Suppose that cot θ = c and 0 < θ < π 2 . what is a formula for cos θ in terms of c?

Answers

Answer 1

Answer:

cosθ = c/√1+c²

Step-by-step explanation:

Given cot θ = c and 0 < θ < π/2

In trigonometry identity:

cotθ  = 1/tanθ = c

1/tanθ = c

cross multiply

tanθ  = 1/c

According to SOH, CAH, TOA:

Tanθ = opposite/adjacent = 1/c

cosθ = adjacent/hypotenuse

To get the hypotenuse, we will use the pythagoras theorem:

hyp² = opp²+adj²

hyp² = 1²+c²

hyp = √1+c²

Find cosθ in terms of c

cosθ = c/√1+c²

Hence the formula for cos θ in terms of c is cosθ = c/√1+c²


Related Questions

7th grade math help me plzzzz

Answers

Answer:

a. -14

b. -13

c. -5

d. -3

e. -12

f. 0

Step-by-step explanation:

hope it helps

Answer:

A is -14.

B is -13

C is -5

D is -3

E is -12

F is 0

Step-by-step explanation:

A, B, E both numbers are negative so you just add them together and add a negative sign.

C would read 4-9

D 10-7 and add a - to the answer

F is 6-6

8 tomatoes for $2 unit rate
I don't have much so please 17

Answers

That would be 16 dollars I’m pretty sure dude

the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 as does living plant material. Determine when the wood was cut

Answers

Answer:

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

[tex]\frac{dm}{dt} = -\frac{m}{\tau}[/tex] (Eq. 1)

Where:

[tex]\frac{dm}{dt}[/tex] - First derivative of mass in time, measured in miligrams per year.

[tex]\tau[/tex] - Time constant, measured in years.

[tex]m[/tex] - Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

[tex]\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt[/tex]

[tex]\ln m = -\frac{1}{\tau} + C[/tex]

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (Eq. 2)

Where:

[tex]m_{o}[/tex] - Initial mass of isotope, measured in miligrams.

[tex]t[/tex] - Time, measured in years.

And time is cleared within the equation:

[tex]t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right][/tex]

Then, time constant can be found as a function of half-life:

[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (Eq. 3)

If we know that [tex]t_{1/2} = 5730\,yr[/tex] and [tex]\frac{m(t)}{m_{o}} = 0.35[/tex], then:

[tex]\tau = \frac{5730\,yr}{\ln 2}[/tex]

[tex]\tau \approx 8266.643\,yr[/tex]

[tex]t = -(8266.643\,yr)\cdot \ln 0.35[/tex]

[tex]t \approx 8678.505\,yr[/tex]

The wood was cut approximately 8679 years ago.

Your teacher invented another game: You will pick one card from a deck of cards. If
you pick a heart, you will win $25.00. Otherwise, you will lose $5.00.
From the standpoint of the player, what is the expected value of this game?
Enter expected value
What does the expected value tell us about the game?
O The game is good to play, you will make money on average.
O The game is NOT good to play, you will tend to lose money.
O It doesn't matter if you play, you will generally break even.

Answers

Answer:

C

Step-by-step explanation:

5 divided 5/6 helpabacon hair please

Answers

Answer:

what? expalint the question

Step-by-step explanation:

Which expression is the coefficient of the n term -1

Answers

Answer:

C. -2n² - n + 5

Step-by-step explanation:

In expression C, the coefficient of the n term is -1;

  The expression in choice C is given as:

               -2n² - n + 5

The coefficient is the number before a variable;

  For n², the coefficient is -2

    for n, the coefficient is -1

In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.

Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.
P
(win) =

A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.
Answer: $
A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.
Answer: $

Answers

Step-by-step explanation:

The order of the numbers doesn't matter, so we'll use combinations instead of permutations.  The number of combinations is:

₄₅C₈ = 215,553,195

So the probability of a ticket having the winning combination is 1 / 215,553,195.

The expected value to the state is:

E(X) = 10,000 (1) ($2) + 10,000 (1 / 215,553,195) (-$1,000,000)

E(X) = $19954

The expected value to you is:

E(X) = 10,000 (1) (-$2) + 10,000 (1 / 215,553,195) ($1,000,000)

E(X) = -$19954

QUICK
solve this equation
a^n+b^n=

Answers

Hey can someone help me with my latest question no one‘s helping me and I really need it

Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the
equation 3x-5=-2x+ 10?

A. X=5. B.—5=x. C.—15=—5x. D.—5x=15

Answers

Answer:

A; (X=5)

Step-by-step explanation:

Move the constants and variable terms to one side:

3x-5= -2x+10

-5+10= -2x+ 3x

Combine like terms:

5=x or x=5

Answer:

The answer is C

Step-by-step explanation:

If you take the equation and simplify it.

3x-5=-2x+10

You would minus 3x from both sides, leaving the equation like

-5=-5x+10

Then you would minus 10 from both sides, leaving the equation like

-15=-5x

If you wanted to go further you could divide both sides by -1 and get rid of the negatives. Leaving the equation like

15=5x

Then to put it into the simpleist   form you would divide both sides by 5, leaving the equation like

3=x

I hope this helps.

30 point question! WILL AWARD BRAINLIEST!

A ball is thrown across a playing field from a height of h = 5 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y = − (32/(20^2))x2 + x + 5


Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)

Answers

y = [-32/(20)^2]x^2 + x + 5
a.) For maximum height, y' = 0
y'= (-32/200)x + 1 = 0
32/200x = 1
x = 200/32 = 6.25
The maximum height attained by the ball is [-32/(20)^2](6.25)^2 + 6.25 + 5 = 8.125 feet.

b.) At the point the ball hits the ground, y = 0
y = [-32/(20)^2]x^2 + x + 5 = 0
x = 16.3 ft

Answer:

Answers are down below ;)

Step-by-step explanation:

y = − (32/(20^2))x2 + x + 5

Plug into the calculator: -32/20^2 = -.08x^2

 Find the maximum height attained by the ball:

Rewrite the equation:

y= -.08x^2 + x +5

This parabola is a negative meaning that it will be maximum

to find the maximum we use the formula -b/2a

-(1)/ 2 (-.08) = -1/ -.16= 6.25

we plug 6.25 back into the equation y= -.08(6.25)^2+ (6.25) +5 = 8.125

The maximum height attained by the ball: 8.125 feet

Find the horizontal distance the ball has traveled when it hits the ground.

This can be found with the quadratic equation, x = [-b ± √(b2-4ac)]/2a

a= -.08 , -b= -1, c= 5 (When you are plugging in the numbers, make sure to break them down).

-(-1)± √(-1)^2-4(-.08)(5)] 2(-.08) -->

[-1 ± √(1 + 1.28)]/-.16 = [-1 ± √(2.6)]/-.16 = [-1 ± 1.61]/-.16 =

The horizontal distance of the ball is x = 16.31 feet

Say thank you by commenting down below :)

I need help nowwwwww !!!!!????

Answers

you should just have to times the yards by three like the second one is 12

Number 10 plzz???????

Answers

%error=(6.5g/mol - 7g/mol)/(7g/mol) * 100= 7.14% error

Which ordered pair, if included in this relation, would cause it to no
longer be a function?

Answers

Answer:

(-6,3)

Step-by-step explanation:

Find the slope of the line

Answers

(0,5) is the answer

What is the first step when solving the equation 3(3x-5x)+2=-8

Answers

Answer:

Collect the like terms

Step-by-step explanation:

(3x-5x)

3x (-2x) + 2 = -8

multiply the parenthesis and then add the like terms

SOMEONE PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

A.

Step-by-step explanation:

Which equation shows y=3x−15 in standard form?

A. 15x−5y=1

B. 15x+5y=−1

C. 5x−15y=1

D. 5x−15y=−1

Answers

Answer:

c  5x -15y =1

Step-by-step explanation:

5x-15y=1

-5x -15y= 1 -5x     change the signs on both sides of the equation

     15y = -1 +5x      divide both sides by 15

         y = -1/15 + 1/3 x    Reorder the terms

         y = 3x-15

              :)

     

     

All options are wrong here.

Given equation is  [tex]y=3x-15[/tex].

the equation given here is in form of [tex]y=mx+c[/tex] . The general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis) .

We have to write [tex]y=3x-15 \\[/tex] in standard form.

The standard form for linear equations in two variables is Ax+By=C.

Now we convert [tex]y=3x-15[/tex] in standard form.

Here [tex]y=3x-15\\[/tex]

[tex]y-3x=-15\\\\-y+3x=15[/tex]

[tex]3x-y=15[/tex]

But no options match with the above standard form of equation.

Hence all options are wrong here.

For more details on standard form for linear equations follow the link:

https://brainly.com/question/7380540

You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?​

Answers

Answer: pretty sure the friend would get 2 donuts

Step-by-step explanation:

anyone in flvs? we should find each other in live lessons lol

Answers

Answer:

nope

Step-by-step explanation:

2
Divide: 4:- =
5
HELP FAST!!!!!!!!!

Answers

10/4  if its right also have a good my dude

You measure the period of a mass oscillating on a vertical spring ten times as follows:

Period (s): 1.06, 1.31, 1.28, 0.99, 1.48, 1.37, 0.98, 1.31, 1.59, 1.55

Required:
What are the mean and (sample) standard deviation?

a. Mean: 1.228, Standard Deviation: 0.2135
b. Mean: 1.325, Standard Deviation: 0.1674
c. Mean: 1.292. Standard Deviation: 0.2211
d. Mean: 1.228, Standard Deviation: 0.2098
e. Mean: 1.292, Standard Deviation: 0.2135

Answers

Answer:

Step-by-step explanation:

Mean is the ratio of sum of the dataset to the sample size. Mathematically:

[tex]\overline x = \frac{\sum Xi}{N}[/tex]

Xi are the individual periods

N is the sample size

[tex]\sum Xi = 1.06+1.31+1.28+0.99+1.48+1.37+0.98+1.31+1.59+1.55\\\sum Xi = 12.92[/tex]

N = 10

Substitute

[tex]\overline x = \frac{12.92}{10}\\\overline x = 1.292[/tex]

hence the mean of the samples is 1.292

For the standard deviation:

[tex]\sigma = \sqrt{\frac{\sum (x-\overline x)^2}{N} } \\[/tex]

[tex]\sum (x-\overline x)^2 = (1.06-1.292)^2+ (1.31-1.292)^2+ (1.28-1.292)^2+ (10.99-1.292)^2+ (1.48-1.292)^2+ (1.37-1.292)^2+ (0.98-1.292)^2+ (1.31-1.292)^2+ (1.59-1.292)^2+ (1.55-1.292)^2\\\sum (x-\overline x)^2 = 0.43996[/tex]

Substitute into the formula:

[tex]\sigma = \sqrt{\frac{0.43996}{10} }} \\\sigma = \sqrt{{0.043996}}} \\\sigma = 0.2098[/tex]

Hence the standard deviation is 0.2098

A circle is inscribed in a square. If the perimeter of the square is 40, what is the area of the circle? Use 3.14 for pi.

Answers

Answer:

78.5

Step-by-step explanation:

We have the perimeter of the square, which is 40, and 40/4=10. In this picture, we see that the circle's diameter is the same as the length of one side of the square. Therefore, the diameter of the circle is 10. The are formula for circles is [tex]\pi r^{2}[/tex], where [tex]r[/tex] is the radius. The radius of the circle is just the diameter divided by 2, and 10/2=5. Now, [tex]5^2[/tex] is 25, and [tex]3.14\cdot25=78.5[/tex].

If b^2 = 25 then b= Answer it please

Answers

Answer:

b = 5

mark me as brainliest plz!! :DD

Michael exercises more than 35 minutes per day.
Use t to represent Michael's amount of exercise (in minutes per day).

Answers

Answer:

t>35

Step-by-step explanation:

Since Michael exercises more than 35 days, t is greater than 35. To express that in an inequality, the answer is t>35. Hope this helped!

-4 (2x + 13) + 3x = 80
How do you solve this out and get the answer

Answers

Answer:

-132/5

Step-by-step explanation:

-4(2x+13) + 3x = 80

-8x - 52 + 3x = 80

-5x = 80+52

5x = -132

x = -132/5

Feel free to mark this as brainliest! :D


If it takes 930 kg of food to feed a pair
of elephants for 3 days, how much food
would you need to feed them for a week?

Answers

Answer:

2170

Step-by-step explanation:

930 divided be 3= 310

310 multiplied by 7=2170

Everglades National Park is 225 mi long. What scale is needed to draw a map of Everglades National Park that is 10 in. long?


A. 1 in. = 22.5 mi

B. 10 in. = 225 mi

C. 1 in. = 0.04 mi

D. 10 in. = 22.5 mi

Answers

Answer:

A. 1 in. = 22.5 mi

Step-by-step explanation:

Since 22.5 x 10 = 225, we can conclude that this will fit the scale needed. B. is incorrect because it is simply illogical in context with a scale and the question. C. is incorrect since 10 x 0.04 is 0.4, which does not equal 10. D. is incorrect since we need the scale to add up to equal 225 mi, not 22.5.

Hope this helps!

Write an equation in the line in slope intercept form

Answers

Answer:

Y=2x-1

Step-by-step explanation:

In order to find the slope, its rise over run. So you would move from (0,-1) to the next point it intercepts, (1,1) and find it from there

As for the Y-Intercept, it would just be wherever the line connects with the Y axis, which happens to be (0,-1) or Negative 1.

What is the measure of an exterior angle of a regular 14-sided polygon? Enter your answer as a decimal in the box. Round to the nearest tenth of a degree.

Answers

Answer:

21.715 degrees.

Step-by-step explanation:

There are 14 vertexes (vertices) for a 14-gon. It is 'regular' so all these angles are equal. So the exterior angle of each is 180-154.285 = 21.715 degrees.

If a roof has a pitch of 5 to 11, how high will the roof rise over a 33-foot run?
a.
3
C.
2
72 feet
1 feet
b. 15 feet
d.
20 feet

Answers

The answer is b. 15ft

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