Please help me out thank you!

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ <u>923.558 m²</u>

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

What is the answer to this

arlik [135]

$S\frac{O}{H} C\frac{A}{H} T\frac{O}{A}$ or $Sin\frac{Opposite}{Hypotenuse}Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Opposite}{Adjacent}$

At the point/angle E:

- the adjacent side(side <u>next to</u> the point/angle) is ED

- the opposite side(side of the triangle <u>across</u> from the point/angle) is DF

- the hypotenuse (the<u> longest side</u> of the triangle) is EF.

sin ∠E = $\frac{opposite}{hypotenuse}$

sin ∠E = $\frac{6}{10} = \frac{3}{5}$ (simplified)

5 0

4 years ago

Read 2 more answers

The expression 3^2*3^3*3^4 is equivalent to?<br> Show all your work please

loris [4]

Cool! So OK I'll take you through it.
You just need to take everything 1 step at a time, as you might already know.

First
3 to the second is 9

Second
The first part included like this 9*(3 to the third) which is 243

Third
The second part is included into the question like 243*(3 to the fourth) which is 243*81

Fourth
243*81 = 19,683

Your Answer
(3^2)*(3^3)*3^4) = 19,693

Hope That Helps and Correct Me If I'm Wrong!

3 0

4 years ago

Read 2 more answers

Give the “best” big-oh notation to describe the complexity of the algorithm that prints all bit strings of length n.

artcher [175]

It is correct to state that a bit can be in one of 2 states, either 1 or 0.

A bit is is a single binary digit. A bit can either be "1" or "0".

<h3>What is the explanation to the above answer?</h3>

We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.

The first time, for generation and
The second for reading.

Hence, Our time is now O(2ⁿ⁺¹) = O(2ⁿ)

Learn more about bits at;
brainly.com/question/2263640
#SPJ1

4 0

2 years ago

Quien me ayuda es suma de polinomios

arsen [322]

Sorry no espanol...sorry

6 0

3 years ago