Answer:
≈ 78.55 cm
Step-by-step explanation:
Using the ratio of arc (AB) to circumference (C) is equal to the ratio of angle subtended at centre by arc AB to 360°, that is
=
, that is
=
( cross- multiply )
110C = 8640 ( divide both sides by 110 )
C = ≈ 78.55 cm ( to 2 dec. places )
Answer:
Step-by-step explanation:
Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form
The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.
Filling in the equation with a vertex of (0, 0) which is our h and k respectively:
which simplifies to
and multiplying both sides by -1:
. This is not standard form, but it matches what your equation is in the choices. So to sum up:
The focus is located at (0, -3) and the first choice is true.
The parabola opens upside down and the second choice is not true.
The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.
We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.
So the fifth choice is not true.
Answer: 8 and 9 or -9 and -8
Step-by-step explanation:
Let be the first of the two integers. Then, since the numbers are consecutive,
is the other integer. We then know that the sum of the squares of
and
is equal to 145. So, now we have the equation
which can be expanded and simplified to
which then gives us the quadratic equation
This can then be factored into
Which can be simplified further into
So either or
. This gives us two solutions: 8 and 9 or -9 and -8.
Hope this helps! CHEERS!
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Work Shown:
s = side length of equilateral triangle = 1 cm
A = area of equilateral triangle with side length 's'
This is just one of the 6 equilateral triangles (see diagram below)
Multiply by 6 to get the area of all 6 equilateral triangles, or the entire hexagonal area
