Tony bought a shirt for $40 and a second one at 50 percent off.

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

Please help I don't know how to do this

Vinil7 [7]

9514 1404 393

Answer:

7.84 to 8.16 ounces

Step-by-step explanation:

The difference between the actual amount in the bottle and the target amount of 8 ounces can be at most 2% of 8 ounces. That amount is ...

0.02×8 oz = 0.16 oz

The amount in the bottle can be this much higher:

8 + 0.16 = 8.16 . . . ounces

or, it can be that much lower:

8 - 0.16 = 7.84 . . . ounces

The range of values the bottle could contain is from 7.84 ounces to 8.16 ounces.

6 0

2 years ago

Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He is going to work 15 hours this week. At least how

RUDIKE [14]

Answer:

12 hours

Step-by-step explanation:

so what you do is take your $180 money amount and then divide it by your 15 or 12 dollar money amount and you should get your answer also your "answer" for the things you gave us is

15 x + 10 y = 180

3 0

3 years ago

A car is traveling at 45mph. What is the equation that models the total distance d traveled after h. What is the graph of the eq

Ostrovityanka [42]

D=45h

For example: 45mph times 2 hours equals 90 miles traveled

4 0

3 years ago

Which number sentence and model shows the quotient of 2/5 divided by 2/3 select two correct answers

murzikaleks [220]

Answer:

I can't understand so don't worry

8 0

2 years ago