Mathematics, 22.01.2020 01:31 elisechavez02

Acircle has a diameter with endpoints at 15 + 25i and –25 – 17i. which point is also on the circle?

Answers: 2

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Answer from: nsg0686

The point 16+24i is the point satisfying the equation

Hence, Option D is correct.

Step-by-step explanation:

We will find mid-point from end points given.

Mid-point formula: $(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

On substituting the values we will get:

$(x,y)=(\frac{-25+15}{2},\frac{-17+25}{2})$

(x,y)=(-5,4)

Now, we have general equation of circle:

(x-a)^2+(y-b)^2=r^2

We will find r that is distance from mid-point to end oint using distance formula

$\text{distance formula}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here, x_1=-5,x_2=-25,y_1=4,y_2=-17

On substituting the values we get:

$\text{distance formula}=\sqrt{(-25+5)^2+(-17-4)^2}$

$\text{distance formula}=\sqrt({20}^2+{21}^2)$

$\text{distance}=\sqrt{841}$

Hence, r^2=841

Substituting the values in general equation we get:

(x-(-5))^2+(y-4)^2=841

[tex]\Rightarrow(x+5)^2+(y-4)^2=841[tex]

And when we substitute x=16 and y=24 the equation will be satisfied

and a=-5 and b=4

Hence, will lie on the circle

Therefore, option D is correct.

Answer from: Quest

I'll do the first one for you. it isn't very hard at all.on number one, you have (50 × 3), which equals 150, and (3 × 3), which equals 9. after you establish that, you add 150 and 9 together. so, (150 + 9) equals 159.this means that 53 × 3 = 159.

Answer from: Quest

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 ☺