find all solutions to the equation in the interval [0,2n) cos x = sin 2x
Answers
Answer:
[tex]\huge\boxed{x\in\left\{\dfrac{\pi}{6};\ \dfrac{\pi}{2}\ \dfrac{3\pi}{2};\ \dfrac{5\pi}{6}\right\}}[/tex]
Step-by-step explanation:
[tex]\cos x=\sin2x\qquad|\text{use}\ \sin\theta=2\sin\theta\cos\theta\\\\\cos x=2\sin x\cos x\qquad|\text{subtract}\ \cos x\ \text{from both sides}\\\\0=2\sin x\cos x-\cos x\\\\2\sin x\cos x-\cos x=0\qquad|\text{distribute}\\\\\cos x(2\sin x-1)=0\iff\underbrace{\cos x=0}_{(1)}\ \vee\ \underbrace{2\sin x-1=0}_{(2)}[/tex]
[tex](1)\\\cos x=0\Rightarrow x=\dfrac{\pi}{2}+k\pi;\ k\in\mathbb{Z}[/tex]
[tex](2)\\2\sin x-1=0\qquad|\text{add 1 to both sides}\\\\2\sin x=1\qquad|\text{divide sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi[/tex]
[tex]\text{From}\ (1)\ \text{and}\ (2)\ \text{we have}\\\\x=\dfrac{\pi}{2}+k\pi\ \vee\ x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi\\\\\text{We have the interval}\ x\in[0;2\pi).\ \text{Therefore the solution is:}\\\\x\in\left\{\dfrac{\pi}{6};\ \dfrac{\pi}{2}\ \dfrac{3\pi}{2};\ \dfrac{5\pi}{6}\right\}[/tex]
Related Questions
5x + y = 7
20x + 2 = y
Answers
Answer:
x=0.2, y=6
Step-by-step explanation:
Since y=20x+2, 5x+y=7 => 5x + (20x +2 ) = 7
25x + 2 = 7
25x = 5
x = 0.2
so y = 20x + 2 = 20* 0.2 +2 = 4 + 2 = 6
so the final solution is [tex]\left \{ {{y=6} \atop {x=0.2}} \right.[/tex]
The values of x and y for the given simultaneous equation are;
x = 0.2 and y = 6
We are given 2 simultaneous equations;
5x + y = 7 ---(eq 1)
20x + 2 = y ----(eq 2)
Put 20x + 2 for y in eq 1;
5x + 20x + 2 = 7
25x + 2 = 7
25x = 7 - 2
25x = 5
x = 5/25
x = 0.2
Put 0.2 for x in eq 2 to get;
20(0.2) + 2 = y
4 + 2 = y
y = 6
In conclusion, the values of x and y are x = 0.2 and y = 6.
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how many solutions does the following equation have ? 12x+18=-3(-4x-6)
Answers
(−∞,∞) infinite solutions
Which of the following are ordered pairs for the equation y = 1/3x - 1?
(0,3) (0,-1) (6,1)
(3,0) (0,-1) (6,1)
(0,-1) (1,-4) (2,-7)
(0,-1) (-3,0) (-4,3)
Answers
Answer:
answer is the 2nd one
Step-by-step explanation:
y = 1/3(3) - 1 = 1 - 1 = 0 (3,0)
y = 1/3(0) - 1 = 0 - 1 = -1 (0, -1)
y= 1/3(6) - 1 = 2 - 1 = 1 (6, 1)
I need help with my homework I did it but it is wrong.
Answers
Answer:
π= 3V/(4r³)Step-by-step explanation:
Solve for π
V = 4/3πr³3/4V = πr³3V/(4r³) = ππ= 3V/(4r³)Answer:
π = 3V 4r³Step-by-step explanation:
V = 4 π r³
3
solve for π
3*V = 4π r³
3V = π
4r³
therefore.
π = 3V
4r³
b)
Which is the largest of the following numbers?
0.1, 0.02, 0.003, 0.0004, 0.00005
PLEASE HELP DUE TONIGHT!!! THANK YOU SO MUCH.
Answers
We need to use the place values to compare different numbers.
By only looking at the place value, we can see that the largest number is: 0.1
Let's see how to get the solution.
We can define place value as the place where a digit is with respect to the decimal point.
The digits that are at the far left are the larger ones, for example in:
11
The left one represents 10, while the right one represents 1:
10 + 1 = 11
The same happens when we look at the right of the decimal point, there the digits at the left will be larger than the ones at the right.
0.10 is larger than 0.01
From this, we can see that for the set:
{0.1, 0.02, 0.003, 0.0004, 0.00005}
The largest number will be the one with the leftmost first digit different than zero, which is the first one: 0.1
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For the sequence 2, 6, 10, 14,. . .
a) Write the recursive rule:
b) Write the explicit rule:
Answers
1
3
5
× 1
1
3
=
8
5
×
4
3
=
Find the product of the mixed numbers. Choose the correct answer.
StartFraction 4 Over 5 EndFraction
1 and StartFraction 3 Over 15 EndFraction
2 and one-half
2 and StartFraction 2 Over 15 EndFraction
Answers
Answer:
2 2/15
Step-by-step explanation:
Answer please! I will give out brainlest!
Answers
Please help!!! How do I go about solving the cardinality of the Venn Diagram shown below?
Answers
. Let x = 20: Evaluate x + x *2 - x/5
Answers
Answer:
Assuming this: * means a multiplication symbol, the answer is 56.
Step-by-step explanation:
1. Replace every single x with 20.
2. 20 + 20 * 2 - 20/5
3. Simplify the equation
4. 20 + 40 - 4 (Order of operations. To remember this use
P(parentheses)
E(exponents)
M(multiplication)
D(division)
A(addition)
S(subtraction)
Top to bottom represents which operations you should do first while simplifiying an equation. Addition and subtraction are in equal places. This is the same with multiplication and division.
5. 20 + 40= 60 - 4= 56
Which equation written in two variables is equivalent to the function: f(x)=-2(x-4)
y=-2(x-4)
Answers
Answer:
16
Step-by-step explanation:
Answer:
y= -2(x-4)
Step-by-step explanation:
I got it right on the tutorial...
Point A is located at (h, k). Point B is located at (h,;). Mis the midpoint of segment
AB. Determine the coordinates of point M.
w
Answers
Answer: 6
Step-by-step explanation:
Why is the answer A?
Answers
Answer:
B) 2 frozen dinners and 2 dozen jelly doughnuts
Step-by-step explanation:
Calculate the total utility for each option.
A) 46
B) 32 + 21 = 53
C) 16 + 30 = 46
D) 28
Option B has the highest total utility.
what is the slope of f(x)=12x-19
Answers
Answer: y=1/4+3
Step-by-step explanation:
1. The slope is 12
2. (6 - 2)/(12+4)= 4/16= 1/4
y - 2 = 1/4(x + 4)
y - 2 = 1/4x + 1
y = 1/4x + 3
What is the image of point (0,2) after a rotation of 90° counterclockwise about the origin?
Answers
Answer:
(-2,0)
Step-by-step explanation:
remember the rule for 90 degree clockwise is (-y,x) opposite y and x
the negative in there DOES NOT mean it will always be negative it means opposite but in this case yes it's negative because the opposite of positive is negative
Hope this helps dude, I'm also learning this in online school lol. ^-^
The image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).
The given coordinate point is (0, 2).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
The rule of 90° counterclockwise rotation: (x, y) becomes (-y, x), here
(-2, 0)
Therefore, the image of point (0,2) after a rotation of 90° counterclockwise about the origin is (-2, 0).
Learn more about the rotation of 90° counterclockwise here:
https://brainly.com/question/1571997.
#SPJ2
Mr. Chang’s class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class?
A. 28 ÷ 4/7 = 49
B. 28 x 4/7 = 16
C. 4/7 ÷ 28 = 1/49
D. 7/4 ÷ 28 = 1/16
Answers
Answer:
b
Step-by-step explanation:
First, multiply it with each other and then it is 28 *4/7 = 16
Meaning that there is 16 girls in Mr. Chang's class
Making the answer B. 28 x 4/7 = 16 to be correct
I hope this helps, love!
A rectangle has a length 5 meters more than five times the
width. The area of the rectangle is less than 100 meters
squared. Write an expression that represents all possible
widths (use the variable x) of the rectangle. Write your answer
as an inequality, a
Answers
Given:
A rectangle has a length 5 meters more than five times the width.
The area of the rectangle is less than 100 meters squared.
To find:
The expression or inequality that represents all possible widths of the rectangle.
Solution:
Let x be the width of the rectangle.
Length of the rectangle is 5 meters more than five times the width.
[tex]length=5x+5[/tex]
Area of rectangle is
[tex]Area=length \times width[/tex]
[tex]Area=(5x+5) \times x[/tex]
[tex]Area=5x^2+5x[/tex]
The area of the rectangle is less than 100 meters squared.
[tex]5x^2+5x<100[/tex]
[tex]5x^2+5x-100<0[/tex]
Divide both sides by 5.
[tex]x^2+x-20<0[/tex]
[tex]x^2+5x-4x-20<0[/tex]
[tex]x(x+5)-4(x+5)<0[/tex]
[tex](x+5)(x-4)<0[/tex]
It is true if one factor is negative and other is positive. So,
[tex]x-4<0\Rightarrow x<4[/tex] ...(i)
[tex]x+5>0\Rightarrow x>-5[/tex] ...(ii)
Using (i) and (ii), we get
[tex]-5<x<4[/tex]
Therefore, the required expression or inequality for possible
widths of the rectangle is [tex]-5<x<4[/tex].
Given j || k and m∠8=150° What is m∠3?
Enter your answer in the box.
m∠3= ___°
Answers
Answer:
30°
Step-by-step explanation:
•angle 8 would be the same as angle 6
•angle 6 is next to angle 3
•if you were to add angle 6 and 3 it should equal 180°
180-150=30°
i rlly hope this is correct and helps <3
What is the vertical distance between 670 feet above sea level and 300 feet below sea level? You answer
Answers
Answer:
970 feet is the difference between 670 feet above sea level and 300 feet below sea level.
Step-by-step explanation:
670-(-300)
970 feet
In a homerun derby competition there was 32 homeruns hit out of 124 hits approximately what percent of his war homeruns
Answers
Answer:
25.81%
Step-by-step explanation:
32/124 were homeruns, to make it into a percentage, multiply it by 100%
32/124 × 100 = 25.81%
Answer:
25%
Step-by-step explanation:
32 divided by 124 =.2580
Wright the number 972,274 in words
Answers
Answer:
Nine hundred seventy two thousand two hundred seventy four. Hope this helps
The table shows the cost for ordering a certain number of pieces of chicken. What is the value of x if the cost is proportional to the number
of chicken pieces ordered?
Pieces of chicken Cost
2 $3.00
3 $4.50
4 $6.00
6 X
Answers
acomoda 2 8 3 y 4 en este orden con las operaciones +-×÷ de forma que el resultado sea 76 y 40
Answers
Answer:
[(2*8) + 3] *4 = 76
[2*(8 - 3)]*4 = 40
Step-by-step explanation:
Los paréntesis ( ), corchetes [ ] y llaves {} son símbolos de agrupación que indican el orden de las cuatro operaciones aritméticas básicas (suma, resta, multiplicación y división). Las reglas del orden de operaciones establece que se debe realizar primero el cálculo dentro de los símbolos de agrupación.
En otras palabras, la jerarquía de operaciones es el orden en el que hay que realizar las distintas operaciones, ya que unas tienen prioridad frente a otras. Y establece primero debes empezar por resolver los paréntesis, luego los corchetes y finalmente las llaves. Es decir, cuando haya símbolos de agrupación dentro de símbolos de agrupación, calcula de adentro hacia afuera. Esto es, empieza simplificando los símbolos de agrupación en el centro.
Para obtener 76, se pueden realizar la siguiente operación combinada:
[(2*8) + 3] *4
Aplicando lo anteriormente mencionado de la jerarquía de operaciones, comienzas por resolver el paréntesis:
[16 + 3]*4
Ahora, resolviendo el corchete:
19*4
Finalmente, resolviendo la multiplicación:
19*4= 76
Entonces [(2*8) + 3] *4 =76
Para obtener 40, se pueden realizar la siguiente operación combinada:
[2*(8 - 3)]*4
Comenzando a resolver el paréntesis:
[2*5]*4
Ahora, resolviendo el corchete:
10*4
Finalmente, resolviendo la multiplicación:
10*4= 40
Entonces [2*(8 - 3)]*4 = 40
How do u do this question?
Answers
A --------¢ D
B --------¢ E
C --------¢ F
Just match like this buddy.
Which is larger: 25% of 38 OR 30% of 41
Answers
In total, Jessica and Jonathan have created 19.64 cups of lemonade. They sell the lemonade in servings of 1.25 cup.
How many FULL servings will they be able to sell?
Answers
The left over would be 70% of a cup so 15
Answer:
15 full servings before not having enough left over for another full serving.
Step-by-step explanation:
A radio transmission tower is 180 feet tall. How long should a guy wire be if it is to be attached 8 feet from the top and is to make an angle of 22° with the ground? Give your answer to the nearest tenth of a foot.
Answers
Answer:
453.95 feet exactly
Step-by-step explanation:
Jolie uses childcare facilities at her gym. Her monthly dues are $32, and childcare is $9 per visit this month she does not wish to spend more than $122 for both dues and childcare. If x represents the number of times she can use childcare services
Which of the following inequalities symbolizes this situation?
x
Answers
Answer:
A
Step-by-step explanation:
Let x= number of visits she makes
9(number of visits she makes) + 32 (less than or equal to) <= 122
9x+32<= 122
I WILL MARK BRAINLEST AND GIVE 100 POINTS! PLZ HELP ME IM STOOPID
Answers
Answer:
it's b and a
Step-by-step explanation:
Answer:
1. C) 15 inches
2. A) 22.5 inches
Step-by-step explanation:
please help me with this and show work thank you!!
Answers
[tex]21x^{2} -16x^{2} = 5x^{2} \\-18x-9x=-27x\\4-8=-4\\25x^{3} +5x^{2} -27x-4\\A[/tex]
