Aspherical balloon is inflating with helium at a rate of 8080piπ startfraction ft cubed over min endfraction ft3 min. how fast is the balloon's radius increasing at the instant the radius is 22 ft? write an equation relating the volume of a sphere, v, and the radius of the sphere, r.

=0.04132 ft/min

Step-by-step explanation:

V = volume of the sphere

r = radius of the sphere

= 80π ft³/min

now,

For sphere, V =

for rate of change of volume with respect to time (t)

or

or

at r = 22ft, = 80π ft³/min

80π =

or

=0.04132 ft/min

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: