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Gemiola [76]
2 years ago
15

IF THE RATIO IN A VALENTINE'S

Mathematics
1 answer:
GalinKa [24]2 years ago
3 0

Answer:

12 dark chocolates

Step-by-step explanation:

Let there are 2x milk chocolates and 3x dark chocolates.

Total no of milk chocolates = 8

ATQ,

2x = 8

x = 4

Dark chocolates = 3x

= 3(4)

= 12

Hence, there are 12 dark chocolates.

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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

 of it lies on the unit circle O

- 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
3 years ago
What is the prime factorization of 43? Enter your answer as a product of prime numbers, like 2 x 3 or as a single prime number,
storchak [24]

Answer:

43

Step-by-step explanation:

43 is a prime number

7 0
2 years ago
Plot the image of point D under a dilation about point P with a scale factor of
Vikentia [17]
It’s at point d and point p
5 0
2 years ago
The average speed of one team in a relay race is about 10 miles per hour. What is the speed in feet per second?
ki77a [65]

10 miles per second in feet per second is 14.67 feet per second

Step-by-step explanation:

The average speed of one team in a relay race = 10 miles per hour.

We need to find the speed in feet per second.

  • The conversion rule is:

             1 mile per hour = 1.467 feet per second

So, Speed in feet per second is:

 1 mile per hour = 1.467 feet per second

10 miles per hour = 10*1.467 feet per second

                             = 14.67 feet per second

So, 10 miles per second in feet per second is 14.67 feet per second

Keywords: Conversion of units

Learn more about Conversion of units at:

  • brainly.com/question/10940255
  • brainly.com/question/13005855
  • brainly.com/question/6436086

#learnwithBrainly

5 0
3 years ago
What number would you multiply (6x-y+4) by so that the result is an equivalent expression to (3x+9x)-(2y-8) Be sure to enter you
frozen [14]

Answer:

2

Step-by-step explana

 (6x-y+4)*2= 12x -2y+8= (3x+9x)-(2y-8)

3 0
3 years ago
Read 2 more answers
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