The equation looks like this
. In an ellipse, a is always the bigger value, so a^2 = 25. This bigger value also tells us which axis is the major one. Sine the bigger value a is under the y^2 of the equation, the major axis is the y-axis. This is a vertical ellipse. The center is always found within a set of parenthesis that exist with the x^2 and the y^2. Since there are no parenthesis with either, there is no side to side movement, nor is there any up or down movement. So the center doesn't move from the origin (0, 0). The vertex is also along the major axis, and if a^2 is 25, then a = 5, so the vertices go up 5 from the center and down 5 from the center. Vertices are (0, 5) and (0, -5). The foci follow the formula
. c is the distance that the foci are from the center.
and c = 3. The foci also lie on the major axis, so the coordinates for the foci are (0, 3) and (0, -3). There you go!
Answer:
<h2>3(cos 336 + i sin 336)</h2>
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336)
The standard form of the equation of a circle is:
Where the point (a,b) represents the centre and r is the radius. So, given your information, the equation will be:
This would be any equation whose slope isn’t -1 or 1.
If the slope was -1, the lines would be parallel because the have the same slope.
If the slope was 1, the lines would be perpendicular because 1 is the negative reciprocal of -1.
Any line with any other slope will intersect with y=-x.
Hope this helps!
Answer:
80x
Step-by-step explanation:
If you pay 80 a month then to find the total you have paid after any number of months you would multiply amount times time which in this case is 80
a constant is the a number on its own so in this case there would be none
a coefficient is the number in front of a variable. Since the equation is 80x the coefficient is 80