Refer to the diagram shown below.

When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)

Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)

From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.

From (1) and (2), obtain
225a + k = 15
2025a + k = 6

Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft

Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125

A graph of the solution verifies that the solution is correct.

6 0

3 years ago

Read 2 more answers

A software company is releasing one of their products on a CD. The manufacturer charges a $9700 setup fee and $1.25 per CD. Appr

Gre4nikov [31]

Answer:

about 4312

Step-by-step explanation:

You want the total cost for n CDs to be 3.50n.

The manufacturer will charge you 9700+1.25n, so you want these to be equal:

3.50n = 9700 +1.25n

2.25n = 9700 . . . . . . . . subtract 1.25n

n = 9700/2.25 ≈ 4311.111...

Producing 4312 CDs will make the cost per CD slightly less than $3.50.

____

Producing 4311 CDs will make the cost per CD be about $3.500058. Producing 4312 CDs will bring it down to $3.499536.

3 0

3 years ago

Assume that 8% of people are left-handed. We select 6 people at random. a) How many lefties do you expect? b) With what sta

klemol [59]

Answer:

a) 0.48

b) 0.6645

c) 12.5

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are left-handed, or they are not. The probabilities of each person being left-handed are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$