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dusya [7]
3 years ago
11

A silk worm wind ts cocoon out of one long silk fiber. to make silk thread, 3 to 10 of these silk fibers are unwound from their

cocoons and combined into a single thread with a typical length of 300 yards. choose a reasonable number of silk fibers in a thread. write an equation to find the total length of the silk fibers used in 300 yards of thread.
Mathematics
1 answer:
In-s [12.5K]3 years ago
5 0
Answer: There would be about 6 or 7 silk fibers per 300 yard length of silk fiber.

The problem states that each thread is made of about 3 to 10 silk fibers. The the problem as for a reasonable estimation of the number of silk fibers. It would be safe to assume that a reasonable estimation would be the average (or mean) of 3 to 10.

(3 + 10) / 2 = 6.5

Since 6.5 is the average, we could use 6 or 7 as a reasonable estimation.
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Answer:

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5 d - 5 d + 3 c

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1st Answer:

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Urgent!! Will mark brainliest!!
horsena [70]

Answer:

1) x is negative and y is positive ⇒ last answer

2) cotФ = -12/35 ⇒ second answer

3) The right identity is cot²Ф - csc²Ф = -1 ⇒ last answer

Step-by-step explanation:

* For any point (x , y) lies on the terminal side of the angle Ф

 in standard position

* x = cosФ and y = sinФ

- If Ф in the first quadrant, then x , y are positive

∴ All trigonometry functions are positive

- If Ф in the second quadrant, then x is negative , y is positive

∴ sinФ only is positive

- If Ф in the third quadrant, then x is negative , y is negative

∴ tanФ only is positive

- If Ф in the fourth quadrant, then x is positive , y is negative

∴ cosФ only is positive

* Lets solve the problems

∵ Ф = 3π/4 ⇒ (135°)

∴ It lies on the second quadrant

∴ x is negative and y is positive

* Lets revise the reciprocal of sinФ, cosФ and tanФ

- cscФ = 1/sinФ

- secФ = 1/cosФ

- cotФ = 1/tanФ

∵ secФ = -37/12

∴ cosФ = -12/37

∵ π/2 < Ф < π

∴ Ф lies on the second quadrant

∴ cotФ is negative values

∵ tan²Ф = sec²Ф - 1

∵ secФ = -37/12

∴ tan²Ф = (-37/12)² - 1 = 1225/144 ⇒ take√ for both sides

∴ tanФ = ± 35/12

∵ cotФ = ± 12/35

∵ cotФ is negative value

∴ cotФ = -12/35

* In the standard position of the angle Ф the terminal

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- By using Pythagorean theorem

∵ x² + y² = 1

∵ x = cosФ and y = sinФ

∴ cos²Ф + sin²Ф = 1 ⇒ (1)

∴ cos²Ф = 1 - sin²Ф

∴ sin²Ф = 1 - cos²Ф

* Divide (1) by cos²Ф

∴ cos²Ф/cos²Ф + sin²Ф/cos²Ф = 1/cos²Ф

* Remember sin²Ф/cos²Ф = tan²Ф and 1/cos²Ф = sec²Ф

∴ 1 + tan²Ф = sec²Ф ⇒ (2) ⇒ subtract 1 from both sides

∴ tan²Ф = sec²Ф - 1 ⇒ subtract sec²Ф from both sides

∴ tan²Ф - sec²Ф = -1

* Divide (1) by sin²Ф

∴ cos²Ф/sin²Ф + sin²Ф/si²Ф = 1/sin²Ф

* Remember cos²Ф/sin²Ф = cot²Ф and 1/sin²Ф = csc²Ф

∴ cot²Ф + 1 = csc²Ф ⇒ (3) ⇒ subtract 1 from both sides

∴ cot²Ф = csc²Ф - 1 ⇒ subtract csc²Ф from both sides

∴ cot²Ф - csc²Ф = -1

* The right identity is cot²Ф - csc²Ф = -1

3 0
4 years ago
Suppose you deposit $1,500 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn fr
forsale [732]

Answer:

The solution is given below.

Step-by-step explanation:

Given that

Deposited amount = $1,500

Rate of interest = 5%

We need to find out the following things

a. The account after 4 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^4

Future value = $1,500 × (1.05)^4

Future value = $1,823.26

b. The account after 16 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^16

Future value = $1,500 × (1.05)^16

Future value = $3,274.312

c. The number of years that contain the amount of $2,000

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 4.94 years

d. The number of years that contain the amount of $2,500

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 8.77 years

7 0
3 years ago
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