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3 years ago

A regular polygon has a exterior of 18 degrees. How many sides does it have?

2 answers:

7 0

The angles of a regular polygon add up to 360 degrees so if it is a REGULAR polygon then all of the angles must be equal/the same. So you do 360 divided by 18 to see how many sides there are so that would give a simple answer of 20. I was able to work this out in my head by doing 36 divided 18 (I took the 0 off the 360 to make the sum easier) which = 2 and then added the 0 back on from the 360 which gave me 20. So the regular polygon has 20 sides

blondinia [14]3 years ago

4 0

The formula of the measurement of an exterior angle of a regular polygon is
β = 360°/n
where β = exterior angle and n = number of sides

Therefore,
n = 360°/β = 360°/18° = 20 sides

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago

Water drips from a faucet at a rate of 41 drops/minute. Assuming there are 15,000 drops in a gallon, how many minutes would it t

worty [1.4K]

Answer:

366 mins

Step-by-step explanation:

first divide 15000 by 41 since there are 41 drops per minute and you get 365.85 so then you round it and get 366

5 0

3 years ago

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Please help with 11c!?

Contact [7]

Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

$F=P(1+r)^t$

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

$F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t$

To solve exponentials, we can take Natural Log (Ln) of both sides:

$2=(1.08)^t\\Ln(2)=Ln((1.08)^t)$

Using the rule shown below we can simplify and solve:

$Ln(a^b)=bLn(a)$

We can write:

$Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064$

To the nearest year, that would be about 9 years

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3 years ago

If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?

GarryVolchara [31]

Answer:

Step-by-step explanation:

Angle 4 × Angle 3 = 90

Complementary angles

11x + 4x = 90

15x = 90

x = 6

Angle 3 = 4x = 4(6) = 24°

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3 years ago

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Irina-Kira [14]

Answer:

x > 125

Step-by-step explanation:

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3 years ago

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