Mathematics College

Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x

Answers

Answer 1

The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

How to find the exact solutions of trigonometric equations?

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

Related Questions

a jet airplane reaches 769. km/h on a certain flight. how long does it take to cover 272 m?Set up the math. But don't do any of it. Just leave your answer as a math expression. Also be sure your answers includes all the correct unit symbols.

Answers

The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.

(272 m) / (769 km/h) x (1 h/3600 s) = 0.0095 s

1. Convert km/h to m/s: 769 km/h x (1000 m/1 km) x (1 h/3600 s) = 213.6 m/s

2. Divide the distance to travel (272 m) by the rate (213.6 m/s): 272 m / 213.6 m/s = 0.0095 s

The airplane's speed on this certain flight is 769 kilometers per hour. In order to calculate how long it will take to cover a distance of 272 meters, we must first convert the speed to meters per second. 769 kilometers per hour is equivalent to 213.6 meters per second. Once we have the rate, we can divide the distance by the rate, which is 272 meters divided by 213.6 meters per second. This calculation yields a result of 0.0095 seconds. Therefore, the airplane will take 0.0095 seconds to cover 272 meters.

The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.

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riley has a farm on a rectangular piece of land that is 200 meters wide

Answers

200 meters wide is the answer

Answer:

Do you mean "Riley has a farm on a rectangular piece of land that is 200 meters wide. This area is divided into two parts: A square area where she grows avocados (whose side is the same as the length of the farm), and the remaining area where she lives.

Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados. That way, she manages to save some money every week." ?

The answer is 7L^2>3l(200-l)

Solve the equation: 9-15x = 28 + 4x

Answers

Answer:

x = -1

Step-by-step explanation:

To solve this, we want to isolate x:

9 - 15x = 28 + 4x

Subtract 9 from both sides:

-15x = 19 + 4x

Subtract 4x from both sides:

-19x = 19

Divide both sides by -19:

x = -1

. If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?

Answers

39 because 54+87=141 and now u have to subtract 141 from 180 so it gives u 39

The answer is:

⇨ x = 39°

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

$\sf{54+87+x=180}$

$\sf{141+x=180}$

Subtract 141 on each side.

$\sf{x=180-141}$

$\sf{x=39}$

Hence, the other angle is 39°.

What would be 82% of 50

Answers

10% = 5
80% = 40
2% = 1
82% = 41

41

Answer:

82% of 50 is 41

Step-by-step explanation:

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PLEASE HELP THIS IS HARD

Answers

The Area of the shaded portion is: 72 square inches

What is the Area of the shaded region?

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ * 17 * 13 = 110.5 square inches

Area of smaller triangle = ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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PlEASE NEED HELP FAST!!!!

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The key features of this quadratic relation y = -3x² - 24x - 36 include;

y-intercept = (0, -36)x-intercept: (-6, 0) and (-2, 0).The equation of the axis of symmetry is x = -4.The vertex is (-4, 12).This quadratic relation has a maximum value of 12.

What is the graph of a quadratic function?

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped.

Since the leading coefficient (value of a) in the given quadratic function y = -3x² - 24x - 36 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (-6, 0) and (-2, 0).

When x = 0, the y-intercept can be determined as follows;

y = -3x² - 24x - 36

y = -3(0)² - 24(0) - 36

y = -36

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-24)/2(-3)

Axis of symmetry, Xmax = -4

For the vertex, we have:

y(-4) = -3x² - 24x - 36

y(-4) = -3(-4)² - 24(-4) - 36

y(-4) = 12

In conclusion, the quadratic function has a maximum value at 12.

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the cement truck can pour 20 pounds of cement I 45 seconds how long will it take the cement truck to pour 150 pounds of cement

Answers

337.5 seconds for 150 pounds of cement to be poured

9. Is the triangle shown below a right triangle? How can you prove your answer? 35 1 28 A. Yes because 352 +212 = 282 B. Yes because 212 +282= 352 C. No because 35 < 28 + 21 D. No because 212 +282 * 352

Answers

Problem

Solution

For this case if we have a right triangle we need to satisfy :

1^2 + 28^2 = 35^2

But this property is not satisfied so then the correct answer would be:

NO because 35 < 28+21

9. Is the triangle shown below a right triangle? How can you prove your answer? 35 1 28 A. Yes because

The ratio of blue marbles to green marbles in the box is 13 to 24.

How many marbles are in the box?

Answers

Answer:

Step-by-step explanation:

13 blue

24 green

(1.2 times 10^9)+(7.6 times 10^8) in scientific nota

Answers

Answer:

1.96x10₉

Step-by-step explanation:

Answer:

1.96 * 10^9 (1,960,000,000)

Step-by-step explanation:

This is basically 1,200,000,000 + 760,000,000

In the gift shop of the History of Flight museum, Elisa bought a kit to make a model of a jet airplane. The actual
plane is 18 feet long with a wingspan of 13.5 feet. If the finished model will be 10 inches long, what will the
wingspan be?
O 13.3 in
O 7.5 in
O 3.75 in.
O 24.3 in.

Answers

Answer:

I would say D.

Step-by-step explanation:

yeah

Cora works at a small airfield where she fuels planes. She fills a Canadian plane with 125 gallons of fuel, but the pilot wants a receipt that shows the total number of liters purchased. How many liters are on the receipt Cora provides? A. 475.250 liters B. 473.176 liters C. 480.005 liters D. 479.215 liters

Answers

Answer: B. 473.176

Step-by-step explanation: 3.78541 Liters are in one gallon, so if you multiply 3.78541 Liters by 125 gallons then you will end up with 473.176 liters. If you have to add tax then it would be A. 475.250

Need help will give brainliest and 5 stars! :)

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The logarithmic function can be written exponentially as follows.$t = 8^y.$

What is logarithmic function?

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is $log_{8}(t) = y.$

We know that if we have an equation in the form $a^x = b$, we can rewrite it in logarithmic form as $log_a(b) = x$ and vice versa.

Thus, $log_{8}(t) = y$

$t = 8^y$

Hence, the logarithmic function can be written exponentially as follows.$t = 8^y.$

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tiana car traveled 111 miles on 3/8 1/2 hot dogs in 3 3/4 minutes. how many dogs did he eat in one minute

Answers

Use a proportion:

111/( 3/8) = x/ 1

Cross Multiply

(3/8)x = 111

Multiply both sides by 8/3 ; reciprocal

x = (8/3) (111)

x = 296 miles

Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x3 + 1. Include the average rate of change in your answer.

Answers

Answer:

147

Step-by-step explanation

Average rate of change of a function is determined using the formula, Given the function, f(x) = 3x³ + 2To find the average rate of change between x = 3 and x = 5, let:a = 3f(a) = f(3) = 3(3)³ + 2 = 83b = 5f(b) = f(5) = 3(5)³ + 2 = 377Plug in the values into the formulaAverage rate of change =

Solve the absolute value equation. 20x - 19 = 0

Answers

To solve this absolute value equation, we can use find the solutions as follows taking into account the definition of absolute value, then, we have:

$|20x-19|=0\Rightarrow20x-19=0,or-(20x-19)=0$

Now, we can solve both equations to find the solution(s):

First case:

$20x-19=0\Rightarrow20x=19\Rightarrow x=\frac{19}{20}$

Second case:

$-(20x-19)=0\Rightarrow-20x+19=0\Rightarrow-20x=-19\Rightarrow x=-\frac{19}{-20}\Rightarrow x=\frac{19}{20}$

Then, both solutions are the same, because of the absolute rule (this is the point when y = 0, that is the x-intercept for this function.)

Therefore, the solution set is {19/20}.

Rewrite 4(30+5) using the Distributive Property of Multiplication over Addition.

Answers

the answer is going to be 120+5

Answer:

Step-by-step explanation:

4(30+5)

4(30)+4(5)

120+20

140

write an expression equivalent to 6 - 2x +5+ 4x that only has two terms

Answers

Answer:23

Step-by-step explanation:

if a point is chosen inside the large circle what is the probability that it will also be inside the small circle?

Answers

Answer:

1/4

Step-by-step explanation:

The probability will be equal to 1 - (probability that it will not be inside the small circle) = 1 - (pi*4-pi)/(pi*4)=1/4

happy valentines day :)

Answers

Answer:

Thank you for the free point happy valentines day!

Step-by-step explanation:

Un profesor de Enseñanza Básica le indica a sus alumnos que escojan tres dígitos
diferentes del conjunto {1, 2, 3, 4, 5} y formen números mixtos colocando los dígitos
en el casillero . También les recuerda que la parte fraccionaria tiene que ser
menor que 1, por ejemplo
2
3
5
. ¿Cuál es la diferencia entre el mayor y el menor de los
números mixtos que se pueden formar?

Answers

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

A mixed number is a number that has both a whole number and a fraction component. To form three-digit mixed numbers, we need to have a whole number that is less than 100 and a proper fraction that has a denominator less than or equal to 99. Here are some examples:123 4/567 2/8109 1/2382 3/47There are a total of 900 three-digit numbers that can be formed using digits 1 to 9 without repetition. To find the number of three-digit mixed numbers that can be formed, we need to count the number of ways we can choose a proper fraction with a denominator less than or equal to 99. There are 99 possible denominators, and for each denominator, there are 98 possible numerators (excluding 0 and the denominator itself). Therefore, the total number of three-digit mixed numbers that can be formed is:900 x 99 x 98 = 8,334,600There are 8,334,600 three-digit mixed numbers that can be formed using digits 1 to 9 without repetition.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

How to solve

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

Answers

The length of the apothem of the pentagon is approximately 11 meters.

What is a polygon?

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here, we have,

To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)

= 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

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How to simplify 3/18 it’s a fraction and it’s really hard can someone go step by step how to do it I need it ASAP

Answers

Answer:1/6

Step-by-step explanation: divide both sides by 3 as 3 itself and 18 can be divided by 3

how did u arrive at the answer?

Answers

You need to rearrive the question

A package contains 20 golf balls. The total
weight of the golf balls is 32 ounces. Use the
model to show the number of ounces per
golf ball and the number of golf balls per
ounce. Write your answers in the blanks.

Answers

Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

(ANSWERED FOR EASY POINTS:)Which products result in a difference of squares? Select three options.

(x minus y)(y minus x)
(6 minus y)(6 minus y)
(3 + x z)(negative 3 + x z)
(y squared minus x y)(y squared + x y)
(64 y squared + x squared)(negative x squared + 64 y squared)

Answers

Answer:

The three options that result in a difference of squares are:

(x minus y)(x plus y)

(6 minus y)(6 plus y)

(64 y squared + x squared)(64 y squared - x squared)

A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?

31 students
40 students
41 students
66 students

Answers

The number of students who will be going on the trip is B. 40 students.

What is a mathematical expression?

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

Data and Calculations:

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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To celebrate the holiday season this year, the Gaylord Texan has created an extreme eight-lane, tubing hill
with real snow called the "Kung Fu Panda Awesome SNOW Tubing Ride." The cost of each ticket for one day
is $21. This can be modeled by the function f(x) = 21x. The number of tickets purchased by groups is given
by the domain (4, 6, 103. which would be a reasonable range for the total cost of the tickets the groups
would pay?

Answers

The reasonable range for the total cost of the tickets the groups

would pay is {84, 126, 2163}.

What is Domain and Range?

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

Given:

The Function modeled for the situation is

f(x) = 21 x where x is the number of tickets sold.

So, For x= 4 Tickets

Fare, F(x) = 21 x 4= $84

and, For x= 6 Tickets

Fare, F(x) = 21 x 6 = $126

and, For x= 103 Tickets

Fare, F(x) = 21 x 103 = $2163.

Hence, the range is {84, 126, 2163}.

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Find the missing length of the triangle.

Answers

Answer:

Step-by-step explanation:

Hypotenuse = sqrt[ (Leg a)2 + (Leg b)2 ]

Hypotenuse = sqrt[ (39)2 + (80)2 ]

Hypotenuse = sqrt[ 1521 + 6400 ]

Hypotenuse = sqrt[ 7921 ]

Hypotenuse = 89

Answer:

45 is your answer c=45 13

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Find the exact solutions of the given equation in the interval . sin 4x= –2sin 2x

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Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x