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2 years ago

A model of a soccer ball is made up of regular pentagons and hexagons.

Mathematics

1 answer:

Monica [59]2 years ago

5 0

An apothem is a line from the center of a regular polygon at right angles to any of its sides.

For part A,

We want to find area of pentagon (5 sided figure) given apothem is 1.38 in and side length as 2 inch.

If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?

$A=0.5bh\\A=0.5(1)(1.38)\\A=0.69$ square inches

How many such triangles are there in a pentagon? 10. So we multiply 0.69 by 10 to get total area of pentagon.

Area of Pentagon = $0.69*10=6.9$ square inches.

For part B,

We want to find area of hexagon (6 sided figure) given apothem is 1.73 in and side length as 2 inch.

If we look at the picture shown (attached), we can see that a triangle is formed. What is the area of this triangle?

$A=0.5bh\\A=0.5(1)(1.73)\\A=0.865$ square inches

How many such triangles are there in a hexagon? 12. So we multiply 0.865 by 12 to get total area of hexagon.

Area of Hexagon = $0.865*12=10.4$ square inches.

ANSWER:

Area of Pentagon is 6.9 square inches.

Area of Hexagon is 10.4 square inches.

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Convert 1/15 into a decimal correct to 2 decimal places

Citrus2011 [14]

Answer:

$\frac{1}{15} = 0.\overline{66}$

Step-by-step explanation:

We proceed to show the procedure to calculate the given fraction into a decimal form:

1) Since numerator is less than denominator, the integer component of the decimal number is zero:

$\frac{1}{15} = 0.xx$

2) We multiply the numerator by 10 and find the tenth digit:

$\frac{10}{15} = 0$

Then,

$\frac{1}{15} = 0.0xx$

3) We multiply the fraction in 2) by 10 and find the hundredth digit:

$\frac{100}{15} = 6$

Then,

$\frac{1}{15} = 0.66x$

And the remainder is:

$r = 100-15\times 6$

$r = 10$

4) We multiply the remainder by 10 and divide this result by the denominator to determine the thousandth digit:

$\frac{100}{15} = 6$

Then,

$\frac{1}{15} = 0.666$

This question asks us to write a decimal correct to 2 decimal places, which has the characteristic that is infinite periodical decimal. Then, the result correct to 2 decimal places is:

$\frac{1}{15} = 0.\overline{66}$

3 0

2 years ago

Answer Is not C please help

Katyanochek1 [597]

Answer:

Step-by-step explanation:

Well since it is arthimetic sequence we know the formula

We know d is difference between second term and first so it will be -5- (-12)= -5+12= 7

$a_{n}= a _{1}+ d (n-1) \\a_{n}= -12+7(n-1)\\a_{n} = -12+7n-7\\a_{n}= 7n-19$

the domain of this is 1,2,3,4.......

range is -12,-5,2,9.......

Therefore answer is B.

5 0

3 years ago

Determine the domain of {(1,-2), (-2,0), (-1,2), (1,3)}

I am Lyosha [343]

Answer:

{-2, -1, 1}

Step-by-step explanation:

Domain is a list of x values

{-2, -1, 1}

3 0

2 years ago

Samiya bought a tree 3 inches long. Each year, the tree expected to grow 5 inches. How long (How many years) it takes the tree t

Ghella [55]

Answer: 19 years to reach 98 inches

Step-by-step explanation:

Its already 3 inches tall, if it grows 5 inches every year or expected to it would take : 3 + 5 = 8

8 + 5 = 13

13 + 5 = 18

18 + 5 = 23

23 + 5 = 28

28 + 5 = 33

33 + 5 = 38

38 + 5 = 43

43 + 5 = 48

48 + 5 = 53

And it goes on until 98 inches. Leaving your answer : 19 years.

4 0

2 years ago

Find the point of intersection between the lines: y=3x-1 and y-x+3=0

Anon25 [30]

Answer:

( - 1 , - 4 )

Step-by-step explanation:

y = 3x - 1

y = x - 3

3x - 1 = x - 3 ⇒ x = - 1

y = 3( - 1 ) - 1 = - 4

y = - 4

( - 1 , - 4 )

8 0

2 years ago