1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lions [1.4K]
3 years ago
5

Please help me solve this exercise.!!

Mathematics
1 answer:
Volgvan3 years ago
8 0
<h3>Answer:  -4/3</h3>

=============================================================

Explanation:

Let's square both sides and do a bit of algebra to get the following.

\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\

Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25

This then means tan(2x) = sin(2x)/cos(2x) = 24/7.

From here, you'll use this trig identity

\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\

which is the same as solving

\tan(2x) = \frac{2w}{1-w^2}\\\\

where w = tan(x)

Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4

So either tan(x) = -4/3 or tan(x) = 3/4.

If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.

Since tan(x) < 0 in this case, we go for tan(x) = -4/3

You might be interested in
the slope of line PQ is m= 1/4. find the equation of the line that is parallel to line PQ and that has the y intercept b= -3
nevsk [136]
For this case we have that the generic equation of the line is given by:
 y = mx + b&#10;
 Where,
 m: slope of the line
 b: intersection with the y axis.
 Since the line is parallel to PQ, then the slopes are equal.
 We have then:
 m = 1/4.&#10;
 On the other hand we have:
 b = -3&#10;
 Substituting values we have:
 y = (1/4) x - 3
 Answer:
 The equation of the line that is parallel to line PQ and that has the and intercept b = -3 is:
 y = (1/4) x - 3
4 0
3 years ago
There are 128 competitors in a tennis tournament. If Milo places in the 85th percentile, how many people
Zarrin [17]
Answer: A


Explanation: multiply 128 by .85
4 0
3 years ago
sam had 70 erasers and rulers. after giving away 1/3 of his erasers and 10 rulers, he had an equal number of erasers and rulers
Radda [10]

Answer:

36 erasers

Step-by-step explanation:

Let number of erasers be e

let number of rulers be r

We can write:

e + r = 70

and

After giving away, he has

Erasers:  2/3e

Rulers:  r - 10

These two are equal, so we can write and solve:

2/3e = r - 10

2/3e + 10 = r

Putting this in initial equation, we have:

e + (2/3e + 10) = 70

5/3e + 10 = 70

5/3 e = 60

e = 36

And rulers is:

r = 2/3(36) + 10 = 34

Hence, he had 36 erasers in the beginning

4 0
3 years ago
(x+2)(4+y)(5+6)(2+x)(4+0.5x)
Yuki888 [10]

(x+2)(4+y)(5+6)(2+x)(4+0.5x)

combine like terms

(x+2) (4+y) (11) (x+2) (4+.5x)

11(x+2)^2 (4+y)(4+.5x)

distribute

11(x^2 +4x+2) (16+4y+2x+.5xy)

(11x^2+44x+22)(16+4y+2x+.5xy)

5.5 x^3 y + 22 x^3 + 66 x^2 y + 264 x^2 + 198 x y + 792 x + 176 y + 704

3 0
3 years ago
Among all rectangles having a perimeter of 25m, find the dimensions of the one with the largest area​
Katen [24]

Answer:

Square with side length 25/4 m

Step-by-step explanation:

The area is always going to be largest for a rectangle when the two dimensions are equal.  You are looking for a square. What square has perimeter 25? 4s=25 so the side length of this rectangle (Square) is 25/4 m.

7 0
2 years ago
Read 2 more answers
Other questions:
  • In a solution,the ratio of salt water by volume is 1:4 .What is the percent of salt in the total solution?
    7·1 answer
  • Find the distance between the points (-9,0) and (2,5)
    9·1 answer
  • Find x if h(x)=-2<br> Please Helppp :) ill mark brainliest
    6·2 answers
  • The measures of two supplementary angles are (2x + 10)° and (6x + 8)°.
    13·1 answer
  • What is the slope of the line through (-7,-8)(−7,−8)left parenthesis, minus, 7, comma, minus, 8, right parenthesis and (0,4)(0,4
    11·1 answer
  • the lines below are parrallel . if the slope of the green line is -2, what is slope of red line? its a algebra question pls help
    14·1 answer
  • Write an expression that represents the
    11·1 answer
  • Jill and ericka made 4 gallons of lemonade for their lemonade stand how many quarts did they make
    14·1 answer
  • Which statement Is always true?
    6·1 answer
  • Gideon took an online math test consisting of 25
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!