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3 years ago

What is the area of a circle with a circumference of 4π^2 ?

1 answer:

8 0

$\bf \textit{circumference of a circle}\\\\
C=2\pi r\qquad\qquad C=4\pi^2\implies 4\pi^2=2\pi r\implies \cfrac{4\pi^2}{2\pi }=r
\\\\\\
\boxed{2\pi =r}\\\\
-----------------------------\\\\
\textit{area of a circle}\\\\
A=\pi r^2\qquad \qquad A=\pi \left( \boxed{2\pi } \right)^2\implies A=\pi \cdot 4\pi^2\implies \boxed{A=4\pi^3}$

You might be interested in

Write the equation of a rational function g(x) with vertical asymptotes at x = -3 and x = 3 , a horizontal asymptote at y = -4 a

Bezzdna [24]

Answer:

The equation for rational function for given asymptotes is

f(x)=(-4x^2-6)/{(x-3)(x+3)}

Step-by-step explanation:

Given:

vertical Asymptotes at x=3 and x=-3 and a horizontal asymptote at

y=-4 i.e parallel to x axis.

To find:

equation of a rational function i.e function in form p/q

Solution;

the equation should be in form of p/q

Numerator :denominator.

Consider f(x)=g(x)/h(x)

as vertical asymptote are x=-3 and x=3

denominator becomes, (x-3) and (x+3)

for horizontal asymptote to exist there should have same degrees in numerator and denominator which of '2'

when g(x) will be degree '2' with -4 as coefficient and dont have any real.

zero.

By horizontal asymptote will be (-4x^2 -6)

The rational function is given by

f(x)=g(x)/h(x)

={(-4x^2-6)/(x-3)(x+3)}.

3 0

2 years ago

2.1 km =

likoan [24]

2,100,000 Centimeters

3 0

2 years ago

Math again yay!...Ew math

Sliva [168]

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

$f(x)=x^2$

New function:

$g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2$

Transformations:

For a > 0

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}$

$\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}$

If the parent function is shifted ¹/₄ unit up:

$\implies g(x)=x^2+\dfrac{1}{4}$

If the parent function is shifted ¹/₄ unit down:

$\implies g(x)=x^2-\dfrac{1}{4}$

If the parent function is compressed vertically by a factor of ¹/₄:

$\implies g(x)=\dfrac{1}{4}x^2$

If the parent function is stretched horizontally by a factor of ¹/₂:

$\implies g(x)=\left(\dfrac{1}{2}x\right)^2$

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

4 0

1 year ago

Over a 3.5 year period, 27.5 inches of snow fell in Jackson City. What was the average yearly snowfall in Jackson Cit

Ilya [14]

27.5 / 3.5 = 7.86; The average yearly snowfall was 7.86 inches.

7 0

2 years ago

What is the value of z in the equation 2(4z − 6 − 6) = 170 − 46? 12.5 15.5 16.5 18.5

vivado [14]

2(4z - 6 - 6) = 170 - 46

2(4z - 12) = 124 |use distributive property: a(b - c) = ab - ac

8z - 24 = 124 |add 24 to both sides

8z = 148 |divide both sides by 8

z = 18.5

4 0

3 years ago

Read 2 more answers