Determine the number(s), x, between 0 and 2π where the line tangent to the function f(x)=2sin(x)+2cos(x) is horizontal.

Answers

Answer 1
The line tangent to (the graph of) a function is horizontal, when it's slope is equal to 0.

The slope of the tangent line at a point, is determined by the derivative of the function, at that point.

So, we find the derivative of f, and find when it is equal to 0:


f'=2cos(x)-2sin(x)

2cos(x)-2sin(x)=0

cos(x)=sin(x), 


then x is 45 degrees or 45+180=225 degrees, which are

[tex] \displaystyle{\frac{ \pi }{4} [/tex] radians, and [tex] \displaystyle{\frac{ 5\pi }{4}


Answer: π/4, 5π/4


Related Questions

What is 26.99 round to the nearest tenth

Answers

Salutations!

To round to the nearest tenth, you need know whether the number next to tenth place is greater than 5 or lesser than 5. If its greater than 5, you need to round up. If its lesser than 5, you need to round down. Now, in the number 26.99 9 is in the tenth place. The number next to 9 is greater than 5, so just add on to the ones place, making the tenth and hundredth place 0. Zero has no value so whether you add the zero or not, it does not matter.

26.99 round to the nearest tenth ≈ 27

Hope I helped (:

Have a great day!

To round 26.99 to the nearest tenth, we increase the tenths place by 1 because the hundredths place is 9, resulting in 27.0.

When rounding 26.99 to the nearest tenth, we need to look at the hundredths place, which is 9. Since 9 is greater than 5, we round up the digit in the tenths place by 1. Therefore, the number rounded to the nearest tenth is 27.0.

Simplify and determine the coefficient of (-x)(3y)(-2x).

a.-4
b.1/3
c.1
d.4

Answers

The coefficients in the equation (-x)(3y)(-2x) are the constants -1, 3, and -2. 
In order to simplify and determine only one coefficient we should multiply all  three constants together to get only one numerical constant .
The commutative law says hat you can rearrange a multiplication any way you want. so, (-1)*3*(-2)=(-3)*(-2)=6
The equation can be also simplified written as:
6x^2y
None of the option is the solution.

well.. i just got the same problem.. With the same multiple choice.. I'm going to put one. I might update with my score on the test after i finish. (this is an old question that i thought i might answer with my guess)


(09.05) A golf ball is hit from the ground with an initial velocity of 208 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground?

Answers

The amount of Time that it would take for the golf ball to hit the ground using the given parameters is; 13 seconds

How to solve projectile problems?

We are given;

Initial Velocity = 208 feet per second

Initial height = 0 ft

Now, the general equation to be used here is;

h(t)= -16t² + 208t

Factorizing the equation gives;

h(t) = -16t(t - 13)

At h = 0, we have;

-16t(t - 13) = 0

Thus;

t = 13 seconds

Read more about projectile problems at; https://brainly.com/question/24216590

#SPJ2

Given the piecewise function shown below, select all of the statements that are true.

Answers

When x = 1 (that is x > 0)  f(1)  = 1^2 - 1 = 0
So b is correct

The statements f(1) = 0 and f(-1) = 2 are true based on the piecewise function.

Options B and C are the correct answer.

We have,

The piecewise function:

f(x) = -x + 1, x < 0

f(x) = -2, x = 0

f(x) = x² - 1. x > 0

Now,

f(-2) = 0

False.

When x = -2, we are in the first condition, so f(-2) = -(-2) + 1 = 3, not 0.

f(1) = 0

True

When x = 1, we are in the third condition, so f(1) = (1)² - 1 = 0.

f(-1) = 2

True

When x = -1, we are in the first condition, so f(-1) = -(-1) + 1 = 2.

f(4) = 7

False.

When x = 4, we are in the third condition, so f(4) = (4)² - 1 = 15, not 7.

Therefore,

The statements f(1) = 0 and f(-1) = 2 are true.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ4

How long does it take $450 to double at simple interest rate of 100%

Answers

depending on when you get your interest rate. but it will double the second you get your interest rate, because it is a 100% interest

hope this helps

(it can be daily, weekly, monthly, etc)

Final answer:

It will take 1 year for $450 to double at a simple interest rate of 100%, as the simple interest formula shows that the interest equals the principal when the rate is 100% and time is one year.

Explanation:

To calculate how long it takes for $450 to double at a simple interest rate of 100%, we can use the formula for simple interest: Interest = Principal × Rate × Time. Since the goal is to double the principal, the interest earned should be equal to the principal of $450.

The simple interest formula in this shape becomes:
$450 = $450 × 1 × Time
When we simplify this, we find that Time equals 1.

Therefore, it will take 1 year for $450 to double at a simple interest rate of 100%.

Corresponding range of Celsius temperature C

Answers

By rearranging the equation, we find that 45 = 9/5 C +32 and 85 = 9/5 C +32
Therefore the answer is, 7.22 < C < 29.44
As the formula says F = (9/5)C + 32 which is the equal to the following:

F - 32 = (9/5)C   =>   C = (F-32)*5/9

F1 = 45
F2 = 85

in Celsius they will be:
C1 = (45 - 32)*5/9 = 13*5/9 = [tex] 13\frac{5}{9} [/tex]
C2 = (85 - 32)*5/9 = 53*5/9 = [tex] 53\frac{5}{9} [/tex]

And the answer will be:

[tex] 13\frac{5}{9} [/tex] < C < [tex] 53\frac{5}{9} [/tex]

Simplify. −2i ⋅ (−3i)  

a.−6i

b. 6

c. −6

d. 6i




HURRY!

Answers

-2i * -3i
6i
6i^2
6 * -1
-6

Answer: C) -6 or the third option.
Final answer:

To simplify -2i * -3i, multiply -2 by -3 to get 6, then multiply i by i to get i². Because i² is equivalent to -1 in the complex number system, multiply 6 by -1 to get your answer, which is -6.

Explanation:

When multiplying two complex numbers like −2i and (−3i), the 'i' terms get multiplied together separately to the numerical terms. This is due to the distributive property of multiplication.

So, if we apply the multiplication, we would have −2 multiplied by −3 which gives us 6. Then, i multiplied by i gives us . The term is defined as -1 in the realm of complex numbers.

Putting these together we get 6 x -1, that results in −6.

Therefore, the simplified value of the expression is -6, which corresponds with option c.

Learn more about Complex Numbers here:

https://brainly.com/question/20566728

#SPJ11

y = 4
y = 1/4 x +2

What is the x coordinate of the solution to the system of the linear equations?

A. 0

B. 2

C. 4

D. 8

Answers

4 = .25x + 2 , .25x = 2 , x = 8. The answer is D
The answer is D.8
4=1/4x+2
2=1/4x
8=x

what us the average rate of change

Answers

the rate of change is -2 for every set shown in the chart on the right

 so 6 to 7 would be -11 -2 = -13

7 to 8 would be -13-2 = -15

8 to 9 = -15-2 = -17

 B is the answer

how do i use parentheses to rewrite 16 - 4 × 3 + 7 so that it equals 120?

Answers

(16-4) x (3+7) when u subtract 16 and 4 you get 12. When u add 3+7 you get 10. After multiplying them together u get 120

(16-4) x (3+7) =120

when we subtract 16 and 4 you get 12.

When we add 3+7 you get 10.

After multiplying them together we get 120.

What are parentheses those called?

parentheses

Parentheses are a pair of punctuation marks that might be most customarily used to feature extra nonessential information or an aside to a sentence. Parentheses resemble two curved vertical lines: ( ). An unmarried one of these punctuation marks is called a parenthesis.

How do you operate parentheses?

Use parentheses to surround additional or supplemental data that clarifies or illustrates a point. Use parentheses to offer a digression or afterthought.Use parentheses to surround numbers or letters introducing objects in a list or outline.

Learn more about parentheses here: https://brainly.com/question/1473593

#SPJ2

PRE-CAL/CAL MASTER NEEDED

f ( 2x − 1 ) = 4x^2 − 10x + 6

from f(x)=x^2-3x+2, h(x)=2x-1, f(h(x))

How is this: f ( 2x − 1 ) = 4x^2 − 10x + 6 derived from ^

Answers

for every x you see in the f function you will replace with the h function 
  

What is the value of digit 0 in 175,028

Answers

Answer:

its in the hundreads place but it has no value becuase its 0

Step-by-step explanation:

Can you use the values in Pascal’s triangle to find the powers of 11? Explain.

Answers

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Yes!

Ultimately (it states) all numbers in existence can be extracted from Pascal's Triangle.  Using his binomial formation of: (a + b)^0 = 1 , where y is the number you are using.  and (a + b)^x is the equation you use to find the answer of that row...  the usage of that row, and the formation of its components is how you find the powers of numbers in a given row...

You would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution, and

If you look at the images below you will notice that to find a power of 11 at it's 6th power, you look at the 6th row of Pascal's Triangle... Although not completely relevant, I also added an image of using his Triangle to find the Powers of 2...

Remember, The images below are of only smaller versions of Pascal's Triangle, as his Triangle is of infinite size...

Yes, we can use the values in Pascal’s triangle to find the powers of 11

What is Pascal triangle?

Pascal triangles contains coefficient of (x + 1)'s expanded form's terms.

For first row, we have:

Thus, 1 is the value in the first row of Pascal triangle.

(x + 1) = 1

The variable x has coefficient 1, and that 1 itself, so second row of Pascal triangle has 1 , 1 as values.

It states that all numbers in existence can be extracted from Pascal's Triangle.

Using his binomial formation;

(a + b)^0 = 1 , where y is the number

(a + b)^x  is the equation that use to find the answer of that row. the usage of that row, and the formation of its components isto find the powers of numbers in a given row.

It would be able to find each row of the Triangle, and by using the association of Multiplication, addition, distribution.

Yes, we can use the values in Pascal’s triangle to find the powers of 11

Learn more about Pascal’s triangle

https://brainly.com/question/29630250

#SPJ3

Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the tunnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 3 inches and the altitude of the cone to be 4 inches.

Answers

check the picture below.

so, bearing in mind that, the radius and height are two sides in a right-triangle, thus both are at a ratio of each other, thus the radius is at 3:4 ratio in relation to the height.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=3\\ h=4 \end{cases}\implies \stackrel{full}{V}=\cfrac{\pi \cdot 3^2\cdot 4}{3}\implies \stackrel{full}{V}=12\pi \\\\\\ \stackrel{\frac{2}{3}~full}{V}=12\pi \cdot \cfrac{2}{3}\implies \stackrel{\frac{2}{3}~full}{V}=8\pi ~in^3 \\\\\\ \textit{is draining water at a rate of }12~\frac{in^3}{min}\qquad \cfrac{8\pi ~in^3}{12~\frac{in^3}{min}}\implies \cfrac{2\pi }{3}~min[/tex]

[tex]\bf \textit{it takes }\frac{2\pi }{3}\textit{ minutes to drain }\frac{2}{3}\textit{ of it, leaving only }\frac{1}{3}\textit{ in it}\\\\ -------------------------------\\\\ \stackrel{\frac{1}{3}~full}{V}=12\pi \cdot \cfrac{1}{3}\implies \stackrel{\frac{1}{3}~full}{V}=4\pi\impliedby \textit{what's \underline{h} at this time?} \\\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=\frac{3h}{4}\\ V=4\pi \end{cases} \implies 4\pi =\cfrac{\pi \left( \frac{3h}{4} \right)^2 h}{3}[/tex]

[tex]\bf 12\pi =\cfrac{\pi \cdot 3^2h^2 h}{4^2}\implies 12\pi =\cfrac{9\pi h^3}{16}\implies \cfrac{192\pi }{9\pi }=h^3 \\\\\\ \sqrt[3]{\cfrac{192\pi }{9\pi }}=h\implies \sqrt[3]{\cfrac{64}{3}}=h\implies \cfrac{4}{\sqrt[3]{3}}=h \\\\\\ \cfrac{4}{\sqrt[3]{3}}\cdot \cfrac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}=h\implies \cfrac{4\sqrt[3]{9}}{\sqrt[3]{3^3}}=h\implies \cfrac{4\sqrt[3]{9}}{3}=h[/tex]

use the model to write an equivalent fraction 3 over 4

Answers

3/4 * 2/2 = 6/8 ;; an equivalent fraction to 3 over 4 would be 6 over 8, or 6/8

6/8 , 9/12 are the equivalent fraction 3 over 4

What is Fraction?

A fraction represents a part of a whole.

The given fraction is 3/4.

In the given fraction the numerator is three and denominator is four.

We need to find the equivalent fractions of 3/4.

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.

Let us multiply with same number in numerator and denominator to find the equivalent fractions.

3/4×2/2=6/8

3/4×3/3=9/12

Hence, 6/8 , 9/12 are the equivalent fraction 3 over 4

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ2

What is the e-file rejection error for an Invalid bank account or routing transit numbers?

Answers

The number error will be 0019 for invalid bank account or routing transit numbers. In the programming system, the error 0019 will be displayed if the program in banking system find No suitable provider for component, which indicates that the bank account or routing transit numbers is not written within the system itself.

Answer;

The Error code "0019".

Explanation;

-The e-file rejection error for an invalid bank account or routing transit numbers is error code "0019".

-This error code may be caused by a variety of reasons and is present in tax accounting software, where an e-file sent to the IRS is rejected, hence the error name. An incomplete installation might be one of the several reasons behind an e-file rejection error.

A child is to receive a dose of 0.5 teaspoon of cough medicine every 6 hours. If the bottle contains 24 ​doses, how many days will the medicine​ last?

Answers

The bottle will last 6 days
it will last 6 days. 

A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth

Answers

a^2 + b^2 = c^2
10^2 + 6^2 = c^2
100 + 36 = c^2
136 = c^2
sqrt 136 = c
11.7 = c.....the ladder is 11.7 ft

The length of the ladder is 11.66 ft.

What is the Pythagoras theorem?

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

a² + b² = c²

Given that a ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 6 ft from the side of the house.

Let the length of the ladder be x

Therefore, using Pythagoras theorem

x² = 10² + 6²

x² = 100 + 36

x = [tex]\sqrt{136[/tex]

x = 11.66 ft

Hence, the length of the ladder is 11.66 ft.

For more references on Pythagoras theorem, click;

https://brainly.com/question/343682

#SPJ2

what is 15.2 rounded to the nearest tenth

Answers

It would stay the same. Hope this helps :)
the answer is 15 because the 2 is not 5 and above.

He burj khalifa is 828,000,000 micrometers tall. how is this value written in scientific notation in the gizmo™?

Answers

To write this in scientific notation, we have to move the decimal place to the left. Moving the decimal place to the left indicate a positive movement, therefore the correct scientific notation in this case is:

8.28 x 10^8 micrometers

The tax rate as a percent, r, charged on an item can be determined using the formula – 1 = r, where c is the final cost of the item and p is the price of the item before tax. Louise rewrites the equation to solve for the final cost of the item: c = p(1 + ). What is the final cost of a $40 item after an 8% tax is applied?

Answers

Sent a picture of the solution to the problem (s).

Answer:$43.20

Step-by-step explanation:

Ok folks 4 questions and 50 points up for grabs for correct answers....Need quickly thanks!!!

Answers

1. 2*0.8 = 1.6 PQ = 1.6

2. arctan(14/12) = 49.4 degrees

3. 15 * cos(70) = 5.1 feet

4.  x = 30 * cos(40) = 22.9813 = 23.0 miles

   y = 30 *sin(40) = 19.2836 = 19.3 miles

Describe and correct the error made in solving the system of equations by elimination

Answers

the mistake was when she multiplied the 2nd equation by 5, she forgot to also multiply that last number 10 by 5 as well.

correction :
5x + 3y - z = 15
-x + 2y + 3z = 10...multiply by 5
---------------------
5x + 3y - z = 15
-5x + 10y + 15z = 50 (result of multiplying by 5)
--------------------add
13y + 14z = 65

The error that was made is that the constant term in the second equation was not multiplied by 5.

How to solve these system of linear equations?

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method and Addition Method.

Based on the information provided, we have the following system of linear equations:

5x + 3y - z = 15               .........equation 1.

-x + 2y + 3z = 10               .........equation 2.

By multiplying the second equation by 5, we have the following:

(-x + 2y + 3z = 10) × 5 = -5x + 10y + 15z = 50      .........equation 3.

By adding equation 1 and equation 3, we have the following:

5x + 3y - z = 15

-5x + 10y + 15z = 50

13y + 14z = 65

Read more on elimination method here: brainly.com/question/28405823

#SPJ2

A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is

Answers

m = -2 and b = 3
so equation
y = -2x + 3

hope it helps

Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Type answer here

Answers

20 mg times 7days = 140 mg/week

Solve the equation, and check the answer
5g+4(-5+3)=1-g

Answers

the answer is 5g - 8 is your answer
1- 4=-3
(-5+3)=-2
-3/-2=1.5
1.5 times 5=7.5
g=7.5

Evaluate the expression for the given value. 
 
36 ÷ m when m = 9



 
A.
324


 
B.
45


 
C.
27


 
D.
4

Answers

Plug 9 in for m
36/9=4

Final answer: D
36 / 9 = 4
answer

D. 
4

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

A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7:2, what is the combined amount of red and green apples sold?

Answers

7/2 = 63/g..7 red apples to 2 green apples = 63 red apples to g green apples
cross multiply
(7)(g) = (2)(63)
7g = 126
g = 126/7
g = 18

so they sold 63 red apples and 18 green apples...for a total of (63 + 18) = 81 apples sold

The total number of apples sold if, A produce store sold 63 red apples, The ratio of red apples to green apples sold was 7:2, which is 81.

What is the ratio?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

Given:

A produce store sold 63 red apples,

The ratio of red apples to green apples sold was 7:2,

Assume the total number of apples sold is x then,

Total number of apple sold = 7x + 2x

But the number of red apples sold is given so,

7x = 63

x = 63 / 7

x = 9

Put the value of x in the above equation,

Total number of apple sold = 7 × 9 + 2 × 9

Total number of apple sold = 63 + 18

Total number of apples sold = 81

To know more about Ratios:

https://brainly.com/question/13419413

#SPJ5

Corey needs 24 boards that ate 47 1/ 2 inches long. How many feet of boards should he buy. Explain

Answers

if each board is going to be 47 and 1/2 inches long, and there'll be 24 of them, then their total is just their product.

keep in mind that there are 12 inches in 1 foot.

[tex]\bf 24\cdot 47\frac{1}{2}\implies 24\cdot \cfrac{47\cdot 2+1}{2}\implies 24\cdot \cfrac{95}{2}\implies \cfrac{24}{1}\cdot \cfrac{95}{2}\implies \cfrac{2280}{2} \\\\\\ \stackrel{inches}{1140}\implies 1140~\underline{in}\cdot \cfrac{ft}{12~\underline{in}}\implies \cfrac{1140~ft}{12}\implies 95~ft[/tex]

A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inches wide. How far is the house from the other side of the lot?

Answers

check the picture below, so the distance of the house from the other side is that blue gap.

so, there are 12 inches in 1 foot, so let's just convert all those feet to inches and subtract them.

[tex]\bf 56'\implies (56\cdot 12)''\implies 672'' \\\\\\ 5'5''\implies (5\cdot 12+5)''\implies 65'' \\\\\\ 34'10''\implies (34\cdot 12 + 10)''\implies 418''\\\\ -------------------------------\\\\ 672''-(65+418)''\implies 189''\implies 15'9''[/tex]

Answer:

132

123


Step-by-step explanation:


Other Questions
Is Since I am so tall, I signed up for basketball. A compound or complex sentence An urn contains 8 red balls, 8 white balls, and 8 blue balls, and a sample of 5 balls is drawn at random without replacement. Compute the probility that all of the balls in the sample are the same color. Which of the following statements explains the position of those who oppose expanding nuclear power plants in the United States? As baby suzanne learns and remembers how to tie her shoes, this is requiring the use of her episodic memory explicit memory procedural memory semantic memory A line blank has endpoints How did the discovery of penicillin impact society? 50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, IF YOU DO ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~Find this a bit complicated. Please explain and show work with steps.Suppose f(x)=x4x+4. Compute the following:A. f(5)+f(5)=B. f(5)f(5)= What is the measure of angle x?mx = __ Why should we practice good health habits? What elements of shared culture and values bound together the diverse Greek city-states? How can you use a number line to add and subtract like fractions? In the study done by helen swain, what percentage of children said that death is unlikely or avoidable? Find the area of the rectangle?! Please :) Imagine that you are living in the year 3000. A specially designed-ship, made from alloys (A mixture of metals like iron and nickel) is about to make a trip to the center of the earth. Write a mini-story no more than 1 page describing their experiences exploring the layers of the earth. Talk about what you see, find, smell, etc. Be creative! Just some ideas. You don't need to write the whole thing. What are some sumerian inventions and advances in learning that influenced the development of later civilization? which of these is a compound noun Garth estimated the height of the door to his classroom in meters.what is a reasonable estimate The temperature outside is dropping at 3/h. Given that the temperature at noon was 0, what would the temperature at 1 PM at 2 PM at 3 PM and 6 PM what was the temperature T hours afternoon In order to simulate epipelagic zone conditions in a model aquarium design, what light and temperature conditions would be required?A) Minimal amount of sunlight, warm temperatureB) Minimal amount of sunlight, cold temperature C)High amount of sunlight, cold temperature When mik has an absolute advantage in the production of two goods over tommy, mik? Steam Workshop Downloader