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Leya [2.2K]
2 years ago
6

If the perimeter of an equilateral triangle is 30cm, find its area. ​

Mathematics
1 answer:
lora16 [44]2 years ago
7 0

Answer:

A ≈ 43.3 cm²

Step-by-step explanation:

the area (A) of an equilateral triangle is calculated as

A = \frac{s^2\sqrt{3} }{4} ( s is a side of the triangle )

given perimeter = 30 cm , then

s = 30 cm ÷ 3 = 10 cm

then

A = \frac{10^2\sqrt{3} }{4} = \frac{100\sqrt{3} }{4} = 25\sqrt{3} ≈ 43.3 cm² ( to the nearest tenth )

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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
BabaBlast [244]

Step-by-step explanation:

the introduction of a fraction tells us that we are dealing with multiplications, and therefore a geometric sequence (where every new term is created by multiplying the previous term by a constant factor, the ratio r).

I think your teacher made a mistake, or you made one when typing the question in here.

there is no factor r that creates

15×r = 9

and

9×r = 5/27

it would mean that

15 × r² = 5/27

r² = 5/27 / 15 = 5/27 × 1/15 = 5/405 = 1/81

r = 1/9

but 15 × 1/9 = 5 × 1/3 = 5/3 is NOT 9

and 9 × 1/9 = 9/9 = 1 is NOT 5/27

so, this can't be right.

on the other hand

15 × r = 9

r = 9/15 = 3/5

and then

9 × 3/5 = 27/5

so, either the sequence should have been

15, 5/3, 5/27

or (and I suspect this to be true)

15, 9, 27/5

under that assumption we have

s1 = 15

r = 3/5

sn = sn-1 × r = s1 × r^(n-1) = 15 × (3/5)^(n-1)

s10 = 15 × (3/5)⁹ = 15 × 19683/1953125 =

= 3 × 19683/390625 = 59049/390625 =

= 0.15116544 ≈ 0.151

6 0
2 years ago
Suppose an=3an-1 -5an-2 -4an-3. and a4= -7, a5=-36, a6=-85 , find a1 , a2, a3​
maria [59]

Answer:

        a_1=4\\\\a_2=0\\\\a_3=3

Explanation:

The equation is:

      a_n=3a_{n-1}-5a_{n-2}-4a_{n-3}

and

      a_4=-7, a_5=-36, a_6=-85

<u>1. Subsittute n = 6 into the equation:</u>

      a_6=3a_{5}-5a_{4}-4a_{3}

      Now subsititute the known values:

       -85=3(-36)-5(-7)-4a_{3}

      You can solve for a_3

      -85=-108+35-4a_{3}\\\\4a_3=12\\\\a_3=12/4\\\\a_3=3

<u />

<u>2. Substitute n = 5 into the equation:</u>

    a_5=3a_{4}-5a_{3}-4a_{2}

     Substitute the known values and solve for a_2

        -36=3(-7)-5(3)-4a_{2}\\\\4a_2=-21-15+36=0\\\\a_2=0

<u>3. Substitute n = 4 into the equation, subsitute the known values and solve for </u>a_1<u />

       a_4=3a_{3}-5a_{2}-4a_{1}

        -7=3(3)-5(0)-4a_{1}\\\\4a_1=9+7=16\\\\a_1=4

7 0
3 years ago
Between which two integers does 35 lie?
iren2701 [21]

The answer is the first choice, "5 and 6."

The square root of 35 is equal to 5.92, which is in between the numbers 5 and 6.

7 0
3 years ago
Express 0.000089 in scientific notation
MrRissso [65]
8.9 x 10^-5 in scientific notation
5 0
3 years ago
A rectangular balcony is 14 feet long and 6 feet wide. What is its area?
Verdich [7]
84 ft² = 14 ft × 6 ft
4 0
3 years ago
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