The circumference of a circle equals 2 r, where r is the radius. Find
the circumference of a compact disc that has a radius of 6.0 cm

Answer:

Point slope form: y − 7 = 3 4 ( x − 3 ) Slope intercept form: y = 3 4 x + 19 4 or y = 3 4 x + 4 3 4

Step-by-step explanation:

hope this helps, have a nice day/night! :D

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Answer:

Slope = 1

Step-by-step explanation:

Slope = change in y / change in x

Slope = 6 - (-4)/7 - (-3)

Slope = 10/10

Slope = 1

-Chetan K

9514 1404 393

Answer:

  a.  h(t) = -20t +400

  b.  θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)

  c.  15 seconds; 100 ft

Step-by-step explanation:

a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...

  h(t) = -20t +400

__

b. The tangent of the angle above the line of sight is "opposite"/"adjacent":

  tan(θ) = (h(t) -100)/(150) = -2/15t +2

  θ(t) = arctan(2 -2/15t) . . . . radians

The derivative of the angle function is ...

  dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)

  dθ/dt = -30/(1125 -120t +4t^2)

__

c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)

The elevator appears to be moving fastest at t=15 seconds.

The height at that time is ...

  h(15) = 400 -20(15) = 100

The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.

Answer:40

Step-by-step explanation: 12 divided by 3

Answer:

Factors are often given as pairs of numbers, which multiply together to give the original number. These are called factor pairs. A square number will have one factor pair consisting of one factor multiplied by itself. This factor is called the square root of the given number.

it will take him 27 years

Answer:

32[tex]\sqrt{22}[/tex]

irrational

cannot be written as a ratio

does not repeat or terminate

Step-by-step explanation:

[tex]\sqrt{4}[/tex] = 2

4[tex]\sqrt{22}[/tex] · 4(2)  =  4[tex]\sqrt{22}[/tex] · 8  =   32[tex]\sqrt{22}[/tex]

Answers:

===================================================

Explanation:

The left hand side is

[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}[/tex]

That -6 outside the matrix is multiplied with each item inside the matrix. This is known as scalar matrix multiplication. Effectively, it's very similar to the idea of the distributive property.

So for the first row, we have the three columns of: -6*3 = -18 and -6*(-1) = 6 and -6*3 = -18

The other two rows are handled the same way. This is what should result:

[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]

From here, you'll then match up the terms in the given right hand side matrix. The top row has the variable 'u' in the middle, which matches with the '6' in the middle of the top row shown. Therefore, u = 6.

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

Now to the second row.

The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.

Also, we have -6x in the middle which matches with the 6 in the same corresponding spot. Solving -6x = 6 leads to x = -1.

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

Finally, the third row.

There's only one variable here and that's the variable y in the bottom right corner. It pairs up with 0 in the same corresponding spot for the right hand side matrix. Therefore, y = 0.

Answer:

Step-by-step explanation:

x + y = 18

y = 18 - x

xy = 72

x(18 - x) = 72

-x² + 18x = 72

0 = 72 - 18x + x²

x = (18 ± √(18² - 4(1)(72))) / (2(1))

x = (18 ± 6)/2

x = 12

x = 6

Answer:X= 41

Step-by-step explanation:

Answer:

y = -2x +4

Step by step explanation:

y = -2x +4

Hello, hope you are having a splendid day.

First, we should calculate the slope of the line (Rise/Run)

The rise is how many units we move up or down; the run is how many units we move left or right.

Here, we move down 2 and over 1, so the slope is -2

Now, the y-intercept is where the graph touches the y-axis.

Here, the y-intercept is 4.

Our equation looks lke so:

y=-2x+4

Hope it helps. Ask me if you have any queries.

~An emotional teen who helps others on Brainly :)

[tex]MagicalNature[/tex]

Good luck.

Answer:

1. B

2. A

Step-by-step explanation:

1.

10^{-2} means that you move the decimal back two times

B is the only option that represents that correctly.

2.

5 * 10^{4} = 50000

2.5 * 10^{2} = 250

50000/250 = 200

Out of the options, A is the only option in which the equation also equals 200.

Recall the half-angle identity for cosine:

cos²(x) = 1/2 (1 + cos(2x))

Then we can rewrite the integrand as

cos³(4x) = cos(4x) cos²(4x) = 1/2 cos(4x) (1 + cos(8x))

So we have

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int (\cos(4x) + \cos(4x)\cos(8x)) \, dx[/tex]

Next, recall the cosine product identity,

cos(a) cos(b) = 1/2 (cos(a - b) + cos(a + b))

so that the integral is equivalent to

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac12 \int \cos(4x) \, dx + \frac14 \int (\cos(4x - 8x) + \cos(4x + 8x)) \, dx[/tex]

[tex]\displaystyle \int \cos^3(4x) \, dx = \frac34 \int \cos(4x) \, dx + \frac14 \int \cos(12x) \, dx[/tex]

Computing the rest is trivial:

[tex]\displaystyle \int \cos^3(4x) \, dx = \boxed{\frac3{16} \sin(4x) + \frac1{48} \sin(4x) + C}[/tex]

a. We have GCD(34, 89) = 1; using the Euclidean algorithm,

89 = 2•34 + 21

34 = 1•21 + 13

21 = 1•13 + 8

13 = 1•8 + 5

8 = 1•5 + 3

5 = 1•3 + 2

3 = 1•2 + 1

b. Working backwards,

1 = 3 - 2

1 = 3 - (5 - 3) = 2•3 - 5

1 = 2•(8 - 5) - 5 = 2•8 - 3•5

1 = 2•8 - 3•(13 - 8) = 5•8 - 3•13

1 = 5•(21 - 13) - 3•13 = 5•21 - 8•13

1 = 5•21 - 8•(34 - 21) = 13•21 - 8•34

1 = 13•(89 - 2•34) - 8•34 = 13•89 - 34•34

c. Using the linear combination find in part b,

1 ≡ 13•89 - 34•34 (mod 89)

1 ≡ (-34)•34 (mod 89)

and

-34 ≡ -34 + 89 ≡ 55 (mod 89)

So, the inverse of 34 modulo 89 is 55.

d. Multiply both sides of the congruence by the inverse of 34:

55•34x ≡ 55•53 (mod 89)

x ≡ 2915 ≡ 32•89 + 67 ≡ 67 (mod 89)

Answer:

They are not.

Step-by-step explanation:

Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.

[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]

At this point we have at least three options:

Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.

Calculate the cross product between the two, if it's non-zero the three point are not in a line.

Try to determine the plane passing for the 3 points: if we find one they are not in a line.

Option 1:

The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:

[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]

So the three points are not in a line.

Option 2:

Let's calculate the cross product of the two vectors we found at the beginning.

[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]

Since the result is not the null vector, the three points are not in a line.

Option 3:

Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.

[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]

Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line

Answer:   5.824 m / min

Step-by-step explanation:

Change in position = -2.1m to -38.6m

Distance = |-38.6 m - (-2.1m) |

=|-36.5| m

= 36.5 m

Time =  

The average change in Michelle's position each minute =  

Hence, the average change in Michelle's position each minute = 5.824 m / min

Answer:

A

Step-by-step explanation:

Answer: A. True.

Step-by-step explanation:

A relationship is linear when the points on a scatterplot follow a somewhat straight line pattern. This is the relationship that we will examine. Linear relationships can be either positive or negative. Positive relationships have points that incline upwards to the right. As x values increase, y values increase.

Answer:

B.

Step-by-step explanation:

im not sure to my answer(●'◡'●)

Answer:

it's 23over 78 and it can reduce

Answer:

4

Step-by-step explanation:

8x - 12

4(2x - 3)

Answer:

D. $7.20

Step-by-step explanation:

9/1.25 = $7.20

All cases where v and x are both negative or both  positive numbers.

Answer:

A) 12.29%

B) 81.33%

C) 1.55%

Step-by-step explanation:

This is a binomial model, and I assume you're meant to use a calculator to solve.

A)

This is what I have in my notes for the binompdf function:

That is exactly what we want in this case, we're looking for exactly 5 people who meet the conditions (successes) given n trials and p probability.

Using a calculator:

binompdf(10, 0.68, 5) ≈ 0.1229

That means you have about a 12.29% chance to randomly select exactly 5 adults who have little confidence in newspapers.

B)

For this one, use the binomcdf function:

In this case, we're looking for more, not less. However, you can think of the probability of getting more than 6 as just the probability of not getting less than 6.

With a calculator:

binomcdf(10, 0.68, 5) ≈ 0.1867

That means you have about an 18.67% chance to randomly select 5 or less people. We're looking for more though. As said above, the probability of getting 6 or more is just the probability of not getting 5 or less. To find the probability of something not happening, just subtract the probability from 1.

1 - 0.1867 = 0.8133

An 81.33% chance to randomly select at least 6 adults who have little confidence in newspapers.

C)

Same as the above, I don't see a need to explain it all again. Use binomcdf:

binomcdf(10, 0.68, 3) = 0.0155

Notice I used 3 rather than 4. binomcdf calculates x or fewer, or 'rather less than or equal to'. We want just 'less than 4', and that means 'less than or equal to 3'.

That's a 1.55% chance to select less than 4 adults with little confidence in newspapers.

Answer:

13 degrees

Step-by-step explanation:

Because of the alternate interior angles, I know that angle EB is also 77. Now, knowing that it's a right angle, I can subtract 77 from 90 to get 13.

Check the picture below.

[tex]-5x+10>-15\\\\\implies -5x> -10 -15\\\\\implies -5x > -25\\\\\implies x< 5\\\\\text{Interval,} ~(-\infty,5)[/tex]

Answer:

add the options, then we'll talk

Step-by-step explanation:

Answer:

Socratic app

Step-by-step explanation:

it will help you

The three coins could land any these 8 ways:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

P(3 heads) = 1 way out of 8  or 1/8

P(2 heads) = 3 ways out of 8 or 3/8

P(1 head) = 3 ways out of 8 or 3/8

P(0 heads) = 1 way out of 8 or 1/8

x=Winnings  P(x)  E(x)=x�P(x)

    $3      1/8      $.375

    $2      3/8      $.75

    $1      3/8      $.375

  -$10      1/8     -$1.25

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

Total expectation =   $ .25