Question

Suppose that a household monthly water bill in dollar is a linear function of the amount of water the household uses (in hundreds of cubic feet,HCF).when graphted,the function gives a line of its a slope if 1.65 . If the monthly cost for 22HCF is $44.68 what is the monthly cost for 25HCF

Answer 1

Find the exact values of the following
Csc5pi /6
Cot5pi/6

Answer 2

Let's call the monthly cost of water, C, and the amount of water used in hundreds of cubic feet, W.

We know that the monthly cost for 22HCF is $44.68. So when W = 22, C = 44.68.

We're also given the slope of the linear function, which is 1.65. This means that for every 1HCF increase in water usage, the monthly cost increases by $1.65.

To find the monthly cost for 25HCF, we can use the equation of a linear function: C = mW + b, where m is the slope (1.65), and b is the y-intercept.

Using the given information of C = 44.68 when W = 22, we can substitute these values into the equation to solve for b:

44.68 = 1.65(22) + b
44.68 = 36.3 + b
b = 44.68 - 36.3
b = 8.38

Now that we have the y-intercept, we can substitute W = 25 into the equation to find the monthly cost for 25HCF:

C = 1.65(25) + 8.38
C = 41.25 + 8.38
C = 49.63

Therefore, the monthly cost for 25HCF is $49.63.

Answer 3

To find the exact values of csc(5π/6) and cot(5π/6), we need to recall the special values of trigonometric functions for common angles.

First, let's determine the reference angle for 5π/6.

The reference angle is the angle between the terminal side and the x-axis in standard position. To find the reference angle for 5π/6, we subtract it from the closest full rotation, which is 2π.

Reference angle = 2π - 5π/6 = 12π/6 - 5π/6 = 7π/6

Now we can find the exact value of csc(5π/6) using the definition of the cosecant function:

csc(θ) = 1/sin(θ)

Since sin(θ) = sin(θ + 2kπ), where k is an integer, we can use the reference angle to find the value of sin(7π/6).

sin(7π/6) = -sin(π/6)

The exact value of sin(π/6) is 1/2.

sin(7π/6) = -1/2

Thus, csc(5π/6) = 1/(-1/2) = -2

Next, let's find the exact value of cot(5π/6) using the definition of the cotangent function:

cot(θ) = cos(θ)/sin(θ)

Again, we can use the reference angle to find cos(7π/6) and sin(7π/6).

cos(7π/6) = cos(π/6) = √3/2
sin(7π/6) = -sin(π/6) = -1/2

Therefore,

cot(5π/6) = cos(7π/6)/sin(7π/6) = (√3/2)/(-1/2) = -√3

The exact values of csc(5π/6) and cot(5π/6) are -2 and -√3, respectively.