
12
Step-by-step explanation:
The 2 lines are equal in length. Therefore:-
ST = 21 - 9 = 12
3x-22+x=180
4x-22=180
4x=202
X=202/4
X=50.5
3(50.5)-22=129.5
5-.5+129.5=180
Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
Combined Area = (2x + 26)*(2x + 8) = 1008
2x*(2x + 8) + 26*(2x + 8 ) = 1008
4x² + 16x + 52x + 208 = 1008
4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.
Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
We replace the middle term of +17x in the quadratic expression with 25x -8x
x² +17x - 200 = 0
x² + 25x - 8x - 200 = 0
x(x + 25) - 8(x + 25) = 0
(x+25)(x -8) = 0
x + 25 = 0 or x - 8 = 0
x = 0 -25 x = 0 + 8
x = -25 x = 8
The width of the path can not be negative.
The only valid solution is x = 8.
The width of the path is 8 meters.
