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Aliun [14]
2 years ago
14

Rodney has 83 goldfish in his pond. In the winter, he wants to put the goldfish into one or more smaller fish tanks inside his h

ouse. He wants each fish tank to hold
the same number of goldfish. How many possible ways can the goldfish be placed into smaller fish tanks?
Mathematics
1 answer:
Leviafan [203]2 years ago
8 0

Answer:

0

Step-by-step explanation:

no number of tanks will hold the same amount of fish. 83 is a prime number, no numbers can be equally divided into it

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The number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the
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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
nikitadnepr [17]

Answer:

* sin Ф = -15/17     * cos Ф = 8/17      * tan Ф = -15/8

* csc Ф = -17/15    * sec Ф = 17/8      * cot Ф = -8/15

Step-by-step explanation:

Lets revise the trigonometric function of angle Ф

- Angle θ is in standard position

- Point  (8, -15) is on the terminal ray of angle θ

- That means the terminal is the hypotenuse of a right triangle x and y

  are its legs

∵ x-coordinate is positive and y-coordinate is negative

∴ angle Ф lies in the 4th quadrant

- The opposite side of angle Ф is the y-coordinate of the point on the

  terminal ray of angle Ф and the adjacent side to angle Ф is the

  x-coordinate of that point

∵ The length of the hypotenuse (h) = √(x² + y²)

∴ h = √[(8)² + (-15)²] = √[64 + 225] = √[289] = 17

∴ The length of the hypotenuse is 17

- Lets find sin Ф

∵ sin Ф = opposite/hypotenuse

∵ The opposite is y = -15

∵ The hypotenuse = 17

∴ sin Ф = -15/17

- Lets find cos Ф

∵ cos Ф = adjacent/hypotenuse

∵ The adjacent is x = 8

∵ The hypotenuse = 17

∴ cos Ф = 8/17

- Lets find tan Ф

∵ tan Ф = opposite/adjacent

∵ The opposite is y = -15

∵ The adjacent = 8

∴ tan Ф = -15/8

- Remember csc Ф is the reciprocal of sin Ф

∵ csc Ф = 1/sin Ф

∵ sin Ф = -15/17

∴ csc Ф = -17/15

- Remember sec Ф is the reciprocal of cos Ф

∵ sec Ф = 1/ cos Ф

∵ cos Ф = 8/17

∴ sec Ф = 17/8

- Remember cot Ф is the reciprocal of tan Ф

∵ cot Ф = 1/tan Ф

∵ tan Ф = -15/8

∴ cot Ф = -8/15

5 0
2 years ago
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