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3 years ago

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)

Mathematics

1 answer:

creativ13 [48]3 years ago

4 0

Answer:

(sin^2 w + 1) / cos w.

Step-by-step explanation:

Note: sec w = 1 / cos w and csc w = 1/ sin w.

So we have:

(sec w(1 + csc^2 w)) / (csc^2 w)

= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)

= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w

= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)

= sin^2 w / cos w + 1 / cos w

= (sin^2 w + 1) / cos w.

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Could I have some help on my patterns assignment

nydimaria [60]

Answer:

1. 13, 18, 23, 28, 33, 38, 43, 48, 53

Conjecture: Each term is 5 more than the previous term.

2. 512, 256, 128, 64, 32, 16, 8, 4, 2

Conjecture: Each term is half of the previous term.

3. 1, 8, 27, 64, 125, 216, 343, 512, 729

Conjecture: Each term is a cube. To find the nth term, cube n.

4. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Conjecture: Each term is the next consecutive prime number.

5. Correct as is

6. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

Conjecture: Each term is the sum of the 2 previous numbers.

Step-by-step explanation:

Given: 13, 18, 23, 28

We add 5 to each number

13 + 5 = 18

18 + 5 = 23

23 + 5 = 28

28 + 5 = 33

33 + 5 = 38

38 + 5 = 43

43 + 5 = 48

48 + 5 = 53

Given : 512, 256, 128, 64

Divide each number by 2

512 ÷ 2 =256

256 ÷ 2 = 128

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

Given: 1, 8, 27, 64

We have to cube n:

n³ = consecutive number cubed

1³ = 1 or 1 × 1 × 1

2³ = 8 or 2 × 2 × 2

3³ = 27 or 3 × 3 × 3

4³ = 64 or 4 × 4 × 4

5³ = 125 or 5 × 5 × 5

6³ = 216 or 6 × 6 × 6

7³ = 343 or 7 × 7 × 7

8³ = 512 or 8 × 8 × 8

9³ = 729 or 9 × 9 × 9

Consecutive prime number: Consecutive prime numbers are those that have no gaps or prime numbers between them.

Look at the picture in the link:

Given: 1, 1, 2, 3, 5, 8

We must add the two previous numbers to get the next term:

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 = 34 = 55

34 + 55 = 89

8 0

1 year ago

2 ( x-4 ) = 5/6 ( x+6 ) -6

givi [52]

Hopes this helps:

Answer: x = 6

3 0

3 years ago

Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and

blsea [12.9K]

Answer:

Step-by-step explanation:

Given

Garden: $x^2+18x+81$

One Bag: $x^2 - 81$

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

$Bags = \frac{x^2+18x+81}{x^2 - 81}$

Expand the numerator

$Bags = \frac{x^2+9x+9x+81}{x^2 - 81}$

$Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}$

$Bags = \frac{(x+9)(x+9)}{x^2 - 81}$

Express 81 as 9²

$Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}$

Evaluate as difference of two squares

$Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}$

$Bags = \frac{(x+9)}{(x - 9)}$

Hence, the number of bags is $Bags = \frac{(x+9)}{(x - 9)}$

3 0

3 years ago

Kent multiplies both sides of the equation below by an expression. k+12/k=8 Then he moves all the terms to one side of the equal

BartSMP [9]

k+12/k=8
Multiply k to remove the k in one side
(k+12/k=8) (k)
Therefore,
k^2+12k-8k=0

Thus,
The equations he must solved now is k^2-8+12=0

3 0

3 years ago

Read 2 more answers

Solve elimination method 3x+4y=0 and x - 2y =-5

Alla [95]

Answer:

x=−2 and y=3/2

Step-by-step explanation:

see picture

5 0

2 years ago

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)​

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)