Answers
Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for cosine
cos2x = 2cos²x - 1
Given
cos( [tex]\frac{0}{2}[/tex] ) = [tex]\frac{1}{2}[/tex]( p + [tex]\frac{1}{p}[/tex] ) , then
cosΘ = 2[ [tex]\frac{1}{2}[/tex](p + [tex]\frac{1}{p}[/tex] ) ]² - 1
= 2 [ [tex]\frac{1}{4}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) ] - 1 ← distribute by 2
= [tex]\frac{1}{2}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) - 1 ← distribute by [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex] p² + 1 + [tex]\frac{1}{2p^2}[/tex] - 1
= [tex]\frac{1}{2}[/tex] p² + [tex]\frac{1}{2p^2}[/tex] ← factor out [tex]\frac{1}{2}[/tex] from each term
= [tex]\frac{1}{2}[/tex] ( p² + [tex]\frac{1}{p^{2} }[/tex] ) ← as required
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]cos(\theta)=2cos^2(\dfrac{\theta}{2})-1\\\\=2\left(\dfrac{p+\dfrac{1}{p}}{2}\right)^2-1\\\\=\dfrac{p^2+\dfrac{1}{p^2}+2}{2}-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})+1-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})[/tex]
Thank you
Related Questions
Loryn,brian,and edna are donating book to the library.loryn donated 7 more books than brian.enda donated twice as many books as loryn. Together they donated a total of 53 books how many books did loryn donate
Answers
Answer:15
Step-by-step explanation: We know L+B+E=53 books
Loryn=L
Enda=2L
Brian=L-7
L+2L+L-7=53
Then solve for L
Leaving you with L=15
Check
15+2(15)+(15-7)
15+30+8=53
Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°.
Answers
Answer:
La altura del globo con respecto al suelo es 449,6 metros.
Step-by-step explanation:
La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?
El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:
Ciudad A
[tex]\tan 27^{\circ} = \frac{h}{1500\,m-x}[/tex]
[tex]0,510 = \frac{h}{1500\,m-x}[/tex]
Ciudad B
[tex]\tan 36^{\circ} = \frac{h}{x}[/tex]
[tex]0,727 = \frac{h}{x}[/tex]
Donde [tex]h[/tex] y [tex]x[/tex] son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.
A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:
[tex]0,727\cdot x = 0,510\cdot (1500\,m-x)[/tex]
[tex]1,237\cdot x = 765\,m[/tex]
[tex]x = 618,432\,m[/tex]
Finalmente, la altura del globo con respecto al suelo es:
[tex]h = 0,727\cdot x[/tex]
[tex]h = 0,727\cdot (618,432\,m)[/tex]
[tex]h = 449,600\,m[/tex]
La altura del globo con respecto al suelo es 449,6 metros.
Find the Slope of the line on the graph. write your answer as a fraction or a whole number, not a mixed number or decimal.
Answers
Answer:
3
Step-by-step explanation:
Geometry CA Find measures
The measure of an angle is 2°. What is the measure of its supplementary angle?
Answers
Answer:
178
Step-by-step explanation:
Supplementary angles add to 180 degrees
Let x be the supplement to 2
2+x = 180
Subtract 2 from each side
2+x-2 = 180-2
x = 178
select all the equations where b=11 solution
Answers
Answer:
b + 18 = 7
77 = 7b
9 = b - 2
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2 1/2. What is the value of x? PLEASE ANSWER ASAP!!
Answers
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Figure B = 2½ the size of figure A
One side of figure B is given as 5, therefore, 5 = 2½ of x in figure A.
Thus, [tex] 5 = 2\frac{1}{2}*x [/tex]
Solve for x
[tex] 5 = \frac{5}{2}*x [/tex]
[tex] 5*2 = \frac{5x}{2}*2 [/tex]
[tex] 10 = 5x [/tex]
[tex] \frac{10}{5} = \frac{5x}{5} [/tex]
[tex] 2 = x [/tex]
[tex] x = 2 [/tex]
explain how a rational number and an irrational number and different
Answers
Answer:
Rational numbers: fractions with an integer numerator and a nonzero integer denominator.
Irrational numbers: numbers that are not rational such as π, root 3, and any non repeating, non ending decimal.
Which operation involving complex numbers requires the use of a conjugate to be carried out?
Answers
Answer:
Step-by-step explanation:
Rationalization.
2 + i
For example: " rationalize the denominator of --------- "
-3 + i
C is between B and D. BC=4x + 10 and CD=25. Find BD.
A: BD=105
B: BD=45
C: BD=17.5
D:BD=80
Answers
Answer:
A: =105
Step-by-step explanation:
please help :) Which expression is equal to 18−15÷3 ? A. 18 - 5 B. 3 divided by 3 C. 18 - 12
Answers
Answer:
A)
Step-by-step explanation:
18 - 15÷ 3 = 18 - 5
Answer:
A!
Step-by-step explanation:
This one is easy peasy using PEMDAS.
1)18-15dividedby3
2)18-(15divided by 3)
3) 18-5
TA DA
What is the inverse of the function g(x)=-2(x-4)? g^-1(x)=___
Answers
Step-by-step explanation:
g(x) = y = 8 - 2x
(A) First transform the function in terms of x :
x = y - 8 / 2
(B) Replace x with y :
[tex] {g}^{ - 1} (x) = y = \frac{x}{2} - 4[/tex]
One card is to be drawn from a deck of 52 cards.The deck includes four types of cards.Red heart, red stars , black triangles , black circles .Each type has 13 cards numbered 1-13.What is the probability of drawing a red one a, black three , or a six of hearts.Give your answer in the simplify form .
Answers
Answer:
1/26 ; 1/26 ; 1/52
Step-by-step explanation:
Given the following :
A deck of 52 cards contains :
Red hearts, Red stars, black triangles, black circles
Each type of card is numbered from 1 - 13
Therefore,
Number of each type of card = 13, all numbered distinctly with digits between 1 - 13
Probability = (number of required outcomes / total number of possible outcomes)
If one card is drawn from the deck:
Probability of picking a red one :
This is either a red heart numbered 1 or a red red star numbered 1,
Therefore, Required outcomes = 2
Total possible outcomes = 52
P(a red one) = 2 / 52 = 1/26
B) A black three
This is either a black triangle numbered 1 or a black heart numbered 1,
Therefore, Required outcome = 2
Total possible outcomes = 52
P(a black three) = 2 / 52 = 1/26
C.) A six of hearts :
A hearts numbered six = 1
Therefore, Required outcome = 1
Total possible outcomes = 52
P(a black three) = 1 / 52 = 1/52
what is the midpoint of 2-3i and -4+6i
O2+31
-4-6i
0 -1+1.51
2-31
Answers
((2-3i)+(-4+6i)) / 2 =
(-2+3i)/2 =
-1+1.5i
please help me on this
Answers
Answer: (1,-1/2)
Step-by-step explanation:
Point C on the coordinate plane has the coordinates (4,-2) after a dilation with a scale factor of 1/4 we will have to multiply the coordinates each by 1/4 to find the new coordinates.
So x = 4 * 1/4 = 1 Now the new x coordinate is 1
-2 * 1/4 = -2/4 = -1/2 Now the new coordinate for y is also -1/2
So we will now have the coordinates (1,-1/2)
Solve this numerical problems
a Convert: 794mm into m and One day into sec.
Answers
To convert mm to m, divide by 1000:
794/1000 = 0.794 m
1 day = 24 hours
1 hour = 3600 seconds
24 x 3600 = 86,400 seconds in a day
Answer:
Step-by-step explanation:
To convert 794mm into m
1000mm = 1m
794mm = xm
m = 794/1000
m = 0.794m
One day to secs is
= 84,400secs
alex is traveling by train to a vacation spot that is 810 miles away. The train is traveling at 90 miles per hour, and it has already covered 180 miles. In exactly how many hours will alex reach his destination from his current position
Answers
Answer:
7 hours
Step-by-step explanation:
810 - 180 = 630
630/ 90 = 7
Answer:
x = 7 h
Explanation:
First, we write the data of the problem.
Alex travels 810 miles away
Train - 90 miles / h
Alex covers 180 miles.
How many hours does Alex walk in the distance?
1. Calculate the distance Alex still has to travel.
810 miles - 180 miles = 630 miles
2. We take into account the speed of the train to calculate how many hours Alex will cover the remaining distance.
90 miles .... 1 h
630 miles .... x h
x = 630 milesx1h / 90 miles
x = 7 h
ally and Anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Each woman’ total is modeled with this expression:
9 + 1.34 +
1
2
(3.50 +1.74)
How would you simplify the expression? Explain your steps.
Answers
Answer:
13.48
Step-by-step explanation:
3x-2y=6 and 5x-5y=5 Solve each system of equations
Answers
Answer:
x=4 and y=3
Step-by-step explanation:
Write the following equation in slope-intercept form.
3x - 2y=5
Answers
Answer:
y = 3/2x -5/2
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
3x- 2y = 5
Solve for y
Subtract 3x from each side
3x -3x- 2y =-3x+ 5
-2y = -3x+5
Divide by -2
-2y/-2 = -3x/-2 +5/-2
y = 3/2x -5/2
Q2. Allen can type 300 words in 3hours. How much word can he type in 5
hours?
Answers
3hour =300words
1 hour = 300/3
=100
5hours=100*5
=500 words
(Solve the following equation: 2 + 8x = 11x - 13 )
A. 5 B. -5 C. 15/19 D. - 15/19
Please help! I usally get these right but I'm completelly stumped! ( Please explain in detail )
Answers
Answer:
A. x = 5
Step-by-step explanation:
2 + 8x = 11x - 13 -------- subtract 2 from both sides
2 + 8x - 2 = 11x - 13 - 2
8x = 11x - 15 -------- subtract 11x from both sides
8x - 11x = 11x - 15 - 11x
-3x = -15
x = -15 / -3
x = 5
Answer:
x=5
Step-by-step explanation:
How to do this question plz answer my question
Answers
Answer:
28 cm
Step-by-step explanation:
vertical side of each parallelogram is (y-6)/2 cm
perpendicular height of each parallelogram is 7 cm
Total area = 4sh
308 = 14(y-6)
y-6 = 22
y = 28 cm
BRAINLIEST PLS
1. Evaluate x2 + 10 if we let x= 3
Answers
Answer:
16
Step-by-step explanation:
[tex]x2 + 10 \\ = 3 \times 2 + 10 \\ = 6 + 10 \\ = 16[/tex]
Answer:
16
Step-by-step explanation:
You plug 3 in for x and then you have (3)2+10 and 3 times 2 is 6 plus ten is 16
You toss a 6-sided number cube and
a coin at the same time. How many
possible outcomes are there?
A 2
B 6
C 8
D 12
Answers
Answer:
12
Step-by-step explanation:
There are 6 outcomes for the cube and 2 outcomes for the coin
6*2 = 12
There are 12 different outcomes total
Find the length of the missing side. Leave your answer in simplest radical form.
Answers
Answer:
The SQ Root of 493
Step-by-step explanation:
Becaues this triangle is a right triangle, we can find the missing side usiing the pythagorean theorum.
The pythagorean theorun states A^2 + B^2 = C^2, so 18^2 + 13^2= 439
Then all you have to do is find the sq root of 439, but this question askes you not to.
Hope this helps :)
What is the value of a?
I need help. Can someone help me out!!! Please
Answers
Answer:
I'm not sure about this one but you can try a=40
Step-by-step explanation:
Answer:
a = 30°
Step-by-step explanation:
Sum of the angles in a triangle is 180°
32° + 2a - 17 + 180° - ( a + 45° ) = 180°
32 + 2a - 17 = a + 45
a = 45 + 17 - 32
a = 30°
Is 2/3+4/5 a rational number
Answers
Answer:
Yes
Step-by-step explanation:
-6 times (-6) times (-6)
Answers
Answer:
-216
Step-by-step explanation:
-6 x -6 =36
36 x -6 = -216
Answer:
-216
Step-by-step explanation:
Where is the answer to the expression 5 − 9 located on a horizontal number line? (1 point)
9 units to the left of 5
9 units to the right of 5
4 units to the right of 5
4 units to the left of 5
Answers
fill in the blank with a possessive pronoun: don't take it this book is
Answers
Answer:
[tex]\large \boxed{\mathrm{mines}}[/tex]
Step-by-step explanation:
Possessive pronouns are pronouns that indicate relationship or ownership.
Don’t take it this book is mines.