Hello from MrBillDoesMath!
Answer:
w = 5
Discussion:
48 = 2 (2w) + (4 + 2w)2 =>
48 = 4w + 4*2 + (2w)*2 =>
48 = 4w + 8 + 4w => as 4w + 4w = 8w
48 = 8w + 8 => subtracting 8 from each side
48 - 8 = 8w => divide both sides by 8
(48 -8 )/8 = w =>
40/8 = w =>
w = 5 =>
Check: 2(10) + ( 4 + 2*5)*2 = 20 + 14*2 = 20 + 28 = 48
Thank you,
MrB
Use the Pythagorean Theorem to solve for the third side. The third side must be the hypotenuse since the height (vertical leg) is 9, and the length (horizontal leg) is 5.
a² + b² = c², where a and b are the legs and c is the hypotenuse. Plug in 5 and 9 for a and b; solve for c.
5² + 9² = c² ⇒ 25 + 81 = c²
106 = c²
Square root both sides.
c = 10.3
Third side: 10.3
Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
