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2 years ago

A regular hexagon has an apothem of 14. 7 inches and a perimeter of 101. 8 inches. What is the area of the hexagon?.

Mathematics

1 answer:

AleksAgata [21]2 years ago

3 0

Answer:

748.23 in²

Step-by-step explanation:

<u>Area of a Regular Polygon</u>

$\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}$

where:

n = number of sides
l = length of one side
a = apothem

Given:

n = 6
l = 101.8 ÷ 6
a = 14.7

Substituting the given values into the formula and solving for A:

$\implies \textsf{A}=\dfrac{6 \cdot \dfrac{101.8}{6} \cdot 14.7}{2}$

$\implies \sf A=\dfrac{101.8 \cdot 14.7}{2}$

$\implies \sf A=\dfrac{1496.46}{2}$

$\implies \sf A=748.23$

Therefore, the area of the hexagon is 748.23 in²

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Ronald Dairo is helping the local indus-

nadya68 [22]

Answer:

Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.

Step-by-step explanation:

Papaya rosette pieces on first day = 5890

Papaya rosette Pieces on second day = 7020

Papaya rosette Pieces of third day = 8150

Let

$a_1 = 5890\\a_2 = 7020\\a_3 = 8150$

We can check if these numbers are part of a sequence.

In order to check, common difference will be found first.

$d = a_2-a_1 = 7020-5890 = 1130\\d =a_3-a_2 = 8150-7020 = 1130$

It can be observed that the common difference is same. When the common difference is same, the sequence is said to be an arithmetic sequence.

The formula for arithmetic sequence is given by:

$a_n = a_1+(n-1)d$

Putting the values

$a_n = 5890+(n-1)(1130)\\a_n = 5890+1130n-1130\\a_n =4760+1130n$

The formula for nth term can be used to find any term. As we have to find the number of papaya rosette pieces after two weeks which means that we need to find the number of pieces on 14th day.

So,

$a_{14}= 4760+1130(14)\\a_{14} = 4760+15820\\a_{14} = 20580$

Hence,

Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.

5 0

3 years ago

1.What is the ratio of v to v max expressed as a percentage when [s] = 30 km

Helga [31]

Answer:

(a)96.77%

(b)3.23%

Step-by-step explanation:

Starting with the Michaelis-Menten equation which is used to model biochemical reactions:

Dividing both sides by $V_{\max }}$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}$

Where: $V_{\max }} =$ maximum rate achieved by the system

$K_{\mathrm {M} }}$ =The Michaelis constant

${\displaystyle {\ce {[S]}}}=$ Substrate concentration

(a) When $[S]=30K_M$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{30K_M}{K_M + 30K_M}\\\dfrac{v}{V_{max}}=\dfrac{30}{1 + 30}\\\dfrac{v}{V_{max}}=\dfrac{30}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{30}{31}X100=96.77\%$

(b)When $K_M=30[S]$

$\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{[S]}{30[S] + [S]}\\\\=\dfrac{1[S]}{30[S] + 1[S]}\\=\dfrac{1}{30 + 1}\\\dfrac{v}{V_{max}}=\dfrac{1}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{1}{31}X100=3.23\%$

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3 years ago

In how many distinct ways an the letters of the word Atlanta be arranged

konstantin123 [22]

Taking into account the repeated ones it would be 7! what is 7*6*5*4*3*2*1

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3 years ago

Producing a musical costs $88,000 plus $5900 per performance. one sold out performance earns $7500 in revenue. If every performa

yan [13]

X = # of perfomances

y = total amount of money

Income: y = 7500x

Expense: y = 5900x + 88000

Substitution:

7500x = 5900x + 88000

1600x = 88000

x = 55

y = 7500(55) = $412,500

55 performances are needed to break-even.

5 0

3 years ago

14 is 4 less than three times k

UkoKoshka [18]

14= 3k-4
_ less than _ = -
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3 years ago