"a "and "b^2-4ac" must be negetive
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:
The system of equation that represent this situations are;
Also 5 hats and 10 scarves can be prepared from 2 kg of yarn.
Step-by-step explanation:
Let number of hat Chevy makes be h.
Also Let number of scarves Chevy makes be s.
Given:
Total Amount of yarns = 2 kg
Total number of items = 15
Since Items need to make are hat and scarves.
Hence the equation can be represented as;
Again Given:
Each hat uses 0.2 kilograms of yarn.
each scarf uses 0.1 kilograms of yarn.
Hence the equation can be represented as;
Hence the system of equation that represent this situations are;
Now Solving these to find number of hats and number of scarves.
Multiplying equation 2 with 10 we get;
Now Subtracting equation 1 from equation 3 we get;
Now Substituting the value of h in equation 1 we get;
Hence 5 hats and 10 scarves can be prepared from 2 kg of yarn.
Answer:
The answer to your question is x = 17.32; y = 8.67
Step-by-step explanation:
Process
1.- Use trigonometric functions to find x and y
a) sin Ф = 
Ф = 60°
opposite side = 15
hypotenuse = ?
hypotenuse = 17.32
b) cosФ = 
y = 8.67
Answer:
96
Step-by-step explanation:
once you fill in the Blanks that are solvable, you will work your way into the answer. For example, the first column, the missing number has to be 155-76 or 79. Now you can find your answer. In the second row, “no Laptop”, you have 79 (solved above) plus 17. So your answer is 79+17 or 96.
