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densk [106]
2 years ago
14

The diagram shows 3 identical circles inside a rectangle.

Mathematics
1 answer:
Ilya [14]2 years ago
5 0

Answer:

11700 mm²

Step-by-step explanation:

A rectangle is a quadrilateral with two equal, opposite and parallel sides. Each of the angles in a rectangle is 90°.

The horizontal distance of the rectangle = r + r + r + r = 4r

The vertical distance = r + h + r = 2r + h

Where h is the distance between the midpoint of the 2 up circles and the midpoint of the down circle.

Using Pythagoras:

 (2r)² = h² + r²

h² + r² = 4r²

h² = 3r²

h = √3r²

h = r√3

Vertical distance = 2r + h = 2r + r√3

Area of rectangle = vertical distance * horizontal distance

Area = 4r * (2r + r√3) = 8r² + 4r²√3 = 4r²(2 + √3)

Substituting:

Area = 4r²(2 + √3) = 4(28²)(2 + √3) = 11703.711 mm²

Area = 11700 mm² to 3 s.f

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3 years ago
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty
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2 years ago
Simplify the expression by combining like terms 2x+8-x+10
svp [43]

Answer:

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Step-by-step explanation:

Let's simplify step-by-step.

2x+8−x+10

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8 0
2 years ago
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choli [55]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
The current (I) varies directly as the voltage (V) in an electric circuit. If the current is 4 amperes when the voltage is 100 v
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\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&&  y={{ k }}x
\end{array}\\\\
-----------------------------\\\\

\bf \textit{l varies directly to V}\implies l=kV
\\\\\\
\textit{now, we also know that }
\begin{cases}
l=4\\
V=100
\end{cases}\implies 4=k100
\\\\\\
\cfrac{4}{100}=k\implies \cfrac{1}{25}=k\impliedby \textit{constant of variation}
\\\\\\
thus\implies l=\cfrac{1}{25}V
\\\\\\
\textit{what is the current when the voltage is 75?}\qquad l=\cfrac{1}{25}\cdot 75
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3 years ago
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