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3 years ago

What is the area of a circle with the equation (x - 3)^2 + (y + 2)^2 = 64

Mathematics

1 answer:

saul85 [17]3 years ago

4 0

Answer:

200.96 square units

Step-by-step explanation:

$(x - 3)^2 + (y + 2)^2 = 64\\(x - 3)^2 + (y + 2)^2 = 8^{2} \\equating \:it\: with\\(x - h)^2 + (y -k)^2 = r^{2}\\we\:find;\\r^{2} =8^{2}\\\therefore radius\: (r) = 8 units\\Area\: of\: circle\\=\pi r^{2} \\=3.14\times8^2\\=3.14\times 64\\=200.96 \:units^{2}$

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Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the

Assoli18 [71]

Answer:

The equation of line is y = 3 x - 1 , i.e option A .

The rate of change = m = 3

Step-by-step explanation:

Given as :

The points are

( $x_1$ , $y_1$ ) = (- 2, -7)

( $x_2$ , $y_2$ ) = (1 , 2)

Let The slope = m

<u>Now, The slope is calculated in points form</u>

So, Slope = $\dfrac{y_2-y_1}{x_2-x_1}$

I.e m = $\dfrac{2-(-7)}{1-(-2)}$

or, m = $\dfrac{9}{3}$

I.e m = 3

So, The slope of points = m = 3

I,e Rate of change = m = 3

<u>Now, the equation of line in slope - point form can be written as</u>

y - $y_1$ = m ( x - $x_1$ )

where m is the slope of line

i.e y - (-7) = ( 3 ) × ( x - (-2) )

or, y + 7 = 3 × (x + 2)

∴ y + 7 = 3 x + 6

Or, y = 3 x + 6 - 7

Or, y = 3 x - 1

So, The equation of line is y = 3 x - 1

Hence, The equation of line is y = 3 x - 1 , i.e option A .

And The rate of change = m = 3 Answer

8 0

3 years ago

On a farm there was a cow. And on the farm there were 2 sheep. There were also 3 chickens. What is the total mass of the 1 cow,

RoseWind [281]

The total mass of the living things on the farm is 588 kg.

<h2><u>Mass calculation</u></h2>

Since on a farm there was a cow, 2 sheep and 3 chickens, to determine what is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm, the following calculation must be performed :

(6.2 x 10) + (4 x 10 x 10) + (2 x 6 x 10) + (3 x 2 x 1) = X
62 + 400 + 120 + 6 = X
588 = X

Therefore, the total mass of the living things on the farm is 588 kg.

Learn more about mass calculation in brainly.com/question/14695611

8 0

2 years ago

PLEASE HELP SUPER EASY!!!

Effectus [21]

A1. 12 i.e option D

A2. 3n-7 i.e option A

A3. -6n+20 i.e option D

A4. -70 i.e option C

Step-by-step explanation:

aₙ = a₁ + (n - 1) × d

aₙ = the nᵗʰ term in the sequence

a₁ = the first term in the sequence

d = the common difference between terms

Using the above formula to solve the first part, we have :

-8 = a₁ + (2-1) × 5

-13 = a₁

a₆ = -13 + (6-1) × 5

a₆ = 12

For the second part, we have :

aₙ = -4 + (n-1)×3

aₙ = -4 + 3n -3

aₙ = 3n-7

For the third part, we have :

a₁=14 ; d=-6

aₙ = 14 + (n-1)×(-6)

aₙ = -6n + 20

For the fourth part, we have :

aₙ = 14 + (15-1)×(-6)

aₙ = -70

7 0

3 years ago

C). The local bus service has 2 lines of buses that start together at 8

jok3333 [9.3K]

Answer:

3 times

Step-by-step explanation:

Firstly we calculate the number of minutes between 8 and 11 am

The number of hours is 3 hours

The number of minutes is 180 minutes since 1 hour is 60 minutes

Now out of 180, to know the number of times that they both leave, we need to get the multiples of both between 0 and 180

The multiples are;

60, 120, 180

This means that they leave together 3 times

8 0

2 years ago

What is the smallest number with the factors 1,2,3,4, and 5? What is the special name for it?

klasskru [66]

To find LCM
factor and eliminate ones already represented
1=1
2=2
3=3
4=2*2
5=5

1*2*2*3*5=60

7 0

3 years ago