How to find the value of x in degrees HELP
1 answer:
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If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below.
In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle.
Midpoint =
So plug in the ordered pairs given to get:
Midpoint =
Midpoint =
Midpoint = (1, - 3)
This is your center.
Now for the distance between the endpoints.
Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26
So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long.
Now we plug in to the equation of a circle:
(x - h)² + (y - k)² = r²
The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r.
So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²
Which simplifies to your final answer:
(x - 1)² + (y + 3)² = 26
In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle.
Midpoint =
So plug in the ordered pairs given to get:
Midpoint =
Midpoint =
Midpoint = (1, - 3)
This is your center.
Now for the distance between the endpoints.
Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26
So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long.
Now we plug in to the equation of a circle:
(x - h)² + (y - k)² = r²
The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r.
So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²
Which simplifies to your final answer:
(x - 1)² + (y + 3)² = 26
Answer:
The volume of the given figure is 150 mm³
Step-by-step explanation:
The formula of the volume of the triangular pyramid is V = AH, where
- A is the area of its base
- H is its height
The formula of the area of a triangle is A = bh, where
- b is the length of its base
- h is the length of its height
In the given figure
∵ The pyramid has a triangular base
∵ The triangle has a base of 12 mm and a height of 7.5 mm
∴ b = 12 mm and h = 7.5 mm
→ By using the 2nd formula above, find the area of the base
∴ A = (12)(7.5)
∴ A = 45 mm²
∵ The height of the pyramid is 10 mm
∴ H = 10 mm
∵ A = 45 mm²
→ Substitute them in the first formula above to find the volume
∴ V = (45)(10)
∴ V = 150 mm³
∴ The volume of the given figure is 150 mm³