Find the perimeter of the semicircular region 22 mm
2 answers:
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Answer:
(x – 1)² + (y +2)² = 5
Step-by-step explanation:
recall that the general form of the equation for the circle is as follows:
(x – h)² + (y – k)² = r²
where, (h,k) are the coordinates for the center of the circle and r is the radius of the circle.
We are given that the center of the circle is at (1,-2). Comparing this with the description of h & k above, we can immediately conclude that h = 1 and k = -2.
Hence the only thing we are missing now is radius r.
It is given that the circle passes through the origin, hence if we draw a line between the origin (0,0) and the center (1,-2), this distance is the radius.
to find the distance between 2 points, we use the attached formula
Distance = radius, r = √ [ (1-0)² + (-2-0)²]
r = √ [ (1² + (-2)²]
r = √ [1 + 4] = √ 5
hence we can assemble the equation
(x – 1)² + (y – (-2))² = (√5)²
(x – 1)² + (y +2)² = 5
We know there are 1000 meters in 1 kilometer, KILO=1000.
so, how many in 3/4 km?
so, how many in 3/4 km?
Considering the definition of vertex, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
<h3>Vertex form</h3>The function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
The quadratic function can be expressed by the vertex form of a quadratic equation: y=a(x−h)²+k , where (h,k)= vertex of the parabola.
The formula to find the value x of the vertex of a quadratic equation is
To calculate the value of y of the vertex, it is necessary to find the numerical value of "x vertex" in the polynomial expression. This is:
(h,k)= (,
)
In this case:
- a= -3
- b= -12
- c= -2
Replacing in the formula to find the value x of the vertex of a quadratic equation, you get:
Solving:
<u><em>x= -2</em></u>
The value of y of the vertex can be calculated as:
y = –3×(-2)² – 12×(-2) – 2
Solving:
y= –3×4 – 12×(-2) – 2
y= –12 +24 – 2
<u><em>y=10</em></u>
Finally, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
Learn more about vertex form of a cuadratic function:
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