Question

Need help with a couple questions..

Answer 1

1) A gas company has the following rate schedule for natural gas usage in single-family residences:

Monthly service charge $8.80

Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm

What is the charge for using 25 therms in one month?
What is the charge for using 45 therms in one month?
Construct a function that gives the monthly charge C for x therms of gas.



2)Verify the identity.

cot2x + csc2x = 2csc2x - 1

Answer 2

@jim_thompson5910 can you help?

Answer 3

it states that it's $0.6686/therm for the first 25 therms

so you multiply 0.6686 by 25, then you add on 8.80 to get the total cost for using 25 therms

Answer 4

Okay for the first question in question 1 the answer would be $25.52??
& than how do i figure the second and third questions?

Answer 5

45-25 = 20

so you multiply 20 by 0.85870, then you add on the result from part a) since it builds on it

Answer 6

did i do part a right?
than part 2 would be $42.69?

Answer 7

can you explain part c to me?

Answer 8

42.69 is correct for part 2

Answer 9

for part c, you'll have a piecewise function

Answer 10

so part a and b are correct? & how do i do that?

Answer 11

and this piece wise function will look something like this


f(x) = 0.6686x + 8.80 if 0 <= x <= 25

or

f(x) = 0.85870(25 -x) + 8.80 if x > 25

Answer 12

notice how there are cases and conditions

the function changes depending on whether x is greater than 25 or not greater than 25

Answer 13

sorry the piecewise function should be

f(x) = 0.6686x + 8.80 if 0 <= x <= 25

or

f(x) = 0.85870(25 -x) + 0.6686x + 17.6 if x > 25

Answer 14

okay thank you .. could you help me with my question 2?

Answer 15

I recommend using these trig identities

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 16

to help you verify the identity in #2

Answer 17

okay

Answer 18

oh and I still messed up on the second part of part c...sorry about that

here is the actual (just verified it) piecewise function

f(x) = 0.6686x + 8.80 if 0 <= x <= 25

or

f(x) = 0.85870(25 -x) + 25.52 if x > 25

Answer 19

its okay thank you!

Answer 20

sure thing

Answer 21

Jim not understanding the concept of #2

Answer 22

Hint: look in the "Pythagorean Identities" section of the page I gave you

Answer 23

okay!

Answer 24

Jim i have one question
Solve the absolute value equation or indicate that the equation has no solution.

│x + 6│ = 9

A. {3}

B. {-15, 3}

C. {-3, 15}

D. ø

Would this be B???

Answer 25

correct

Answer 26

thanks !

Answer 27

yw

Answer 28

Can i ask one more cause i havent done math in a while i feel stupid but is this A or D??
Write the number in scientific notation.

0.000 779

A. 7.79 x 10-4

B. 7.79 x 104

C. 7.79 x 10-3

D. 7.79 x 10-5

Answer 29

start with 7.79 and move the decimal until you get 0.000 779

how many spaces did you have to move it to the left?

Answer 30

4?

Answer 31

so the exponent over the 10 is -4

Answer 32

okay!

Answer 33

Jim i need help with one more question ...