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
Kruka [31]
2 years ago
11

Help please!!

Mathematics
2 answers:
Free_Kalibri [48]2 years ago
7 0
Tan²( θ ) - (1 + √3) tan (θ) + √3 = 0

tan²( θ ) - (tan (θ) + √3 tan (θ)) + √3 = 0

tan²( θ ) - tan (θ) - √3 tan (θ) + √3 = 0

tan( θ ) ( tan (θ) - 1) - √3 ( tan (θ) - 1 ) = 0

( tan( θ ) - 1 ) ( tan( θ ) - √3 ) = 0


tan( θ ) - 1 = 0

θ = π/₄

tan( θ ) - √3 = 0


θ = π/₃


so θ = π/₄ and θ = π/₃
irinina [24]2 years ago
7 0

Answer:

\huge \boxed{  \red{  \boxed{\begin{cases} \theta   =   {45}^{ \circ} \\    \theta=      {60}^{ \circ}  \end{cases} }}}

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • trigonometry
  • PEMDAS
<h3>let's solve:</h3>

distribute tan(θ):

=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0

remove parentheses:

=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0

so this equation is now in standard form i.e ax²+bx+c=0

we can solve by factoring as we solve quadratic equation

factor out tanθ:

=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0

factor out -√3:

=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0

group:

=>(tan(θ)-√3)(tan(θ)-1)=0

separate it as two different equation:

\implies  \begin{cases} \tan( \theta)  - 1 = 0 \\   \tan( \theta)  -  \sqrt{3} = 0  \end{cases}

add 1 and √3 to both sides to first and second equation respectively:

\implies  \begin{cases} \tan( \theta)  - 1 + 1 = 0 + 1 \\   \tan( \theta)  -  \sqrt{3} +  \sqrt{3}  = 0   +  \sqrt{3} \end{cases}

\implies  \begin{cases} \tan( \theta)   =  1 \\   \tan( \theta)  =     \sqrt{3} \end{cases}

\therefore  \begin{cases} \theta   =   {45}^{ \circ} \\    \theta=      {60}^{ \circ}  \end{cases}

You might be interested in
The height in feet of a ball dropped from a 150 ft building is given by h(t)=-16 ft^2 +150, where t is the time in seconds after
ipn [44]

Answer:

Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft

Step-by-step explanation:

we have

h(t)=-16t^{2}+150

where

t ----> is the time in seconds after the ball is dropped

h(t) ----> he height in feet of a ball dropped from a 150 ft

Find h(2)

That means ----> Is the height of the ball  2 seconds after the ball is dropped

Substitute the value of t=2 sec in the equation

h(2)=-16(2)^{2}+150=86\ ft

therefore

After 2 seconds, the height of the ball is 86.00 ft.

7 0
3 years ago
the utility industry has 428.5 thousand jobs in 2010 and is expected to decline at an average rate of 3 thousand jobs per year f
Aleksandr-060686 [28]

Answer: 7%

Step-by-step explanation:

Given: Initial jobs = 428.5 thousand

Average rate of declining of jobs  from 2010 to 2020 =  3 thousand jobs per year

From 2010 to 2020 , there are 10 years.

Total jobs declines till 2020 = 10 x (3 thousand)

= 30 thousand  (Change in jobs)

Now, utilities percent change for 2010 to 2020​ : \dfrac{change \  in \  job\  numbers}{Initial\ jobs}\times 100

=\dfrac{30}{428.5}\times100\\\\\approx7.00\%

Utilities percent change for 2010 to 2020 = 7 %

7 0
3 years ago
What are values of X mean in maths​
GaryK [48]

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown".

Step-by-step explanation:

In x + 2 = 7, x is a variable, but we can work out its value if we try:)

5 0
3 years ago
Read 2 more answers
D2-9k+3 for d=10 and k=9
AVprozaik [17]

Answer:

22

Step-by-step explanation:

10^2-9(9)+3

100-81+3

19+3

22

8 0
3 years ago
A basket contains 14 white eggs, 15 brown eggs, and 11 lemons. Taylor is in a hurry to make breakfast and picks something from t
guajiro [1.7K]
Okay so probability is just percentage of a whole, right?

So you have 14 White Eggs + 15 Brown Eggs + 11 Lemons.

Add all those numbers together and you get your whole.

14 + 15 = 29    29+11 = 40

40 is your whole. 

So because you want to know how likely it is to pick up an egg, you would follow these steps.

100/40 = 2.5 (For each part of the 40, it is worth 2.5 percent.)

2.5 x 29 = 72.5

Your probability of picking an egg out of the bask is 72.5 percent or 72.5 out of 100. 
8 0
3 years ago
Read 2 more answers
Other questions:
  • Number 9 please I need help hurry
    12·1 answer
  • Find the amount paid for the loan.<br><br> $2000 at 12% for 3 years
    6·1 answer
  • The area of a circle is 100 π.what is the lenght of the side of a tegular hexagon inscribed in a circle.
    7·1 answer
  • Brain has reduced his cholesterol level by 15% by following a strict diet and regular exercise. If his original level was 240, w
    6·1 answer
  • Jill was going to meet at the bus depot if she went during rush hour she would travel 15 mph and arrive 1 hour later if she went
    10·1 answer
  • Find the volume of the figure?l
    5·1 answer
  • What is the value of the expression? (-3)(-4)(-5)
    12·1 answer
  • Elise bought 8 1/2 yards of material. She used 3 3/4 yards for pants and 2 2/3 yards for a jacket. How many yards of material do
    13·2 answers
  • There were 340 shoppers at an electronics store on opening day. The specials that day allowed 21% of shoppers to receive a free
    15·2 answers
  • Help me find the angles B and C thanks
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!