Franco is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. the shape of his satellite can be modeled by y^2+6y-3x+3=0, where x and y are modeled in inches. he realizes that the static is a result of the feed antenna shifting slightly off the focus point. what is the focus point of the satellite?

focus point of  satellite is (-125,-3)

Step-by-step explanation:

The question is on finding the focus point of a parabola

Given y²+6y-3x+3=0

Rewrite the equation

y²+6y=3x-3

Complete square on both sides

y²+6y+9=3x-3+9

Factorize

(y+3)²= 3x+6(a)

(y+3)²= 3(x+2)

Compare  equation (a) to standard equations for parabola

(y+3)²= 3(x+2)

(y-b) ²= 2p(x-a)(b)

2p=3divide both sides by 2

p=3/2

Vertex (a,b)=( -2,-3)from equation (b)

Focus point is given by  (a+p/2 , b)(c)

Substitute values in equation c above;

(-2+3/4 , -3) = (-5/4 ,-3) =(-1.25, -3)

correct

step-by-step explanation:

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺