A manufacturer of tennis balls has a daily cost of C(x) = 200 − 10x + 0.01x 2
, where C(x) is the
total cost in dollars and x is the number of tennis balls produced. The manufacturer has to
produce between 1500 and 3000 balls. What number of tennis balls will produce the minimum
cost?

1000 tennis balls will produce the minimum  cost

Step-by-step explanation:

Daily cost equation of tennis ball :

Where C(x)  is the  total cost in dollars

x is the number of tennis balls produced

We are supposed to find number of tennis balls will produce the minimum

cost.

Lead coefficient = 0.01

The lead coefficient is positive, the parabola opens up.

Thus ,the minimum is at the vertex.

So,

Substitute the value of x in given equation:

C(x)=200-10(1000)+0.01(1000)^2

C(x)=200

Hence 1000 tennis balls will produce the minimum  cost

∠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.

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s