Our aim is to calculate the Radius so that to use the formula related to the area of a segment of a circle, that is: Aire of segment = Ф.R²/2
Let o be the center of the circle, AB the chord of 8 in subtending the arc f120°
Let OH be the altitude of triangle AOB. We know that a chord perpendicular to a radius bisects the chord in the middle. Hence AH = HB = 4 in
The triangle HOB is a semi equilateral triangle, so OH (facing 30°)=1/2 R. Now Pythagoras: OB² = OH² + 4²==> R² = (R/2)² + 16
R² = R²/4 +16. Solve for R ==> R =8/√3
OB² = OH² +
Answer:
the slope is positive 2
the slope-intecept form would be, y=2x+3
Step-by-step explanation:
hope this helps!❆
Answer:
30 degrees
Step-by-step explanation:
P+Q+R=180
80+70+Q=180
Q=30
PQR = angle Q
Answer:
16 ft by 22 ft
Step-by-step explanation:
The Area of the carpeting she must have = 352 ft²
To solve for this, we have:
Length × Width = Area of a rectangle
352ft² = Length × Width
352ft² = (20 - x) (26 - x)
352 = 520 - 20x - 26x + x²
352 = 520 - 46x + x²
Collect like terms
x² - 46x + 520 - 352
x² - 46x + 168
We factorise
x² - 4x - 42x + 106
(x² - 4x) -(42x + 106)
x(x - 4) -42(x - 4)
(x - 4)(x - 42)
x - 4 = 0, x = 4
x - 42 = 0, x = 42
We choose the least value for x
Hence, x = 4
Length = 20 - 4 = 16ft
Width = 22- 4= 22ft
The dimensions the rug should have is 16ft by 22 ft, meaning 16ft wide and 22ft long
