Solve sin 4x - cos 2x = 0.

Answers

Answer 1

Answer: sin 4 x - cos 2 x = 0
2 sin 2 x cos 2 x - cos 2 x = 0
cos 2 x ( 2 sin 2 x - 1 ) = 0
cos 2 x = 0
2 x = π/2 + nπ / : 2
x 1 = π/4 + nπ/2, n ∈ Z
2 sin 2 x - 1 = 0
2 sin 2 x = 1
sin 2 x = 1/2
2 x = π/6 + 2 nπ
2 x = 5π/6 + 2 nπ
x 2 = π/12 + nπ
x 3 = 5π/12 + nπ , n ∈ Z

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Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per week. This week, her goal is to make at least $75. A. Use a system of inequalities to model the scenario above. Let x represent babysitting hours and y represent tutoring hours. B. Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week. C. Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model.
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What is a proportional relationship

Quadratic formula 2x²+9x-4=0

Answers

$2x^2+9x-4=0 \n \na=2 , b =9 , \ c=- 4 \n \n\Delta = b^(2)-4ac = 9^(2)-4*2* (- 4)= 81+32 =113 \n \nx_(1)=(-b-√(\Delta ))/(2a) =(-9- √(113))/(4) \n\nx_(2)=(-b+√(\Delta ))/(2a) = (-9+√(113))/(4)$

$2x^2+9x-4=0\ \ \ \ /:2\n\nx^2+(9)/(2)x-2=0\n\nx^2+2x\cdot(9)/(4)+((9)/(4))^2-((9)/(4))^2=2\n\n(x+(9)/(4))^2-(81)/(16)=2\n\n(x+(9)/(4))^2=(32)/(16)+(81)/(16)\n\n(x+(9)/(4))^2=(113)/(16)\iff x+(9)/(4)=-\sqrt(113)/(16)\ \vee\ x+(9)/(4)=\sqrt(113)/(16)\n\nx=-(9)/(4)-(√(113))/(4)\ \vee\ x=-(9)/(4)+(√(113))/(4)\n\nx=-(9+√(113))/(4)\ \vee\ x=-(9-√(113))/(4)$

10% of what number is 30

Answers

'is' in mathematics means equal
'of' in mathematics means multiplication

10% can also be written as 10/100

$(10)/(100) * x = 30\n\n(1)/(10)x = 30\n\n\boxed{\bf{x=300}}$

10% of 300 is 30

Convert percentage into decimal: 10%/100 = 0.1
Divide decimal by 30: 30 ÷ 0.1 = 300

Yosai is making a kimono for her father, The belt for the kimono should be one hundred sixty-three centimeters long. She has two meters of fabric. How much fabric will she have left after making the belt? (State your answer in meters.)

Answers

Answer:

Amount of fabric left = 0.37m

Step-by-step explanation:

Yosai has 2 meters of fabric, and the belt for the kimono should be 163 centimeters long.

In order to find out how much fabric she will have left after making the belt, we need to calculate the length of fabric used for the belt and then subtract that from the total amount of fabric.

$\sf 1 meter = 100 centimeters$

So, the length of fabric needed for the belt is:

$\sf 163 \, \text{cm} = (163)/(100) \, \text{m} = 1.63 \, \text{m}$

Now, subtract the length of fabric used for the belt from the total amount of fabric:

$\begin{aligned} \textsf{ Remaining fabric } &\sf = \textsf{ = Total fabric - Fabric used for the belt }\n&\sf = 2 m - 1.63 m\n&\sf \approx 0.37 m \end{aligned}$