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zimovet [89]
2 years ago
6

Could someone please explain how to solve for the area?

Mathematics
2 answers:
mixas84 [53]2 years ago
8 0

9514 1404 393

Answer:

  779.4 square units

Step-by-step explanation:

You seem to have several problems of this type, so we'll derive a formula for the area of an n-gon of radius r.

One central triangle will have a central angle of α = 360°/n. For example, a hexagon has a central angle of α = 360°/6 = 60°. The area of that central triangle is given by the formula ...

  A = (1/2)r²sin(α)

Since there are n such triangles, the area of the n-gon is ...

  A = (n/2)r²sin(360°/n)

__

For a hexagon (n=6) with radius 10√3, the area is ...

  A = (6/2)(10√3)²sin(360°/6) = 450√3 ≈ 779.4 . . . . square units

IRINA_888 [86]2 years ago
6 0

Given

=> An Equilateral Hexagon with s = 10√3

To Find

=>The area of the Figure

Step-by-step explanation:

The area of an Equilateral Hexagon = 3√3s²/2

Inserting the value of <em>S</em>

<em>=</em><em>></em><em> </em><em>3</em><em>√</em><em>3</em><em>*</em><em>(</em><em>1</em><em>0</em><em>√</em><em>3</em><em>)</em><em>²</em><em>/</em><em>2</em>

<em>=</em><em>></em><em> </em><em>3</em><em>√</em><em>3</em><em>*</em><em>3</em><em>0</em><em>0</em><em>/</em><em>2</em>

<em>=</em><em>></em><em>3</em><em>√</em><em>3</em><em>*</em><em>1</em><em>5</em><em>0</em>

<em>=</em><em>></em><em>4</em><em>5</em><em>0</em><em>√</em><em>3</em>

<em>=</em><em>></em><em>7</em><em>7</em><em>9</em><em>.</em><em>4</em><em>4</em><em>2</em><em>8</em>

<h2><em>=</em><em>></em><em> </em><em>7</em><em>7</em><em>9</em><em>.</em><em>4</em><em>4</em><em> </em><em>squared</em><em> </em><em>units</em></h2>
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1. Occasionally a savings account may actually pay interest compounded continuously. For each​ deposit, find the interest earned if interest is compounded​ (a) semiannually,​ (b) quarterly,​ (c) monthly,​ (d) daily, and​ (e) continuously. Use 1 year = 365 days.

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Step-by-step explanation:

The formula to find the total amount earned using compound interest is given as:

A = P(1 + r/n)^nt

Where A = Total amount earned after time t

P = Principal = $1031

r = Interest rate = 1.4%

n = compounding frequency

t = Time in years = 3 years

For each​ deposit, find the interest earned if interest is compounded

(a) semiannually

This means the interest is compounded 2 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/2) ^2 × 3

A = 1031 (1 + 0.007)^6

A = $ 1,075.07

A = P + I where

I = A - P

I = $1075.07 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.07

​(b) quarterly

This means the interest is compounded 4 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/4) ^4 × 3

A = 1031 (1 + 0.014/4)^12

A = $ 1,075.15

I = A - P

I = $1075.15 - $1031

A = P + I where

P (principal) = $ 1,031.00

I (interest) = $ 44.15

(c) monthly,

​ This means the interest is compounded 12 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/12) ^12 × 3

A = 1031 (1 + 0.014/12)^36

A = $ 1,075.20

A = P + I where

I = A - P

I = $1075.20 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.20

(d) daily,Use 1 year = 365 days

This means the interest is compounded 365 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/365) ^2 × 3

A = 1031 (1 + 0.00365)^365 × 3

A = $ 1,075.22

A = P + I where

I = A - P

I = $1075.22 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.22

(e) continuously. .

This means the interest is compounded 2 times in a year

Hence:

A = Pe^rt

A = 1031 × e ^0.014 × 3

A = $ 1,075.22

A = P + I where

I = A - P

I = $1075.22 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.22

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2 years ago
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