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3 years ago

Verify the identity. cot x / 1 + csc x = csc x - 1 / cot x

Mathematics

1 answer:

svetlana [45]3 years ago

5 0

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)

Distribute the denominator:

cot x (1 − csc x) / (1 − csc²x)

Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

(csc x − 1) / cot x

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The population of a city increases by 2.2% per year. If this year's population is 230,000, what will next year's population be,

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Answer:

235,060

Step-by-step explanation:

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2 years ago

On a recent trip to the convenience store, you picked up 3 gallons of milk, 6 bottles of water, and 8 snack-size bags of chi

SVETLANKA909090 [29]

Answer:

The answers to the question are as follows

A bottle of water costs $2.00

A gallon of mik cots $4.10 and

A bag of chips costs $1.00

Step-by-step explanation:

To solve the question, it is important to note that it is a word problem hence we read the question carefully to clearly understnd and be able to interprete the message from any perspective

We list out the variables as follows

Number of gallons of milk = 3

Number of bottles of water = 6

Number of chips bags = 8

Bill before tax = $32.30

Price of a bottle of water = twice the price of a bag of chips

Price of a gallon of mlk = $ 2.10 + price of a bottle of water

Therefore in order to find out how much each item costs let us call the price of bottle of water $x say

This means that the price of a bag of chips = x/2 and

The price of a gallon of milk = x + $2.10

Therefore we have by multiplying the prices of the items to their respective quantities and summing up

$(6x + 3(x+2.1)+ 8 x/2) = $32.3

This gives by expanding the values 6x+3x+6.3+4x =32.3

13x+6.3 =32.3

13x = 32.3 - 6.3 = 26

Dividing both sides by 13 gives

x = $2.00

This means that a bottle of water costs $2.00

A gallon of mik cots $2.00+$2.10 = $4.10

A bag of chips costs x/2 which is equal to $2.00/2 = $1.00

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3 years ago

Write a function rule for the statements

WINSTONCH [101]

Step-by-step explanation:

x. | y

1 | -4

2 | 0

3 | 4

Is this correct?

3 0

2 years ago

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A statue is mounted on top of a 16 foot hill. From the base of the hill to where you are standing is 77 feet and the statue subt

DanielleElmas [232]

Consider right triangle with vertices B - base of the hill, S - top of the statue and Y - you. In this triangle angle B is right and angle Y is 13.2°. If h is a height of the statue, then the legs YB and BS have lengths 77 ft and 16+h ft.

You have lengths of two legs and measure of one acute angle, then you can use tangent to find h:

$\tan 13.2^{\circ}=\dfrac{\text{opposite leg}}{\text{adjacent leg}} =\dfrac{16+h}{77}, \\ \\ 0.2345=\dfrac{16+h}{77},\\ \\ 16+h=0.2345\cdot 77=18.0565,\\ h=18.0565-16=2.0565$ ft.

Answer: the height of the statue is 2.0565 ft.

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2 years ago

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A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimension

snow_tiger [21]

Answer:

6.51

Step-by-step explanation:

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2 years ago

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