Find all solutions
for cotx=-1​

Answers

Answer 1

Answer:

[tex]\cot(x) = -1[/tex] whenever [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] radians, where [tex]k[/tex] could be any integer ([tex]k \in \mathbb{Z}[/tex], which includes positive whole numbers, negative whole numbers, and zero.)

Step-by-step explanation:

[tex]x = 45^\circ[/tex] (as in isoscele right triangles) would ensure that [tex]\displaystyle \cot(x) = 1[/tex]. Since cotangent is an odd function, [tex]\cot(-45^\circ) = -1[/tex].

Equivalently, when the angles are expressed in radians, [tex]\cot(-\pi / 4) = -1[/tex].

The cycle of cotangent is [tex]\pi[/tex] (or equivalently, [tex]180^\circ[/tex].) Therefore, if [tex]k[/tex] represents an integer, adding [tex]k\, \pi[/tex] to the input to cotangent would not change the output. In other words:

[tex]\displaystyle \cot\left(k\, \pi - \frac{\pi}{4}\right) = \cot(-\pi / 4) = -1[/tex].

Hence, [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] would be a solution to [tex]\cot(x) = -1[/tex] whenever [tex]k[/tex] is an integer.

Since [tex](-\pi / 4)[/tex] is the only solution to this equation in the period [tex](0,\, \pi)[/tex], all real solutions to this equation would be in the form [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] (where [tex]k[/tex] is an integer.)


Related Questions

20% of the patron's order the chef's special. The probability that 2 out of the next ten customers will order the chef's special is

Answers

Answer:

[tex]P(x =2) = 0.3020[/tex]

Step-by-step explanation:

Given

[tex]p =20\% = 0.20[/tex]

[tex]n = 10[/tex]

Required

[tex]P(x = 2)[/tex]

This question is an illustration of binomial distribution where:

[tex]P(X = x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]

So, we have:

[tex]P(x =2) = ^{10}C_2 * 0.20^2 * (1 - 0.20)^{10-2}[/tex]

[tex]P(x =2) = ^{10}C_2 * 0.20^2 * 0.80^8[/tex]

This gives

[tex]P(x =2) = \frac{10!}{(10 - 2)!2!} * 0.20^2 * 0.80^8[/tex]

[tex]P(x =2) = \frac{10!}{8!2!} * 0.20^2 * 0.80^8[/tex]

Expand

[tex]P(x =2) = \frac{10*9*8!}{8!2*1} * 0.20^2 * 0.80^8[/tex]

[tex]P(x =2) = \frac{10*9}{2} * 0.20^2 * 0.80^8[/tex]

[tex]P(x =2) = 45 * 0.20^2 * 0.80^8[/tex]

[tex]P(x =2) = 0.3020[/tex]

The probability that 2 out of the next ten customers will order the chef special is 0.3020. and this can be determined by using the binomial distribution.

Given :

20% of the patron's order the chef's special. Sample size, n = 10

To determine the probability formula of the binomial distribution is used, that is:

[tex]\rm P(x = r) = \; ^nC_r \times p^r \times (1 - p)^{n-r}[/tex]

Now, at n = 10 and r = 2, the probability is given by:

[tex]\rm P(x = 2) = \; ^{10}C_2 \times (0.2)^2 \times (1 - 0.2)^{10-2}[/tex]

[tex]\rm P(x = 2) = \; ^{10}C_2 \times (0.2)^2 \times (0.8)^{10-2}[/tex]

[tex]\rm P(x = 2) = \; \dfrac{10!}{(10-2)!\times 2!} \times (0.2)^2 \times (0.8)^{8}[/tex]

[tex]\rm P(x = 2) = \; 45 \times (0.2)^2 \times (0.8)^{8}[/tex]

P(x  = 2) = 0.3020

The probability that 2 out of the next ten customers will order the chef special is 0.3020.

For more information, refer to the link given below:

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A government agency estimates the number of young adults (ages 18 to 24) in a particular country to be 31,000 (in thousands) in 2010 and changing at the rate of −x2 + 90x − 200 thousand per year, where x is the number of years since 2010. Find a formula for the size of this population at any time x. [Hint: Keep all calculations in units of thousands.]

Answers

Answer:

[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]

Step-by-step explanation:

From the given information:

Let assume the population is denoted by L

The rate of change of the young adults per year given  can be represented as;

[tex]\dfrac{dL}{dx}= -x^2 +90x - 200[/tex]

where;

x = 0 since 2010

[tex]dL = -x^2 +90x -200 dx[/tex]

[tex]L = \int( -x^2 +90x -200 ) \ dx[/tex]

[tex]L = - \dfrac{1}{3}x^3 + 45x^2 -200x +C[/tex]

here;

L(0) = 31000

[tex]- \dfrac{1}{3}(0)^3 + 45(0)^2 -200(0)+C= 31000[/tex]

C = 31000

[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]

Given that ABCD is an inscribed quadrilateral and m(∠DAB)=78°. What is m (DAB)

Answers

Answer:

Step-by-step explanation:

I'm going to go out on a limb here and guess that you are looking for the answer to the measure of arc DAB, since we already know that angle DAB is 78. Angle DAB is an inscribed angle. That inscribed angle intercepts arc DCB, and the theorem for that is that an inscribed angle is half the measure of the arc it intercepts. That means that arc DCB measures twice 78, so arc DCB measures 156 degrees. Since the measure around the outside of any circle is 360 degrees, arc DAB is 360 - 156 which is 204 degrees. If this is not what you are looking for, sorry and be more specific next time.

Can someone please help, ty!
Will mark brainliest!

Answers

Answer:

I and II

Step-by-step explanation:

I used a graphing calculator to find the answers.

The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle? (5 points) a 2 square feet b 4 square feet c 6 square feet d 8 square feet

Answers

Answer:

B. 4 square feet

Step-by-step explanation:

The formula for area of a triangle is length x height / 2 so 4 x 2 is 8 then divided by 2 is 4.

Answer: 4

Base 4

hight 2

4x2=8 ÷ 2 or 1/2 Equals 4

Formula L x W ÷ 2 or 1/2

Given f (x) = StartLayout Enlarged left-brace first row x squared minus one-third x, for x not-equals negative 1 second row negative 1, for x = negative 1 EndLayout. What is Limit of f (x) as x approaches negative 1?

Negative five-thirds
Negative four-thirds
Four-thirds
Five-thirds

Answers

Answer:

It's C, 4/3! Just did the question and got it right

Step-by-step explanation:

The limit of f(x) as x approaches negative 1 is four thirds.

What is Limits?

Limits are defined as the value of a function as the input approaches a certain number. Limits are the concepts used essentially in calculus to define continuity, integrals and derivatives.

Given function is,

[tex]f(x) =\left \{ {{x^{2} -\frac{1}{3}x, x\neq -1 } \atop {-1, x=-1}} \right.[/tex]

We have to find the value of the limit as x approaches to negative 1.

This is not the same value as the value of the function at negative 1. Limit of the function as x approaches some value is the value of the function which is closest to the exact value of the function at the input.

We have,

f(x) = x² - [tex]\frac{1}{3}[/tex] x when x ≠ -1

Substitute x = -1 in the above equation

x² - [tex]\frac{1}{3}[/tex] x  = (-1)² - (1 / 3) (-1)

            = 1 + [tex]\frac{1}{3}[/tex]

            =  [tex]\frac{4}{3}[/tex]

[tex]\lim_{x \to -1} x^{2} -\frac{x}{3}[/tex] = [tex]\frac{4}{3}[/tex]

Hence the limit of f(x) = x² - [tex]\frac{1}{3}[/tex] x when x tends to -1 is 4/3.

To learn more about Limits, click on the link given below :

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What is the additive inverse of 36?​

Answers

Answer:

The additive inverse of 36 is −36.

Step-by-step explanation:

Answer:

-36.

Step-by-step explanation:

Additive inverses are basically the opposite of the number, for example, since 36 in this case was positive you need to make it negative.

If Sofia randomly picks a number from 1 to 25, what is the probability that the number will have “1” as one of the digits?

Answers

12/25 is your answer

Determine the area of the triangle.

Answers

Answer:

no triangle given try to use a = 1/2(b x h) for the area

Step-by-step explanation:

Find each quotient.

494 ÷ 95 =


136.8 ÷ 24 =


96.9 ÷ 19 =


43.2 ÷ 8 =

Answers

Answer:

1. 5.2

2. 5.7

3. 5.1

4. 5.425 or 5.4

Step-by-step explanation:

hope this helps :)

Answer:

1. 5.2

2. 5.7

3. 5.1

4. 5.4

Step-by-step explanation:

you can use the app photo math, you just take a picture of the problem and it will give you the answer and explain the steps.

Identify the percent of change as an increase or decrease. $24 to $18​

Answers

Answer:

Step-by-step explanation:

$24-$18

-6$

it is decrease

so,

decrease %=$6/$24*100

=600/24

=25%

Answer:

its a decrease of 25%

Step-by-step explanation:

1/4 of 24 is 6 and if you subtract 6 from 24 its 18 and 1/4 is 0.25 so its 25%.

girlcome 5324611502
p:1234​

Answers

Answer:

ok then

Step-by-step explanation:

Answer:

Subscribe to my animations Y0UTUBE channel! Channel name: Let Me Explain Studios. Have a nice day!

Step-by-step explanation:

What is the length of BD?

Answers

Answer:

From -6 to positive 1 the length is 7

Step-by-step explanation:

you still add'em.

Answer:

length of BD is 18

just count on the number line and ×2 because it is counting on by 2

Which one is the least value?

Answers

Answer:

6/20

Step-by-step explanation:

trust

Matt can plant 27 trees in 3 hours. At that
rate, how many trees can Matt plant in an
8 hour day?

Answers

Answer:

72 trees.

Step-by-step explanation:

27 divided by 3 equals 9. so that means Matt can plant 9 trees in one hour so 9 is our unit rate ( what we multiply by) so now you multiply 9 by 8 and your answer is 72

Make an equation that is equal to 2/3

Answers

Answer:

Replace the 4 with a 3 to make the equation true

8/12 you can put 8 in the first box and make 8 times 1 = 8 and make the second box 12 the 8 in the first box would be put over 1 so it can multiply. When rounded down you are left with 2/3

Find the area and the circumference of a circle with diameter 10 m.

Write your answers in terms of pi, and be sure to include the correct units in your answers.

Answers

Step-by-step explanation:

area of a circle= πr²

and r= half diameter

therefore we have r=10/2=5

area= 5² x π

area= 25π

circumference=2πr

circumference= 2xπx5

circumference=10π

Yesterday, there were 60 problems assigned for math homework. Albert did 30% of them correctly. How many problems did Albert get right?

Answers

Take 60/100 x 30 =ans

The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What lateral area of the cone would produce a volume of 100m^3.

Answers

9514 1404 393

Answer:

  ∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

  V = 1/3πr²h

  V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

  100 m³ = 2πr³

  r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

  s² = r² +(6r)² = 37r²

  s = r√37

Then the lateral area is ...

  LA = πrs

  LA = π(∛(50/π) m)(∛(50/π) m)√37

  LA = ∛(2500π)√37 m² ≈ 120.911 m²

The lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

What is the lateral area of the cone?

The lateral area of the cone is the curved area of the cone, therefore, the total area of the cone is without the base area.

As we know that the volume of the cone is given by the formula,

[tex]V = \dfrac{1}{3}\pi r^2h[/tex]

Now, for the right circular cone to be economical, the height must be 3 times the diameter or it should be 6 times the radius. Therefore, the economical volume can be written as,

 [tex]V = \dfrac{1}{3}\pi r^2h\\\\V = \dfrac{1}{3}\pi r^2(6r)[/tex]

Now, if cancel out the 3 in the remainder with the six in the numerator, the volume of the cone can be written as,

[tex]V = 2\pi r^3[/tex]

Further, we need to calculate the lateral area of the cone, whose volume is 100 m³. Now, in order to get the radius of the economic cone with the volume of 100 m³, substitute it with 2πr³,

[tex]V = 2\pi r^3\\\\100 = 2\pi r^3\\\\r = 2.5154\rm\ m[/tex]

We know that in order to calculate the lateral area of the cone we need to calculate the slant height. Thus, according to the Pythagorean theorem, the slant height can be written as

[tex]s^2 = r^2 +(6r)^2\\\\ s^2 = 37r^2\\\\ s = r\sqrt{37}[/tex]

Now, the lateral area of the economical cone with the volume of 100 m³ can be written as,

[tex]LA = \pi rs\\\\LA = \pi \times r \times r\sqrt{37}\\\\LA = \pi \times r^2 \times \sqrt{37}\\\\LA = \pi \times (2.5154)^2 \times \sqrt{37}\\\\LA = 120.911\rm\ m^2[/tex]

Hence, the lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

Learn more about the Lateral Area of the Cone:

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Khloe is thinking of a number that is 2 times the value of Carl's number. Khloe's number is also 2 more than 4 times the value of Carl's number. What is Khloe's number?

Answers

0 = 2c +2.

Subtracting 2 from both sides, we get

0-2 = 2c +2 -2

-2 = 2c

Dividing both sides by 2, we get

-2/2 = 2c/2

-1 =c.

Plugging c=-1 in first equation,

k=2(-1) = -2.

So the answer is -2.

A garden table and a bench cost $672 combined. The garden table costs $78 less than the bench. What is the cost of the bench?

Answers

Answer:

b = $375

Step-by-step explanation:

b = cost of the bench

t = cost of the table

t = b - 78

b + b - 78 = 672

2b = 750

b = $375

Write the equation of the line in slope-intercept form.

Answers

Answer:

y = 50x+40

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

First find two points on the line

(0,40) and (2 ,140)

The slope is

m= (y2-y1)/(x2-x1)

   = (140-40)/(2-0) = 100/2= 50

The y intercept is where it crosses the y axis which is 40

y = 50x+40

plz plz plz plz help me​

Answers

Answer:

240 plants

Step-by-step explanation:

Find the area of the garden:

A = 1/2bhA = 1/2(8)(15) = 60 m²

Number of plants:

60*4 = 240 plants

Answer:

Solution given:

perpendicular [P]=15m

base[B]=8m

hypotenuse [H]=17m

rate :4 plants per square metre

no of plants=?

we have

Area of triangular garden: ½(P*B)=½(15*8)=60m²

Now

Total no of plants =rate ×Area =4×60=240

Michael needs 240 plants in the garden.

Tyrone is building a skateboard ramp with a piece of plywood that is 33 feet long.He wants the height of the ramp to be 22 feet.To make a strong ramp, the base must form a right angle with the back of the ramp.What will be the length of the base rounded to the nearest tenth of a foot?

please hurry and and please show your work!!

Answers

Answer:

24.6 ft

Step-by-step explanation:

Use the Pythagorean theorem.

a^2 + b^2 = c^2

a^2 + (22 ft)^2 = (33 ft)^2

a^2 + 484 ft^2 = 1089 ft^2

a^2 = 605 ft^2

a = 24.6 ft

Answer: 24.6 ft

Which of the following functions has a vertical asymptote at x=3?

Answers

Answer:

the last one: f(x) = 1/(x-3)

Step-by-step explanation:

Vertical asymptote at x=3 means dividing by zero for x=3. If you examine all denominators with x=3, you find that the last one divides by zero (3-3).


1. María expandió el siguiente cuadrado de la manera que sigue: (x+3)2 = x² + 9,
¿Está correcta la forma que usó María?

Answers

Answer:

La expansión de María

[tex](x + 3) {}^{2} = x {}^{2} + 9[/tex]

Correcta expansión

[tex](x + 3) {}^{2} \\ = {x}^{2} + 2 \times x \times 3 + 3 {}^{2} \\ = x {}^{2} + 6x + 9[/tex]

Note - (a + b)² = a² + 2ab + b²

La expansión de Mary está mal. Correcta expansión + 6x + 9

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, -64,
Ο Ο Ο Ο
2

Answers

Step-by-step explanation:

[tex]r = \frac{4}{2} \\ r = 2[/tex]

Answer:

-2

Step-by-step explanation:

The "common ratio" is the number you multiply a term by to get the next term.

-4 = 2 x -2

8 = -4 x -2

-16 = 8 x -2

A farmer sells 8.2kg of apples and pears at the farmers market. 4/5 of this weight is apples and the rest is pears. How many kg of pears did she sell at the market?

Answers

9514 1404 393

Answer:

  1.64 kg of pears

Step-by-step explanation:

If 4/5 of the weight is apples, the remaining 1/5 is pears.

  (1/5)(8.2 kg) = 1.64 kg

She sold 1.64 kg of pears.

Answer:

Solution :-

Weight of pears = 1 - Weight of apple

=> 1 - 4/5

=> 5 - 4/5

=> 1/5

Now

Weight of pears = ⅕ × 8.2

Weight of pears = 1.64 kg

[tex] \\ [/tex]

fx= ab*2÷t*2, make t the subhect of the formulae
[tex]fx = ab { }^{2} \div t {?}^{2} [/tex]

Answers

Answer:

t = √ab²/fx

Step-by-step explanation:

fx= ab*2÷t*2, make t the subject of the formulae

​Given the function

fx = ab²/t²

We are to make t the subject of the formula

fxt² = ab²

t² = ab²/fx

Take the square root of both sides

√t² = √ab²/fx

t = √ab²/fx

Hence the required value of t is √ab²/fx

brainliestt
for righto

Answers

Answer:

Hello! answer: 13/16

Hope that helps!

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