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Rainbow [258]
3 years ago
5

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0). Find the coordinates of S in terms of a.

Mathematics
2 answers:
FromTheMoon [43]3 years ago
4 0
The x  coordinate of S will be 1/2 * 2a = a.
and since  the half triangle is 30-60-90 the y coordinate will be sqrt3 a

so S  is (a , sqrt3a)
Serhud [2]3 years ago
3 0

Answer:

The S coordinate :

(a,\sqrt{3}a)\text{ and }(a,-\sqrt{3}a)

Step-by-step explanation:

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0)

We need to find the third coordinate of triangle RST.

R(0,0)

T(2a,0)

S(x,y)

RT=RS=ST (because RST is an equilateral triangle)

Using distance formula,

\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}=2a

\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}

x^2=(x-2a)^2

x^2=x^2+4a^2-4ax

x=a

\sqrt{x^2+y^2}=2a

x^2+y^2=4a^2

y^2=4a^2-a^2=3a^2

y^2=3a^2

y=\pm \sqrt{3}a

Hence, The S coordinate : (a,\pm \sqrt{3}a)

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Step-by-step explanation:

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2 years ago
Can you help me with this??<br> please explain
zepelin [54]
Hello!

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7 0
3 years ago
Read 2 more answers
For an upcoming field trip to the science center, the school will allow students to select one extra activity. The school survey
Pani-rosa [81]

The total amount that would be spent on all the activities is  $1605.40.

<h3>What is the total amount?</h3>

The total amount that would be spent on movies = (14/25) x 1200 x 1.55  = $1041.60

The total amount that would be spent on planetarium tickets = (7/25) x 1200 x 1.05 =352.80

The total amount that would be spent on backstage passes = (4/25) x 1200 x 1.10 =211.20

Total amount = 211.20 + 352.80 +  $1041.60 = $1605.40

Please find attached the complete question. To learn more about addition, please check: brainly.com/question/349488

7 0
2 years ago
(-----×1/4)÷6×3/9 I need the step to this problem so that I explain to my grandson how he he gets the answer
lesya692 [45]

Answer:

-----×1/72

Step-by-step explanation:

The <em>order of operations</em> says do these operations in order left to right. Please note that ÷ means the same as / unless you define it otherwise in your problem statement.

If you intend the ÷ symbol to be used to indicate everything to its left is divided by everything to its right, it is appropriate to use parentheses for that grouping, as in ...

  (-----×1/4)÷(6×3/9) = (-----×1/4)÷2 = -----×1/8

_____

Here, we're going to evaluate what you have written according to the usual rules as described above.

  (-----×1/4)÷6×3/9 = -----×1/24×3/9 = -----×(3/24)/9

  = -----×1/8/9

  = -----×1/72

_____

<em>Comment on the arithmetic</em>

Fractions are multiplied and divided in the usual way:

  a/b×c = (a×c)/b

  a/b/c = (a/b) × (1/c) = a/(b×c)

___

<em>Comment on fractions and parentheses</em>

Please note that parentheses are required on any numerator or denominator that consists of anything other than a single number or variable. (The exception is the case where the numerator is a product, because a·b/c = (a·b)/c with or without the parentheses.)

6 0
3 years ago
$10,000 for 20 years at 5% compounded annually
saveliy_v [14]

Answer:

$26532.98

Step-by-step explanation:

<u>Given:</u>

  • Principal = $10000
  • Profit rate = 5% PA compounded
  • Time = 20 years
  • Compounds = 20*1 = 20

<u>Sum is:</u>

  • 10000*(1 + 5/100)²⁰ ≈ 26532.98
3 0
3 years ago
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