if you vertically stretch the linear parent function, f(x)=x, by a factor of 12, what is the equation of the new function

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

3 years ago

^2\left(\frac{d}{dx}\left(\frac{\partial }{\partial x}\left(\right)\right)\right)^'\frac{\partial }{\partial x}\left(\log _{ }\l

LenaWriter [7]

Answer:

ok what

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

16 cm + B 11 cm 4 cm

yawa3891 [41]

Answer:

31

Step-by-step explanation:

5 0

3 years ago

What is the answer ?how can I find it?

satela [25.4K]

The per store donated 11 and 3/8 pounds of cat food... first you gotta make the denominators equal so 19 and 3/4 becomes 19 and 6/8 then you add the puppy and dog food together (19 6/8 +18 7/8= 38 5/8) then you take 50 and subtract the value you just got (50 - 38 5/8) and you get tour answer at 11 and 3/8 pounds

6 0

3 years ago

Help please!:( right answers only please

bagirrra123 [75]

Answer:

100 dollars a month I think

3 0

3 years ago

Read 2 more answers