All categories

3 years ago

Find the ratio of the areas.

Mathematics

1 answer:

pshichka [43]3 years ago

3 0

9514 1404 393

Answer:

3 -2√2

Step-by-step explanation:

For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...

small area / large area = (1/(1+√2))^2 = 1/(3+2√2)

small area/large area = 3 -2√2

_____

The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.

You might be interested in

How do I graph y=3tanx?

galben [10]

Answer:

by graphing it

Step-by-step explanation:

Identify one hormone produced by an endocrine gland and state how it aids in the maintenance of homeostasis.

5 0

3 years ago

Which proportion could you use to convert 4.5 pints to fluid ounces

poizon [28]

In 1 pint there is 16 fluid ounces
16 x 4.5 = 72 fluid ounces

i hope this helps :)

5 0

2 years ago

Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find

postnew [5]

Answer:

a) 16.7% probability that E will speak first.

b) 3.33% probability that C will speak fifth and B will speak last.

c) 0.14% probability that the students will speak in the following order: DECABF.

d) 33.33% probability that A or B will speak first.

Step-by-step explanation:

The first speaker can be any of them. The second can be any of them bar the first. It continues until the last one. So the total number of outcomes is 6! = 720.

(a) E will speak first

The first one to speak is E.

The other five can be selected in any order. So there are 5! = 120 total outcomes in which E speaks first.

There is a 120/720 = 0.167 probability that E will speak first.

(b) that C will speak fifth and B will speak last

The fifth can only be C and the sixth can only be B.

The first four can be selected in any order. So there are 4! = 24 outcomes in which C speaks fifth and B last.

There is a 24/720 = 0.0333 probability that C will speak fifth and B will speak last.

(c) that the students will speak in the following order: DECABF

This is the only possible outcome in this order.

So there is a 1/720 = 0.0014 = 0.14% probability that the students will speak in the following order: DECABF.

(d) that A or B will speak first.

For A first, the following five can be in any order. So there are 5! = 120 outcomes in which A speaks first. The same logic and result for B.

So there are 240 outcomes in which A or B speaks first.

There is a 240/720 = 0.3333 = 33.33% probability that A or B will speak first.

5 0

3 years ago

The nth term of 50, 80, 110 is...

Olenka [21]

Answer:

$a_n=50+(n-1)30$

Step-by-step explanation:

Given series is,

50,80,110....

First term, a = 50

Common difference, d = 80-50 = 30

We need to find the nth term of the given sequence.

The nth term of an AP is given by :

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

Put a = 50 and d = 30 in the above formula

$a_n=50+(n-1)30$

Hence, the nth term of the sequence is $a_n=50+(n-1)30$ .

5 0

3 years ago

A pole that is 3m tall casts a shadow that is 1.22m long. At the same time, a nearby building casts a shadow that is 38.5m long.

vichka [17]

Refer to the diagram shown below.

The height of the pole is CD (3 m), and its shadow is AB (1.22 m).
The height of the building is h m, and its shadow is AD (38.5 m).

The two triangles ΔABC and ΔADE are similar because of AAA.
Therefore
$\frac{DE}{BC} = \frac{AD}{AB} \\\\ \frac{h}{3} = \frac{38.5}{1.22}$

Cross multiply.
1.22 h = 3*38.5 = 115.5
h = 115.5/1.22 = 140.91 m

Answer: 141 m (nearest meter)

5 0

4 years ago

Read 2 more answers