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dusya [7]
3 years ago
9

Triangle ABC is an equilateral triangle.Find the angle of rotation that maps A to B

Mathematics
1 answer:
svet-max [94.6K]3 years ago
3 0

The sum of the inner angles of any triangle is always 180°, i.e. you have


\alpha + \beta + \gamma = 180


In the particular case of an equilater triangle, all three angles are the same, so

\alpha = \beta = \gamma


and the expression becomes


\alpha + \beta + \gamma = \alpha + \alpha + \alpha = 3\alpha = 180


which implies \alpha = 60


So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.


Of course, this is equivalent to a clockwise rotation of 120 degrees.


Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)

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How to find the square root of complex numbers?? Find the square root of (6+8i) ??​
ivann1987 [24]

Answer:

2 \sqrt{2}  + i \sqrt{2}

Step-by-step explanation:

The square of a complex number is a complex number. Here, we have:

{(a + bi)}^{2}  = 6 + 8i

{a}^{2}  + 2abi -  {b}^{2}  = 6  + 8i

We then have this system of equations:

{a}^{2}  -  {b}^{2}  = 6

2ab = 8

Solving this system:

ab = 4

b =  \frac{4}{a}

{a}^{2}  -  {( \frac{4}{a}) }^{2} = 6

{a}^{2}  -  \frac{16}{ {a}^{2} } = 6

{a}^{4}  - 16 =  6{a}^{2}

{a}^{4}  - 6 {a}^{2}  - 16 = 0

( {a}^{2}  - 8)( {a}^{2}  + 2) = 0

{a}^{2}   = 8

a = 2 \sqrt{2}

b =  \frac{4}{2 \sqrt{2} } =  \sqrt{2}

6 0
2 years ago
Read 2 more answers
Jill invested $20,000 in an account that earned 5.5% annual interest, compounded annually. What is the value of this account aft
noname [10]

The value of this account in 10 years is given by the formula:

FV = P*(1+r)^t

where FV is the future value in the account after 10 years(to be calculated)

P is the principal invested at the beginning

r is the interest rate and

t is the time horizon in years

Given, Invested Amount (P) = 20,000

Interest rate (r) = 5.5% = 0.055

Time horizon (t) = 10 years = 10

Substituting the formula, FV = 20,000*(1+0.055)^10 = 20,000*1.055^10 = 20,000*1.708144458 =  34,162.89

The value of this account after 10 years =$34,162.89 (Rounded to the nearest cent)

7 0
3 years ago
2x + 2x2 + 2x3 + ... + 2x<br> O arithmetic<br> O geometric<br> O both<br> O neither
Mkey [24]

Answer:

16 ALB

Step-by-step explanation:

ayudame wey andale

6 0
3 years ago
At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At t
DENIUS [597]

Answer: 34%

Step-by-step explanation:

Creating a table with the information will help us.

<6h of sleep - 75% reported tired | 25% reported ok

>6h of sleep - 70% reported ok | 30% reported tired

80% of all interns received <6h of sleep

Let's imagine that we have 100 interns at this hospital

             <6h               |          >6h          Total

Tired       75% of 80          30% of 20    

 ok         25% of 80          70% of 20

Total        80                |             20            100

             <6h                |          >6h            Total

Tired   |    60                |             6                66

 ok     |     20               |            14               34

Total   |     80               |             20             100

what percent of the interns report no feelings of tiredness during their shifts?

34/100 = 34%

7 0
2 years ago
Please help me on this
Vika [28.1K]
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