Let f be the function that determines the area of a circle (in square cm) given the radius of the circle in cm, r. That is, f(r) represents the area of a circle (in square cm) whose radius is r cm. Use function notation to complete the following tasks a. Represent the area (in square cm) of a circle whose radius is 4 cm. Preview syntax error b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm. # Preview syntax error c. Represent the area of 5 circles that all have a radius of 12.7 cm *Preview syntax error d. A circle has a radius of 28 cm. Another larger circle has an area that is 59 square cm more than the first circle. Represent the area of the larger circle. # Preview) syntax error

Answer :

Answer:

The answers to each question are:

a)[tex]A=f(r=4cm)=50.26cm^2[/tex]

b)[tex]\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2[/tex]

c)[tex]C=5\cdot f(r=12.7cm)=2533.54cm^2[/tex]

d)[tex]D=f(r=28cm)+59cm^2=2522.01cm^2[/tex]

Step-by-step explanation:

The function f(r) that represents the area of a circle (in square cm) is:

[tex]f(r)=\pi r^2[/tex]

a) To represent the area (in square cm) of a circle whose radius is 4 cm, you just have to evaluate the function with a radius of 4cm:

[tex]A=f(r=4cm)=50.26cm^2[/tex]

b) To represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm, you have to represent the difference between the final area with a radius of 10.91cm and the initial area of a radius of 10.9cm:

[tex]\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2[/tex]

c) To represent the area of 5 circles that all have a radius of 12.7 cm, we can use the function f(r) to represent the area of a circle with a radius of 12.7cm and multiply it for 5:

[tex]C=5\cdot f(r=12.7cm)=2533.54cm^2[/tex]

d) To represent the area of the larger circle that is 59 square cm more than the first circle (with a radius of 28 cm), we can use the function f(r) to obtain the area of the first circle and addition 59 square cm:

[tex]D=f(r=28cm)+59cm^2=2522.01cm^2[/tex]

Part(a):[tex]f(r)=f(4)[/tex]

Part(b):[tex]f(10.91)-f(10.9)[/tex]

Part(c):[tex]5 f(r)=5 f(12.7)[/tex]

Part(d):[tex]28+59 =f(28)+59[/tex]

Area of the circle:

The area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula,

[tex]A= \pi r^2[/tex]

where [tex]r[/tex] is the radius of the circle

The formula for the area of the circle is,

[tex]A=\pi r^2[/tex]

Part(a):

Given,

Radius([tex]r[/tex])=4 cm

So, the area is [tex]f(r)=f(4)[/tex]

Part(b):

Given,

[tex]r=10.91\\r=10.9[/tex]

The difference in area is,

[tex]f(10.91)-f(10.9)[/tex]

Part(c):

Area of 5 circles are,

[tex]5 f(r)=5 f(12.7)[/tex]

Part(d):

The area of the larger circle is,

Area of the circle of radius [tex]28+59 =f(28)+59[/tex]

Learn more about the topic Area of the circle:

https://brainly.com/question/10645610

Other Questions