x² + y² = 5
y = 2x/3 + 1
In a simple way to find the intersections you can just throw the y value in the other equation, so
x² + y² = 5
x² + (2x/3 + 1)² = 5
x² + (2x/3)² + 2.2x/3.1 + 1² = 5
x² + 4x²/9 + 4x/3 + 1 = 5
13x²/9 + 4x/3 + 1 - 5 = 0
13x²/9 + 4x/3 - 4 = 0
Multiply by 9
13x² + 12x - 36 = 0
Δ = b² - 4.a.c
Δ = 12² - 4 . 13 . -36
Δ = 144 - 4. 13 . -36
Δ = 2016
There are 2 real roots.
x = (-b +- √Δ)/2a
x' = (-12 + √2016)/2.13
x'' = (-12 - √2016)/2.13
x' = 32,8998886412873 / 26
x'' = -56,8998886412873 / 26
x' = 1,2653803323572037
x'' = -2,188457255434127
Rounding
x' = 1,27
x'' = -2,19
Now we need to put this value in the y equation to know the y coordinate.
y = 2x/3 + 1
y' = 2.1,27/3 + 1
y' = 2,54/3 + 1
y' = 1,8466666...
y' = 1,85
y = 2x/3 + 1
y'' = 2.(-2,19)/3 + 1
y'' = -4,38/3 + 1
y'' = -0,46
So the points are: (1,27;1,85) and (-2,19;-0,46)
no se nada de eso por favor no me preguntes eso y siueme
37.5 miles per hour is the speed of the car
The circumference is π times the diameter (2r). So if you divide the given 18.84 by π, you get the diameter. Rounded, the answer is 6.00 inches.
The area of the washer will be found by calculating the area of the shaded part.
Area of larger circle:
A=πr²
r=4.4+(13.2/2)=11 mm
thus
A=π×11²=380.13
Area of the small circle:
A=π×(13.2/2)²=136.85 mm
The area of the washer will be:
380.13-136.85
=243.28
~243.3 mm²
