All categories

3 years ago

How to find the equation of a circle

Mathematics

1 answer:

Finger [1]3 years ago

4 0

Hmmm lemme do the first one only

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{5}{ h},\stackrel{3}{ k})\qquad \qquad 
radius=\stackrel{2}{ r}
\\\\\\
(x-5)^2+(y-3)^2=2^2\implies (x-5)^2+(y-3)^2=4$

You might be interested in

Solve the compound inequality 4x – 7 > 5 or 5x + 4 ≤ –6

bija089 [108]

Answer:

inequality form: x $\leq$ -2 or x > 3

interval notation form: (-∞,-2] ∪ (3,∞)

Step-by-step explanation:

I attached a picture that shows all the work. You begin by isolating then solving for x on both sides. Then form a solution using the information found out about x. For example, you can combine the found inequalities for x to solve that x must be GREATER than 3 while being LESS than -2. Using that you can form an line and make a line. Remember, when writing in interval notation form you always begin from the left to the right (in reference) to the number line.

5 0

2 years ago

Find the exponential function that passes through the points (2,80) and (5,5120)

juin [17]

Answer:

y = 5·4^x

Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

y1 = a·b^(x1)

y2 = a·b^(x1)

Divide the second equation by the first:

y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)

Take the inverse power (root):

(y2/y1)^(1/(x2 -x1) = b

Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.

a = y1/(b^(x1))

In summary:

b = (y2/y1)^(1/(x2 -x1))
a = y1·b^(-x1)

For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).

b = (5120/80)^(1/(5-2)) = ∛64 = 4

a = 80·4^(-2) = 80/16 = 5

The exponential function is ...

y = 5·4^x

3 0

3 years ago

Last year the population of Spoon Forks grew from 1250 to 1300. If the population of the town grows by the same percent this yea

Reptile [31]

Answer:

1352

Step-by-step explanation:

Firstly, we get the percentage growth last year. This is calculated as:

(1300-1250)/1250 * 100

= 4%

Now, we are assuming the growth rate is constant. So let’s calculate a 4% growth rate for this year. That would be:

4/100 * 1,300 = 52

The population this year would thus be 1300 + 52 = 1352

4 0

4 years ago

Solve the equation

NNADVOKAT [17]

Answer:

Step-by-step explanation:

ln x = -3

x = e^(-3)

x = 1/e^3

x = 0.04979

8 0

3 years ago

Read 2 more answers

Dante and Mia have a total of 350 pennies in their piggy banks, altogether. After Dante lost half of his pennies and Mia lost on

tatuchka [14]

Answer:

150 pennies were lost altogether

Step-by-step explanation:

Let the initial number of pennies owned by Dante be x pennies

Let the initial number of pennies owned by Mia be y pennies

Mathematically ;

x + y = 350 •••••••(i)

So after losing half, dante will have x/2 pennies left.

Mia lost 1/3 so she will have 2/3y left

So after all the losses, they both had equal amount of pennies

This means that;

x/2 = 2y/3

Cross multiply;

3x = 4y •••••••(ii)

Let’s solve both equations simultaneously;

From i , x = 350-y

Substitute this into equation ii

3(350-y) = 4y

1050-3y = 4y

7y = 1050

y = 1050/7

y = 150

since x = 350-y

x = 350-150 = 200

Now Dante loss x/2 = 200/2 = 100

Mia lost 1/3y = 1/3 * 150 = 50

Total pennies lost = 100 + 50 = 150

7 0

3 years ago