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
Umnica [9.8K]
2 years ago
10

Help, Help, Please

Mathematics
2 answers:
Lesechka [4]2 years ago
8 0

Answer:

θ = \frac{\pi }{3} (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ  ≤ 1

2cosθ - 1 = 0

cosθ = \frac{1}{2} , so

θ = cos^{-1} (\frac{1}{2} ) = \frac{\pi }{3} ( or 60° )

pishuonlain [190]2 years ago
8 0

Answer:

\huge  \boxed{  \boxed{\blue{ { \theta = 60}^{ \circ} }}}

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • trigonometry
  • PEMDAS
<h3>let's solve:</h3>
  1. \sf \: rewrite \:  \sin ^{2} ( \theta) \: as \: 1 -  \cos ^{2} ( \theta)  :  \\  \sf \implies \:  \cos ^{2} ( \theta)  - (1 -  \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta)
  2. \sf \: remove \: parentheses \: and \: change \: its \: sign  :  \\  \sf \implies \:  \cos ^{2} ( \theta)   - 1  +   \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta)
  3. \sf \: add  :  \\  \sf \implies \:  2\cos ^{2} ( \theta)   - 1  = 2 - 5 \cos( \theta)
  4. \sf \:  move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \:  :  \\  \sf \implies \:  2\cos ^{2} ( \theta)  + 5 \cos( \theta)   - 1 -2  = 0
  5. \sf \: rewrite \:  5\cos( \theta)  \: as \: 6 \cos( \theta) -  \cos( \theta)  :  \\  \sf \implies \:  2\cos ^{2} ( \theta)  + 6 \cos( \theta)    -  \cos( \theta) - 3  = 0
  6. \sf \:factor \: out \: 2 \cos( \theta)  \: and \:  - 1  :  \\  \sf \implies \:  2\cos  ( \theta)( \cos( \theta)   + 3 ) -1(  \cos( \theta)  +  3)  = 0
  7. \sf \: group:  \\  \sf \implies \:  (2\cos( \theta)  - 1) ( \cos( \theta)   + 3 )   = 0
  8. \sf \: rewrite \: as \: two \: seperate \: equation:  \\  \sf \implies \:   \begin{cases}2\cos( \theta)  - 1   = 0\\  \cos( \theta)   + 3 = 0   \end{cases}
  9. \sf add \: 1 \: to  \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation:  \\  \sf \implies \:   \begin{cases}2\cos( \theta)     = 1\\  \cos( \theta)    =  - 3 \end{cases}

\sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1  \leqslant  \cos( \theta)  \leqslant 1 \:  \\  \sf but \: we \: can \: still \: work \: with \: the \: second \: equation

  1. \sf substract \: both \: sides \: by \: 2 :  \\   \implies\frac{ 2\cos( \theta) }{2}  =  \frac{1}{2}  \\   \implies\cos( \theta)  =  \frac{1}{2}  \\   \therefore \:  \theta \:  =  {60}^{ \circ}

You might be interested in
Students plant 148 flowers at a community park. Seventy-eight percent of the flowers are pansies. Use
Mashcka [7]
About 115 are pansies when you round down from the original number (115.44)
6 0
2 years ago
Help with this one please
ivann1987 [24]

with what? you need to explain whats going on in order to get the help you need!

4 0
3 years ago
Find all real solutions to the equation (x² − 6x +3)(2x² − 4x − 7) = 0.
Jet001 [13]

Answer:

x = 3 + √6 ; x = 3 - √6 ; x = \frac{2+3\sqrt{2}}{2} ;  x = \frac{2-(3)\sqrt{2}}{2}

Step-by-step explanation:

Relation given in the question:

(x² − 6x +3)(2x² − 4x − 7) = 0

Now,

for the above relation to be true the  following condition must be followed:

Either  (x² − 6x +3) = 0 ............(1)

or

(2x² − 4x − 7) = 0 ..........(2)

now considering the equation (1)

(x² − 6x +3) = 0

the roots can be found out as:

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

for the equation ax² + bx + c = 0

thus,

the roots are

x = \frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times(3)}}{2\times(1)}

or

x = \frac{6\pm\sqrt{36-12}}{2}

or

x = \frac{6+\sqrt{24}}{2} and, x = x = \frac{6-\sqrt{24}}{2}

or

x = \frac{6+2\sqrt{6}}{2} and, x = x = \frac{6-2\sqrt{6}}{2}

or

x = 3 + √6 and x = 3 - √6

similarly for (2x² − 4x − 7) = 0.

we have

the roots are

x = \frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-7)}}{2\times(2)}

or

x = \frac{4\pm\sqrt{16+56}}{4}

or

x = \frac{4+\sqrt{72}}{4} and, x = x = \frac{4-\sqrt{72}}{4}

or

x = \frac{4+\sqrt{2^2\times3^2\times2}}{2} and, x = x = \frac{4-\sqrt{2^2\times3^2\times2}}{4}

or

x = \frac{4+(2\times3)\sqrt{2}}{2} and, x = x = \frac{4-(2\times3)\sqrt{2}}{4}

or

x = \frac{2+3\sqrt{2}}{2} and, x = \frac{2-(3)\sqrt{2}}{2}

Hence, the possible roots are

x = 3 + √6 ; x = 3 - √6 ; x = \frac{2+3\sqrt{2}}{2} ; x = \frac{2-(3)\sqrt{2}}{2}

7 0
2 years ago
Question is in the picture, please help me out!!
Grace [21]

The arithmetic sequences are as follow:

<h3>What is Arithmetic Sequence?</h3>

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

1) t(n) = 5n + 4

t(1) = 9, t(2) = 14, t(3) = 19

So,

9,14,19,...

d= 14-9 = 5

d= 19-14 =5

Hence, it is an AP

2) 1, 2, 4, 8 , 16

Hence, it is not an AP

3) 3, 6, 9 ,...

It is an AP

4)It is given that it is an AP

5) tn =  2*3^n

 t1= 6, t2= 18, t3= 54

So, 6, 18, 54,...

Hence, it is not an AP

6) 3 , 1, 1/3,...

It is not an AP

7) t(n+1)= 6*t(n)

t(1) = -1

t(2)=-6

t(3)= -36

Hence, it is not an AP

8) -3, 1, 5, 9

Hence, it is an AP.

9) 1, 4, 9,...

Hence, it not an AP

10) 2,1,0,1,2,...

It is not an AP

11) t(n)= -2n-5

t(1)= -7, t(2)= -9, t(3)= -11

Hence, it is an AP

12) tn= (1/2)^n

 t1= 1/2, t2= 1/4, t3= 1/8

It is not an AP

Learn more about AP here:

brainly.com/question/24873057

#SPJ1

6 0
2 years ago
Evaluate.<br> 21 + } + (-)) -<br> Enter your answer as a mixed number in simplest form in the box.
andrew-mc [135]

Evaluate: 2(1/4) + 2/5 ÷ (-1/2) - 1/4

⇛9/4 + 2/5 ÷ (-1/2) - 1/4

Take the LCM of the 4 and 5 is 20.

Again, 2 and 4 is 4.

⇛[(54+8)/20] ÷ [(-2 - 1)/4]

⇛62/20 ÷ (-3/4)

⇛62/20 × 4/-3

⇛62/{5*(-3)}

⇛62/-15.

3 0
2 years ago
Other questions:
  • Calculate the number of hours in 3 1/2 days.<br><br><br> so 3 1 and 2 and the bottom like a fraction
    8·2 answers
  • Multiplying using arrays(with factors of ten) 10×25=
    8·1 answer
  • Two boys are throwing a baseball bat back and forth. The ball is 4ft above the ground when it leaves one child's hand with an up
    13·2 answers
  • What is 9/12 simplified to the lowest terms
    10·2 answers
  • List the next four multiples of the fraction 2/5
    11·2 answers
  • What variable expression represents the phrase "the difference of twice a number and 3"?
    5·2 answers
  • Question 7 of 10
    9·1 answer
  • Complete the square to write each ellipse in standard form. x^2 + 4y^2 + 24y = 32​
    11·1 answer
  • The length of one base of a trapezoid is 19 meters and the length of the median is 23 meters. Find the length of the other base,
    10·2 answers
  • #14 i
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!