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
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.
Find the exact values of the following
Csc5pi /6
Cot5pi/6
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.
To find the monthly cost for 25HCF, we need to determine the linear equation that relates the amount of water used (in HCF) to the monthly cost (in dollars).
From the given information, we know that the slope (m) of the line is 1.65. We also have a point on the line: (22, 44.68), where 22HCF corresponds to a cost of $44.68.
The general equation for a linear function is y = mx + b, where y represents the dependent variable (monthly cost), x represents the independent variable (amount of water used), m is the slope, and b is the y-intercept.
Using the given point (22, 44.68), we can plug in the values into the equation to solve for b:
44.68 = 1.65(22) + b
44.68 = 36.3 + b
Subtracting 36.3 from both sides of the equation:
44.68 - 36.3 = b
8.38 = b
So, the y-intercept (b) is 8.38.
Now we have the slope (m = 1.65) and the y-intercept (b = 8.38). We can substitute these values into the linear equation to find the monthly cost for 25HCF (x = 25):
y = 1.65x + 8.38
y = 1.65(25) + 8.38
y = 41.25 + 8.38
y = 49.63
Therefore, the monthly cost for 25HCF is $49.63.