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ki77a [65]
2 years ago
15

NO LINKS!! PART 2: Find the EXACT area and Circumference of each circle​

Mathematics
2 answers:
Tema [17]2 years ago
7 0

Answer:

  2. center: (2, 5); radius: 3; Area: 9π; Circumference: 6π

  4. center: (0, 0); radius: 8; Area: 64π; Circumference: 16π

Step-by-step explanation:

The standard form equation for a circle is ...

  (x -h)² +(y -k)² = r² . . . . . . center (h, k), radius r

The value of r is used in the formulas for area (A) and circumference (C):

  A = πr²

  C = 2πr

__

<h3>2.</h3>

Comparing the given equation to the standard form, we see ...

  (x -h)² +(y -k)² = r²

  (x -2)² +(y -5)² = 9

  (h, k) = (2, 5) . . . . center

  r² = 9

This tells us ...

  r = √9 = 3 . . . . radius

The Area formula uses r² directly:

  Area = πr² = π(9)

  Area = 9π

The Circumference formula uses r:

  Circumference = 2π(3)

  Circumference = 6π

__

<h3>4.</h3>

Comparing the given equation to the standard form, we find ...

  (h, k) = (0, 0) . . . . center

  r² = 64   ⇒   r = √64 = 8 . . . . radius

  Area = 64π

  Circumference = 2π(8) = 16π

AfilCa [17]2 years ago
5 0

#2

  • (x-2)²+(y-5)²=9
  • (x-2)²+(y-5)²=3²

Radius=3

Circumference

  • 2π(3)
  • 6π units

Area

  • πr²
  • 3²π
  • 9π units²

#4

  • x²+y²=64
  • x²+y²=8²

Radius=8

Circumference

  • 2π(8)
  • 16π units

Area

  • πr²
  • π(8)²
  • 64π units ²
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PLS HELP
Anika [276]

The chairs in the auditorium illustrates an arithmetic sequence

  • The recursive rule is:  an = an-1 + 8; a1 = 26
  • The explicit rule is:  an = 18 + 8n
  • There are 74 seats in the 7th row
  • 840 chairs can fit the auditorium

<h3>The recursive rule</h3>

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

<h3>The explicit rule</h3>

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

<h3>The number of seats in the row 7</h3>

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

<h3>The sigma notation</h3>

We have the maximum number of rows to be 12.

So, the sigma notation would be:

\sum\limits^{12}_{n=1} {18 + 8n}

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

brainly.com/question/6561461

7 0
2 years ago
A square has a side length of 21 + 11s. Select TWO equivalent
Misha Larkins [42]

Answer:

I choose option c hope it helps

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3 years ago
Earlier this month, 69% Californians voted 'yes' on Measure H: a sales tax measure to fund homeless services and prevention.Samp
VashaNatasha [74]

Answer:

0.59

Step-by-step explanation:

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2 years ago
Which statement below compares the decimals correctly? (3 points) A 0.63 &lt; 0.48 B 0.48 = 0.63 C 0.63 &gt; 0.48 D 0.48 &gt; 0.
Bad White [126]

Answer:

(c)\ 0.63 > 0.48

Step-by-step explanation:

Given

0.63 and 0.48

Required

Which compares them correctly

(a)\ 0.63 < 0.48

This is incorrect because 0.63 is greater

(b)\ 0.48 = 0.63

This is also incorrect because 0.63 is greater

(c)\ 0.63 > 0.48

This is also correct because 0.63 is greater

(d)\ 0.48 > 0.63

This is also incorrect because 0.63 is greater

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3 years ago
In a different dimension, cows have $x+3$ legs, with 3 toes on each leg. Chickens have $2x-4$ legs, with 7 toes on each leg. If
Juli2301 [7.4K]

Answer:

20x-10

Step-by-step explanation:

Cows have x+3 legs and 3 toes on each leg, if we want to find the number of toes of ONE cow we have to multiply the legs by the toes giving the following:

3(x+3) \quad (1)

But we have two cows so (1) we have to multiply it by 2 giving a total of:

2(3(x+3))\\6(x+3)\\6x+18 \quad (2)

By the other hand chickens have 2x-4 legs and 7 toes on each leg, if we want to find the number of toes we have to multiply the legs by the toes giving the following:

7(2x-4)\\14x-28 \quad (3)

To find the total amount of toes we have to add (2) and (3)

(6x+18)+(14x-28)\\20x-10

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2 years ago
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