Respuesta :
Answer:
a) [tex]r(t)=5t[/tex]
b) [tex]A=\pi\cdot r^2[/tex]
c) [tex]A=\pi\cdot (5t)^2[/tex]
d) [tex]A=25\pi t^2[/tex]
Step-by-step explanation:
We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.
This can be expressed as:
[tex]r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t[/tex]
a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:
[tex]r(t)=5t[/tex]
b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):
[tex]A=\pi\cdot r^2[/tex]
c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:
[tex]A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2[/tex]
d) Expanded form for the area A:
[tex]A=\pi\cdot (5t)^2=25\pi\cdot t^2[/tex]
