Find the diagonal of a square whose sides each measure 3v2 units.

Mathematics

1 answer:

Aleksandr [31]4 years ago

3 0

Answer:

6 units

Step-by-step explanation:

Use the Pythagorean theorem:

diagonal² = side² +side²

diagonal² = (3√2)² +(3√2)² = 18 + 18 = 36

diagonal = √36 = 6

The diagonal of a square whose sides are 3√2 units is <u>6 units</u>.

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Answer:

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Step-by-step explanation:

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y = ln(x) -5

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4 years ago

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Answer:D

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Can anyone help me with these question

Kazeer [188]

So hmm notice the picture below

a)

the center of the circle is the midpoint of those two folks

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -10}}\quad ,&{{ -2}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 6}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left(\cfrac{4-10}{2}\quad ,\quad \cfrac{6-2}{2} \right)\impliedby \textit{center of the circle}$

b)

the diameter is the distance between P and Q, or the length of that segment, and the radius is half the diameter

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -10}}\quad ,&{{ -2}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 6}})
\end{array}\quad 
% distance value
d = \sqrt{({{ 4}}-{{ (-10)}})^2 + ({{ 6}}-{{ (-2)}})^2}
\\\\\\
d=\cfrac{\sqrt{(4+10)^2+(6+2)^2}}{2}\impliedby \textit{radius of the circle}$

c)

so, from a), you found the h,k coordinates for the center, from b) you've got the radius

so, just plug them in here then $\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}
\end{array}$