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4 years ago

Help me please, match the number to the letter

Mathematics

1 answer:

kenny6666 [7]4 years ago

8 0

Answer: 1b 2c 3e? 4d 5a

<u>Step-by-step explanation:</u>

There are 2 items that need to be checked.

The midpoint of the coordinates is the center of the circle
The diameter of the coordinates is the diameter of the circle.

Midpoint:

$Midpoint = \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\1)\ \bigg(\dfrac{-4+2}{2},\dfrac{-1+10}{2}\bigg)=\bigg(\dfrac{-2}{2},\dfrac{9}{2}\bigg)=(-1, 4.5)\implies \text{equation b}\\\\\\2)\ \bigg(\dfrac{1+7}{2},\dfrac{3-10}{2}\bigg)=\bigg(\dfrac{8}{2},\dfrac{-7}{2}\bigg)=(4, -3.5)\implies \text{equation c}\\\\\\3)\ \bigg(\dfrac{4-8}{2},\dfrac{-2+6}{2}\bigg)=\bigg(\dfrac{-4}{2},\dfrac{4}{2}\bigg)=(-2,2 )\implies \text{none of the equations}$

$4)\ \bigg(\dfrac{6-4}{2},\dfrac{3-13}{2}\bigg)=\bigg(\dfrac{2}{2},\dfrac{-10}{2}\bigg)=(1, -5)\implies \text{equation d}\\\\\\5)\ \bigg(\dfrac{7-1}{2},\dfrac{5+8}{2}\bigg)=\bigg(\dfrac{6}{2},\dfrac{13}{2}\bigg)=(3, 6.5)\implies \text{equation a}$

Diameter:

distance between coordinates = 2√r² (from circle equation)

$\text{formula for coordinates is: }d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\1)\ \text{Coordinates: } d=\sqrt{(-4-2)^2+(-1-10)^2}=\sqrt{36+121}=12.5\\b)\ \text{Circle: }2\sqrt{39.25}=12.5\\\\\\2)\ \text{Coordinates: } d=\sqrt{(1-7)^2+(3+10)^2}=\sqrt{36+169}=14.3\\c)\ \text{Circle: }2\sqrt{51.25}=14.3\\\\\\4)\ \text{Coordinates: } d=\sqrt{(6+4)^2+(3+13)^2}=\sqrt{100+256}=18.9\\d)\ \text{Circle: }2\sqrt{89}=18.9$

$5)\ \text{Coordinates: } d=\sqrt{(7+1)^2+(5-8)^2}=\sqrt{64+9}=8.5\\a)\ \text{Circle: }2\sqrt{18.25}=8.5$

Check:

Graph to confirm your answers are correct (see attached)

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The y-intercepts are given by the y values such that x = 0. Replacing x = 0 in the definition f(x), we see that the denominator of the second term diverges. So we conclude that there are no y-intercepts.

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Horizontal asymptotes are horizontal lines that the graph of the function approaches when x → ±∞. We consider the limit of the function f(x) when x → ±∞:

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When a linear asymptote is not parallel to the x- or y-axis, it is called an oblique asymptote or slant asymptote.

A function ƒ(x) is asymptotic to the straight line y = mx + n (m ≠ 0) if

${\displaystyle\lim _{x\to+\infty}\mleft[f(x)-(mx+n)\mright]=0\, {\mbox{ or }}\lim _{x\to-\infty}\mleft[f(x)-(mx+n)\mright]=0.}$

We consider the line given by:

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Answer

1) x-intercepts: (-0.34975, 0), (0.35757, 0), (15.9922, 0)

2) y-intercepts: none

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Help me please, match the number to the letter​

Help me please, match the number to the letter