Trigonometric Equations

Solve the equation over the interval [0°, 360°)

cos(theta) = -1/2

Answers

Answer 1

Answer:

[tex]\frac{2\pi }{3};\frac{4\pi }{3}.[/tex]

Step-by-step explanation:

1) cos(θ)=-0.5;

theta=±2π/3+2πn, where n∈Z;

2) if θ∈[0;360], then

[tex]\theta=\frac{2\pi }{3}; \frac{4\pi }{3}.[/tex]


Related Questions

(1 point)
A hot air balloon is launched from the ocean beach. As it moves inland, it rises and then falls, having a path given by
p(x)= - 2x^2/2500 +0.7x where x is in metres. The land rises at a rate of 2 vertical metres for each 20 horizontal metres. See the
diagram



a. At what horizontal distance does the balloon reach maximum height above sea level?
b. What is the maximum height of the balloon above seal level?
c. What is the maximum height of the balloon above ground level?
m and
d. At what horizontal distance is the balloon 50 m above the ground? List the smaller value first.

Answers

The launching of the hot air balloon is from the ocean beach is an illustration of a projectile motion

The horizontal distance which it attains a maximum height

The function is given as:

[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]

Differentiate

[tex]p'(x) =-\frac{4}{2500}x + 0.7[/tex]

Set to 0

[tex]-\frac{4}{2500}x + 0.7 = 0[/tex]

Subtract 0.7 from both sides

[tex]-\frac{4}{2500}x =- 0.7[/tex]

Multiply through by -2500/4

[tex]x =437.5[/tex]

Hence, the horizontal distance which a maximum height is attained is 437.5 meters

The maximum height above the sea level

In (a), we have:

[tex]x =437.5[/tex]

Substitute [tex]x =437.5[/tex] in p(x)

[tex]p(437.5) =-\frac{2}{2500} * 437.5^2 + 0.7 * 437.5[/tex]

Evaluate

[tex]p(437.5) =153.125[/tex]

Hence, the maximum height above the sea level is 153.125 metres

The maximum height above the ground level

In (b), the maximum height above the sea level is 153.125 metres

The ratio of the height on land and sea is given as:

Land : Sea = 2 m : 20 m

For the maximum height, we have:

Land : 153.125 m= 2 m : 20 m

Express as fraction

Land / 153.125 m = 2 /20

Multiply both sides by 153.125

Land = 15.3125

Approximate

Land = 15.3

Hence, the maximum height above the ground level is 15.3 meters

The horizontal distance where the balloon 50 m above the ground

We have:

[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]

Substitute 50 for P(x)

[tex]-\frac{2}{2500}x^2 + 0.7x = 50[/tex]

Using a graphing calculator, we have:

x = 78.465 and 796.535

Hence, the horizontal distances where the balloon 50 m above the ground are 78.465 and 796.535 meters

Read more about projectile motion at:

https://brainly.com/question/1130127

Find the rule from the given table

A.Divide by 2
B.Divide by 3
C.Divide by 5
D.Divide by 6

Answers

Answer:

the answer b

Step-by-step explanation:

te answer b because I guessed

Solve each of the following equations. Show its solution set on a number line. Check your answers. 3(x-2)=12
PLS HELP WILL GIVE BRAINLIEST

Answers

x = 6

Step-by-step explanation:

[tex]\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6[/tex]

Answer: (negative solution): x=-2, (positive solution): x=6

What is the answer for this question?

Answers

Answer:

is this from flvs?

Step-by-step explanation:

The circumference of a circle is 62.8 centimeters. What is the circle's radius?
C=62.8 cm
Use 3.14 for ​.
centimeters

Answers

Hello!

To solve this exercise, we must use the formula below:

[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]

C = 62.8cmπ = 3.14r = ?

Knowing these values, let's replace them in the formula to obtain r:

[tex]\mathrm{62.8=2\cdot\ 3.14\cdot r}\\\mathrm{62.8=6.28r}\\\mathrm{6.28r=62.8}\\\\\mathrm{r=\dfrac{62.8}{6.28}}\\\\\boxed{\mathrm{r=10}}[/tex]

So, the radius of this circle is 10cm.

Hope this helps!

You need 3 sticks of butter for every 24 giant cookies you bake.

Answers

Answer:

Sticks of butter : 2

Number of cookies : 40

Step-by-step explanation:

Given that :You need 3 sticks of butter for every 24 giant cookies you bake.

----------------------------------------------------------------------------------------------------------

Sticks of butter                    Number of cookies

 3                                           24

 x                                             16

5                                                 y

----------------------------------------------------------------------------------------------------------

Let the unknown be x and y..

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 24/3 = 8

Since the number of cookies is 16 then 16/8 = 2

Thus x = 2

Next for y.

Since you need 3 sticks of butter for every 24 giant cookies you back

Then 5 * 8 = 40

Thus, y = 40

----------------------------------------------------------------------------------------------------------

Completed table below:

Sticks of butter                    Number of cookies

 3                                           24

 2                                             16

5                                                 40

----------------------------------------------------------------------------------------------------------

~lenvy~

Answer:

See below ↓

Step-by-step explanation:

Given

You need 3 sticks of butter for every 24 cookies

Base rate

no. of butter sticks / no. of cookies3 / 241 stick of butter for every 8 cookies

16 cookies

No. of sticks = 16/8No. of butter sticks = 2

5 butter sticks

No. of cookies = 8 x 5No. of cookies = 40

Juan and Matthew each have gardens. Juan's garden is 16 feet long and 12 feet wide. Matthew's garden is 18 feet long and 21 feet wide. Area is found by multiplying length and width. What is the total area of the two gardens?

Answers

Answer:

570 ft²

Step-by-step explanation:

Basically, you find the area of Juan and Matthew's gardens then add them up.  

First let's find the area of Juan's garden.

Area is equal to length times width ([tex]a = lw[/tex])

So you do 16 * 12 which equals 192.

Now let's find the area of Matthew's garden.

So you do 18 * 21 which equals 378.

Then you add up both areas.

192 + 378 = 570

What fraction is equivalent to six tenths and has a denominator of 100?

Answers

Answer:

3/5

Step-by-step explanation:

3/5=6/10

3/5=60/100

Question 3 of 5 How many solutions does 6 + = -5 - Lo have? 31 10 ? O A. One solution O B. Infinitely many solutions O C. Two solutions O D. No solutions​

Answers

Answer:

En la Imagen adjunta

Step-by-step explanation:

Toca Para Abrir Imagen

Espero haberte ayudado si es así dame Corona

Answer:

One Solution

Step-by-step explanation:

Given:

6 + x/5 = x/5 - 5 - 3x/10

To Find:

How many solutions?

Solve:

[tex]6+\frac{x}{5}=\frac{x}{5}-5-\frac{3x}{10}[/tex]

[tex]\mathrm{Subtract\:}\frac{x}{5}\mathrm{\:from\:both\:sides}[/tex]

[tex]6+\frac{x}{5}-\frac{x}{5}=\frac{x}{5}-5-\frac{3x}{10}-\frac{x}{5}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]6=-5-\frac{3x}{10}[/tex]

[tex]\mathrm{Add\:}5\mathrm{\:to\:both\:sides}[/tex]

[tex]-5-\frac{3x}{10}+5=6+5[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-\frac{3x}{10}=11[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]

[tex]10\left(-\frac{3x}{10}\right)=11\cdot \:10[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-3x=110[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]

[tex]\frac{-3x}{-3}=\frac{110}{-3}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=-\frac{110}{3}\;or\;\left(\mathrm{In \;Decimal\;form}:\quad x=-36.66666\dots \right)[/tex]

~lenvy~

Help me please anybody. And I am in my school iPad

Answers

Answer:

(0,5)

Step-by-step explanation:

I'm really not sure but I'm pretty positive that this is the answer if not than my bad

Mario loaned Robert $390 at an interest rate of 18% for 229 days. How much will Robert pay Mario at the end of 229 days? Round your answer to the nearest cent.

Answers

Answer:

Amount Robert will pay back = $434.04

Step-by-step explanation:

Formula for interest is;

I = (P * R * T)/100

We are given;

P = $390

Rate = 18%

Time; T = 229 days = 229/365

Thus;

I = (390 * 18 * (229/365))/100

I = $44.04

Thus, total amount Mario will pay back = $390 + $44.04 = $434.04

The diameter of a circular field is 56 cm. Find the length of wire required to
fence it? How
many times it can be fenced with 704 m of wire ?

Answers

Answer:

176cm

400 times

Step-by-step explanation:

A cake for 6 people requires 4 eggs.How many eggs are needed to make a cake big enough for 9 people​

Answers

Answer:

6

Step-by-step explanation:

Divide the amount of eggs by the amount of people this gives you the amount of eggs needed for one person then times by 9

(4÷6) x9

axis of symmetry f(x) = −4(x − 8)^ 2 + 3

Answers

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

For an equation in the form of [tex]y=a(x-h)^2+k[/tex], the axis of symmetry is where [tex]x=h[/tex]. In this case, the axis of symmetry is the line [tex]x=8[/tex]

A can of soda can be modeled as a right cylinder. Aubrey measures its height as 10.1
cm and its circumference as 14 cm. Find the volume of the can in cubic centimeters.
Round your answer to the nearest tenth if necessary.

Answers

The volume of the cylinder is the amount of space in the cylinder

The volume of the cylinder is 218.4 cubic centimeter

How to determine the volume of the cylinder?

The given parameters are:

Circumference (C) = 14 cm

Height (h) = 10.1 cm

Start by calculating the radius (r) using:

[tex]C = 2\pi r[/tex]

So, we have:

[tex]2\pi r = 14[/tex]

Make r the subject

[tex]r =\frac 7\pi[/tex]

The volume of the cylinder is then calculated as:

[tex]V =\pi r^2h[/tex]

This gives

[tex]V =\pi * (\frac{7}{\pi})^2 * 14[/tex]

Evaluate

[tex]V =218.4[/tex]

Hence, the volume of the cylinder is 218.4 cubic centimeter

Read more about volumes at:

https://brainly.com/question/10171109

An exponential function has a growth factor or 3.76. What is the percentage growth rate?

Answers

The exponential function with a growth factor has a rate greater than 1

The percentage growth rate is 276%

How to determine the percentage growth rate?

The growth factor (b) is given as:

b = 3.76

The growth factor (b) is greater than 1.

So, the percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 3.76 - 1

Evaluate the difference

r = 2.76

Express as percentage

r = 276%

Hence, the percentage growth rate is 276%

Read more about exponential functions at:

https://brainly.com/question/11464095

A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?

3
4
5
6

Answers

The clock skipped 3 seconds every 30 mins (on average)

The number of times that the clock was skipping every 30 minutes from Friday noon to Monday 6 pm is; 3 seconds

What is the clock skip reading?

We know that from time conversion;

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48 times of 30-minutes in a day. However on Friday, we start counting at noon, which is half of the day.

Thus, on Monday, the mark is only up to 6 pm, which is three-fourths of the day. Thus;

Friday = 48 × (3/4)  = 24

Saturday = 48

Sunday = 48

Monday = 48 × (3/4)  = 36

Total times = 24 + 48 + 48 + 36 = 156

Thus, it means that there was 156 times of  30-minutes that have passed during the time period.

x = 468 seconds ÷ 156

x = 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

Read more about Least common multiple at; https://brainly.com/question/10749076

Which list of numbers could be used to name each point plotted on the number line?

A nuimber line goes from 3.45 to 3.6 in increments of 0.01. Blanks are located as follows: above the first tick mark after 3.45, above the second tick mark after 3.45, above the third tick mark after 3.5, and above the first tick mark after 3.55.

Answers

Answer:

Step-by-step explanation:

numbers are {3.46,3.47,3.48,3.49,3.50,3.51,3.52,3.53,3.54,3.55,3.56,3.57,3.58,3.59}


Please help 300 points

Answers

Answer:

4x + 9 ≥ 0

Step-by-step explanation:

The inside of the square root, the radicand, cannot be negative.

It can only be zero or positive.

Zero or positive is also described as being greater than or equal to 0.

Set the radicand to be greater than or equal to zero.

4x + 9 ≥ 0

Answer:

4x+9>=0

Step-by-step explanation:

The domain of a square root is that it can’t be less than 0. So we have the equation 4x+9>=0.

Convert the unit of length. Round the answer to one decimal place if necessary. 180 cm ≈ _____ ft
180 cm ≈ _____ft ?

Answers

Answer:

that would be the circumference of  the circle

= 2 pi  r

= 2 * pi * 2

=  6.28 feet   to 2 DP's.

Step-by-step explanation:

Answer:

6 ft

Step-by-step explanation:

Convert the unit of length. Round the answer to one decimal place if necessary. 180 cm ≈ _____ ft

[tex]Ft=\frac{cm}{30.48}\\\\Ft=\frac{180}{30.48}\\\\Ft=5.90551181\\\\Ft\approx 6[/tex]

180 cm ≈ 6 ft

Hope this helps!


The quadratic function

Answers

Answer:

Four and three arithmetic numbers of this equation are then

Step-by-step explanation:

[tex]x = 3 = x = 4 > - 4 > < - 3 = x = 4[/tex]

And the numbers are equal

[tex]x = 4 \\ y = 3 \\ x \times y = 12 = 12 > 4 > 3 = xy = 0 = \\ xy = - 12[/tex]

What is g(-2) for g(x) =1/2x^2+2x?
Does anyone know this

Answers

Step-by-step explanation:

please mark me as brainlest

on
Find the distance between -1/2 and 1 2/3
on
a number line.

units

Answers

Answer:

Step-by-step explanation:

1 2/3 -(-1/2)

=5/3+1/2

[tex]=\frac{10+1}{6} \\=\frac{11}{6} \\=1\frac{5}{6}[/tex]

which of the following steps were applied to ABCD to obtain A'B'C'D'?

A. shifted 3 units left and 2 units up
B. shifted 2 units left and 4 units up
C. shifted 2 units left and 3 units up
D. shifted 3 units left and 4 units up ​

Answers

Answer:

A. shifted 3 units left and 2 units up

Answer:

shifted 3 units left and 2 units up

Brian Orcard supplies apple to markets in Albany. The apple can be packed into a large bag that holds 9 apples or a small bag that holds 6 apples.

A market orderd 140 apples packed in small bags. How many small bags can be filled? Divide using a eectangle area modle and show the remainder.

The orchard needa to fill an order for 156 apples using both large and small bags. What is the least number of each type of baf that could be used if wach bag is completely filled?​

Answers

Answer:

10 large bags and 11 small bags because 10*9=90 and 156-90=66 and 6*11=66 so 90+66=156

Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

EZ

Based on a survey, assume that 35% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when six consumers are randomly selected,
delivery by drones. Identify the values of n, ×, p, and q.

Answers

Answer:

Suppose that we want to find the probability that when six consumers are randomly selected, actually three of them are comfortable with delivery by drones.

Step-by-step explanation:   hopes this helps you!

What is the outlier for the data set? PLS HELP I REALLY NEED HELP :(
Heart Rate
5 0 7
6 3 5 6 8 8
7 0 2
8
9 0
5 0 = 50 beats per minute
40
50
68
90

Answers

Answer:

6 3 5 6 8 8

Step-by-step explanation:

number is farthest apart from others

Answer:

The correct answer is 90

Step-by-step explanation:

90 is the biggest number in the number set so therefore it is an outlier.

Have an amazing day!!

Please rate and mark brainliest!!

PLEASE HELP PLEASE I WILL GIVE BRAINLIEST

Answers

Answer

Parallelogram: A quadrilateral with 2 pairs of parallel sides. Rectangle: A parallelogram with 4 right angles.

-(4-x)=3/4(x-6) i need help pls

Answers

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−2

hope this is what your looking for

Answer:

x = -2

Step-by-step explanation:

[tex]-4+x=\frac{3}{4}x-\frac{9}{2}[/tex]

[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]

[tex]-4+x+4=\frac{3}{4}x-\frac{9}{2}+4[/tex]

[tex]Simplify[/tex]

[tex]x=-\frac{1}{2}+\frac{3}{4}x[/tex]

[tex]\mathrm{Subtract\:}\frac{3}{4}x\mathrm{\:from\:both\:sides}[/tex]

[tex]x-\frac{3}{4}x=-\frac{1}{2}+\frac{3}{4}x-\frac{3}{4}x[/tex]

[tex]\frac{1}{4}x=-\frac{1}{2}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]

[tex]4\cdot \frac{1}{4}x=4\left(-\frac{1}{2}\right)[/tex]

[tex]x=-2[/tex]

~lenvy~

5.Find the area of the parallelogram. *
10 m
16 m
8 m
16 m
10 m

Answers

Answer:

128 because formula is bh

Step-by-step explanation:

Other Questions
What does appropriation have in common with street art?HELP MEEEEEEEEEEEEEEE what is the solution of the system of equations 4x+2y=-1 and 3x+4y=3 The researcher had to throw out some surveys because theparticipants didn't complete them in full. What happenedto the power? Why? The measures of heights (in inches) of a class of students are shown. 60, 60,54, 62, 62, 57,58, 65, 54,67, 63,57, 62, 54, 72, 66, 54, 69, 55, 61 Find the mean, median, mode, range, and standard deviation of the heights.b. A new student who is 7 feet tall joins your class. How would you expect this students height to affect the measures in part (a)? How and why did the USA win World War 2 Pretend that you are the administrative assistant for the marketing department of ABC Technologies. You are coordinating travel for an upcoming meeting in another state. You need to ask the director of the Marketing Department who is going to the meeting, the dates they will be gone, and how many rental cars and hotel rooms they will need. Write an e-mail to the director asking for this information. Be sure to include the elements of an e-mailthe sender, recipient, date, subject, and message. (Make up the names and any other information, as needed.) The day before the drawing of a $600 million Powerball letter, you notice that a line of people waiting to buy their Powerball tickets is stretched outside the door of a nearby convenience store. Based on what you've learned, provide some perspective on why these people are doing this, and what would likely happen if you or one of these individuals happened to pick the right numbers. How would winning the Powerball alleviate stress and change a persons lifestyle? How do you believe it could create stress for a person? Evaluate the degree to which Third World countries were successful in their quest to end colonialism and establish new ways of serving their populations. Teachers are being trained to standardize the scores they give students essays. The results are shown in the tablesCalculate the MADs for the teachers scores. Did the teachers make progress in standardizing their scores?____,(Yes or No) The MAD before the training was ______(MAD for the top chart) and the MAD at the end of the training is _______,(MAD for bottom chart) so _______ (progress or no progress)was made toward standardizing test scores In the process of . DNA is used as a template for making another type of Nucleic acid? what is the cap of ia? my history question How the circulatory and respiratory systems work together to deliver oxygen to the bodys tissues Frank grows evergreen trees. He grew 535 trees forthe holiday season. In November he sold 215 treesand in December he sold 275.a. Write an expression. Then solve.b. Frank replanted the left over trees with theaddition of 650 more trees. How many trees willhe have for next season? please help I will give brainlyist to the first answer!!!How do taxes benefit children, families, and communitys? Whats 36 km=?m into a desmal If a given set of cash flows is expressed in nominal terms and discounted at the nominal rate, the resulting present value will be the same as if the cash flows were expressed in real terms and discounted at the ____ rate. Sandra bought 4 pounds of sweet potatoes for $5.36. What is the cost per pound of the sweet potatoes? A. $0.75 B. $1.34 C. $1.26 D. $9.36 3. In the formula F = kx , what does the minus sign indicate?It indicates that the restoring force is in the direction of the displacement.It indicates that the restoring force is in the direction opposite the displacement.It indicates that mechanical energy in the system decreases when a system undergoes oscillation.None of the abovePlease show all of your work. Imagine that we randomly select a day from the past 10 years The scores on a psychology exam were normally distributed with a mean of 52 and a standard deviation of 6. About what percentage of scores were less than 40?