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3 years ago

Determine the center and radius of the following circle equation: x^2+y^2-6x-8y+24=0

Mathematics

1 answer:

slega [8]3 years ago

6 0

Center is (3, -4) and radius is 1

Step-by-step explanation:

Step 1: Find center and radius of the circle with equation x² + y² - 6x - 8y + 24 = 0

The standard form of the equation of a circle is x² + y² + 2gx +2fy + c = 0, where center is (-g, -f) and radius = √g² + f² - c

By comparing the 2 equations, 2g = -6, 2f = 8 and c = 24

⇒ g = -6/2 = -3

⇒ f = 8/2 = 4

⇒ c = 24

Step 2: Find center.

Center = (-g. -f) = (3, -4)

Step 3: Find radius.

Radius = √g² + f² - c = √3² + (-4)² - 24

= √9 + 16 - 24 = √1 = 1

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3 years ago

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3 years ago

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Describe a sequence of transformations that transform the graph of the parent function f into the graph of the function g.

olganol [36]

Answer:

The sequence is: Refection across y-axis, Horizontal Shrink, Horizontal Translation and Reflection across x-axis.

Step-by-step explanation:

Since, we are given f(x) = square root x.

The sequence of transformations which transform f(x) into g(x) is given by:

1. Reflection across y-axis i.e. f( x ) to f( -x )

2. Horizontal Shrinking i.e. f( -x ) to f( -x/2 )

3. Horizontal Translation i.e. f( -x/2 ) to f( -x/2 + 3 )

4. Reflection across x-axis i.e. f( -x/2 + 3 ) to -f( -x/2 + 3).

The step by step graphical representation can also be viewed below.

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3 years ago

How many 1/10's are in 2/5?

goblinko [34]

There is 4 1/10's in 2/5.

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4 years ago

A skateboarder starting from rest accelerates down a ramp at 2 m/s for 2 s. What is the final speed of the skateboarder

Sedaia [141]

Initial speed of the skateboard (u) = 0 m/s (Starts from rest)

Acceleration of the skateboard (a) = 2 m/s²

Time taken by the skateboard (t) = 2s

By using equation of motion, we get:

$\bf \longrightarrow v = u + at \\ \\ \rm \longrightarrow v = 0 + 2 \times 2 \\ \\ \rm \longrightarrow v = 4 \: m {s}^{ - 1}$

$\therefore$ Final speed of the skateboard(v) = 4 m/s

7 0

3 years ago