Sarah is 25 years older than her son gavin in 10 years sarah will be twice gavin's age how old was sarah and gavin now

Find the center and radius of the circle whose equation is x2 + y2 - 6x-2y+4= 0

marin [14]

Answer:

The center of the circle = (3, 1)

The radius of a circle is given as r = √6

Step-by-step explanation:

The equation of a circle is given as:

( x - a)² + (y - b)² = r²

where ( a , b) = center of the circle

r = radius of the the circle

In the question above, we are given the equation of a circle as

x² + y² - 6x - 2y + 4= 0

In order to find the center and radius of this circle we would use completing the square method to solve it

Step 1

Collect the like terms

x² - 6x + y² - 2y + 4= 0

Step 2

Complete the square for both x and y

x² - 6x + (-6/2)² + y² - 2y + (-2/2)² = - 4 +(- 6/2)² + (-2/2)²

x² - 6x + (-3)² + y² - 2y + (-1)² = -4 + (3)² + (1)²

x² - 6x + 9 + y² - 2y + 1 = -4 + 9 + 1

(x² - 6x + 9) + (y² - 2y + 1 )= -4 + 9 + 1

(x² - 3x - 3x +9) + ( y² - y - y +1) = 6

x(x - 3) -3( x - 3) + y( y - 1) - 1( y - 1) = 6

(x - 3) (x -3) +(y - 1) ( y - 1) = 6

(x - 3)²(y - 1)² = 6

Since,

The equation of a circle is given as:

( x - a)² + (y - b)² = r²

where ( a , b) = center of the circle

r = radius of the the circle

The equation of the the circle for the above question is calculated as:

(x - 3)²(y - 1)² = 6

where ( a , b) = center of the circle = (3, 1)

r = radius of the the circle

r² = 6

r = √6

8 0

3 years ago

Problem: A scuba diver swam 30 feet below sea level. After a couple of minutes, he went down 10 feet more. Find the total distan

QveST [7]

Answer: -40 feet

Step-by-step explanation: the scuba diver starts at sea level (0) then swims down 30 feet (-30). after a couple minutes, goes down 10 feet more (-40) the scuba diver will now be -40 down from sea level. so it should be -40 because the scuba diver swam that much down.

lmk if this is incorrect, i'm not quit sure if it is or not. if i'm wrong, i'm so sorry!!

:)

3 0

3 years ago

What is the slope of the equation below?<br> 2y = 10x – 8<br> A.2<br> B.-8<br> C.10<br> D.5

blondinia [14]

Answer:

D) 5

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Divide 2 from all terms within the equation:

(2y)/2 = (10x - 8)/2

y = (10x)/2 - (8)/2

y = 5x - 4

Note the slope-intercept form:

y = mx + b

y = y

x = x

m = slope

b = y-intercept.

In this case, 5 is in place of m, or your slope.

D) 5 is your answer.

~

8 0

3 years ago

Read 2 more answers

Show all work to identify the asymptotes and state the end behavior of the function f(x)=3x/x-9

lorasvet [3.4K]

Using the asymptote concept, we have that:

The vertical asymptote is x = 9.

The horizontal asymptote is y = 3.

The end behavior is that as $x \rightarrow \infty, y \rightarrow 3$ .

<h3>What are the asymptotes of a function f(x)?</h3>

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

$f(x) = \frac{3x}{x - 9}$

For the vertical asymptote, we have that:

x - 9 = 0 -> x = 9.

For the horizontal asymptote:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{3x}{x - 9} = \lim_{x \rightarrow \infty} \frac{3x}{x} = \lim_{x \rightarrow \infty} 3 = 3$