Mathematics, 01.08.2021 06:50 fallenangelsayshush

Can someone help please! I need this last question answered

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Answer from: travashouston4873

$\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\$

This is the same as writing (x^2)/16 + (y^2)/49 = 1

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Explanation:

The general equation for an ellipse is

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

where

(h,k) is the center'a' is half the total width (along the x axis)'b' is half the total height (along the y axis)

Notice how 'a' pairs with the x term, so that's why 'a' describes the horizontal width along the x axis. The horizontal width is 8 ft, which cuts in half to 4 ft. So a = 4.

The vertical length is 14 ft, which cuts in half to 7 ft. So b = 7.

The center isn't mentioned (other than the fact that the actor is located here), but I'm assuming by default it's at the origin (0,0).

With that all in mind, we then get the following:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{7^2} = 1\\\\\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\$

The graph is below. I used GeoGebra to make the graph.

From the graph, we can see that the horizontal width spans from x = -4 to x = 4. This is a total distance of |-4-4| = 8 feet. Similarly, the vertical length spans from y = -7 to y = 7 which is a distance of 14 feet.

Can someone help please! I need this last question answered

Answer from: Quest

step-by-step explanation:

14 x 3 = 42

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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