23° 20' 48" in degrees
Minutes are 1/60 of a degree and seconds 1/60 of a minute.
Let's convert the 48" to minutes.
48/60 = 0.8
23° 20' 48" ⇒ 23° 20.8'
Let's convert the 20.8' to degrees.
20.8/60 ≈ 0.3466667
23° 20.8' ⇒ 23.35°
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
3t-2
Step-by-step explanation:
- Multiply the terms 3t and 2t. You should get 5t.
- Subtract 7 from 5; you should get -2.
- Now, your equation is 3t-2, you're done!
Answer:
y-intercept = 275
x-intercept = 125
Step-by-step explanation:
The y-intercept is the point on your line where x=0. On this line, the y-intercept is the point (0,275) (x,y)
The x-intercept is the point on your line where y=0. On this line, the x-intercept is the point (125,0) (x,y)
Answer:
The equation of the graph in slope-intercept form is y = 3x + 7. 2. slope-intercept form is y = x + 2.