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

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.

Answer:

nope

Step-by-step explanation:

Answer: pretty sure the friend would get 2 donuts

Step-by-step explanation:

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

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

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

Answer:

A.

Step-by-step explanation:

Answer:

(-6,3)

Step-by-step explanation:

Answer:

Collect the like terms

Step-by-step explanation:

(3x-5x)

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

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!

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.

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.

The answer is b. 15ft

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 :)

Answer:

what? expalint the question

Step-by-step explanation:

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].

Answer:

b = 5

mark me as brainliest plz!! :DD

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

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.

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

Answer:

C

Step-by-step explanation:

Answer:

2170

Step-by-step explanation:

930 divided be 3= 310

310 multiplied by 7=2170

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

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!

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

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