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4 years ago

If pn= pn-1 +4 and p17=74, then p3=

1 answer:

5 0

$p_n=p_{n-1}+4$
$\implies p_{17}=p_{16}+4$
$\implies p_{17}=p_{15}+2\cdot4$
$\implies p_{17}=p_{14}+3\cdot4$
$\implies p_{17}=\cdots=p_3+14\cdot4$

$\implies74=p_3+56\implies p_3=18$

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Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

4 0

3 years ago

There are 60 players on a high school football team. The ratio of juniors and seniors to freshmen and sophmores on the team is 2

nata0808 [166]

You know that the ratio of J&S to F&So is 2:3. You need two numbers that have that same ratio to total 60 players. When you multiply both numbers by 12, you have a ratio of 2:3 but the number of players is 24 to 36. Thus, the total players is 60. When looking at the ratio of Juniors to Seniors, the ratio remains 1:2, but must total 24 players. Dividing the total players by 3, you can find where 1 part of the players equals 2 parts of the others. Keeping that same ratio in mind, you are able to calculate that the ratio of Juniors to Seniors is 8:16 but when reduced, still remains a 1:2 ratio.

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3 years ago

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