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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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Create your own GCF word problem with 3 numbers

svet-max [94.6K]

Number set:
18, 36, 900
GCF:
9

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4 years ago

What is the vertex of the graph of the function f(x) = x² + 8x - 2?

chubhunter [2.5K]

Answer:

(4, -18)

Step-by-step explanation:

First Use this formula for the x -axis -b/2a

-8/2(1) is -4

Then plug in -4 to the equation

(-4)^2+8(-4)-2 = -18

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3 years ago

Find three consecutive odd integers such that the sum of the smallest and four times the largest is 61. Please list the numbers

Kipish [7]

Answer:

$9,11,13$

Step-by-step explanation:

Given: sum of the smallest integer and four times the largest integer out of three consecutive odd integers is 61

To list: numbers from least to greatest

Solution:

Let the three consecutive odd integers be $x,x+2,x+4$ .

According to question,

$x+4(x+4)=61\\x+4x+16=61\\5x=61-16\\5x=45\\x=9$

So, the integers are $x=9,x+2=9+2=11,x+4=9+4=13$

Numbers from least to the greatest: $9,11,13$

7 0

3 years ago

Find the value of y, given that m_ KLM = 137º.

Musya8 [376]

Answer:

y ≈ 5.63

Step-by-step explanation:

m∠KLN and m∠NLM have to add up to m∠KLM

m∠KLN = 47°

m∠NLM = 16y°

m∠KLM = 137°

47 + 16y = 137

16y = 90

y = 45/8

y = 5.625

y ≈ 5.63

6 0

4 years ago

Read 2 more answers

The difference in cost between a large bag of chips and a small bag of chips was 90 cents. Alicia bought 5 large bags and 3 smal

jek_recluse [69]

X-small bag
x+0.9-large bag

5(x+0.9)+3(x)=17.22
5x+4.5+3x=17.22
8x=12.72
x=1.59

the small bag costs 1.59 while the big bag costs 2.49

hopw this helps :)

6 0

3 years ago