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3 years ago

Find all solutions in the interval [0, 2π). tan x + sec x = 1

1 answer:

6 0

Use the identity
sec^2x = 1 + tan^2 x
- so sec x = sqrt(1 + tan^2 x) then:-
tan x + sqrt( 1 + tan^2 x) = 1
sqrt ( 1 + tan^2 x) = 1 - tan x
1 + tan^2 x = 1 + tan^2x - 2 tan x
0 = -2 tanx

tan x = 0

x = 0, π
π is an extraneous root because sec 180 = -1
So the answer is 0 degrees

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write a numerical expression to represent "20 minus the product of 5 and 2. then evaluate your expression. PLEASE HELP I DON'T H

Shalnov [3]

Answer:

Step-by-step explanation:

20-(5×2)

5×2=10

20-10=10

6 0

2 years ago

Read 2 more answers

Mrs Tan bought 4 times as many pens as notebooks and each notebook cost $8.20 more than each pen. She spent $26 more on the book

lilavasa [31]

Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20

Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4

She spent $26 more on books than on pens which means

Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26

Sinplifying it

(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104

She spent $394 which means

Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394

Simplifying it

(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576

Now, we have two equations,

(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576

Now we need to find a third equation with either x or y as the subject of any of both the previous equations.

Let's make y the subject of (2) equation

8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)

Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)

8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3

Now find the value of y by substituting the value of x in either equation, preferably (3)

y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80

Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50

8 0

3 years ago

CAN SOMEONE HELP ME PLEASEEE

Tom [10]

Answer:

a. 45 degrees

b. 315 degrees

c. 8π

d. π

e. 7π

f. 16π

g. 2π

6 0

3 years ago

Write 100 times 100as multiplying 10 to a power by 10 to a power?

SCORPION-xisa [38]

Answer:

10^2 × 10^2

Step-by-step explanation:

Given that

Write 100 times 100 that would be multiplying to the power by 10

So based on the above information

The equation that would be developed is

10^2 × 10^2

The same would be represented as an answer

4 0

2 years ago

Find the range, mean, median, and mode of the following data set.

attashe74 [19]

Answer:

The answer to your question would be D.

D. Range: 20

Mean: 10

Median: 9

Mode: none

Step-by-step explanation:

1, 2, 3, 8, 9, 12, 14, 20, 21

Range: 21 - 1 = 20

Mean: 1 + 2 + 3 + 8 + 9 + 12 + 14 + 20 + 21 = 90/9 = 10

Median: 9

Mode: there are no mode in the following given data set.

8 0

2 years ago