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3 years ago

Find the value of x , if log₂ [log₅ (log₃x)] = 0

1 answer:

3 0

$\log_2 (\log_5( \log_3x)) = 0\\
D:x>0 \wedge \log_3x>0 \wedge \log_5(\log_3x)>0\\
D:x>0\wedge x>1 \wedge\log_3x>1\\
D:x>1 \wedge x>3\\
D:x>3\\
\log_5(\log_3x)=1\\
\log_3x=5\\
x=3^5\\
x=243$

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The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

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ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

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$\cos(60 \degree) = \frac{altitude}{8}$

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

$\sin(60 \degree) = \frac{4 - y}{y}$

$y\sin(60 \degree) = 4 - y$

$y\sin(60 \degree) + y= 4$

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$y= \frac{4}{\sin(60 \degree) + 1}$

$y = 16 - 8 \sqrt{3}$

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The length of a Diameter is 3.714

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3 years ago

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An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are s

Kay [80]

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

<h3>Find the expression for the area of the shaded regions:</h3>

From the question we can say that the Hexagon has three shapes inside it,

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Square

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Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

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Area of second shaded region = Area of the square - Area of equilateral triangle

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,

⇒ Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle.

Learn more about area of a shape here:

brainly.com/question/16501078

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1 year ago

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