cos (3 X +6 ) =sin 30

Answer:

0.20 seconds

Step-by-step explanation:

Given the function:

For the distance traveled by a pendulum in time [tex]t[/tex]:

[tex]P(t)=-5cos(2\pi t)+5[/tex]

Where [tex]t[/tex] is in radians.

Also, given that [tex]P(t)=3.5\ cm[/tex]

To find:

The time [tex]t[/tex] = ? to the nearest hundredth.

Solution:

Putting the values as per given statements, it can be observed that:

[tex]3.5=-5cos(2\pi t)+5\\\Rightarrow -1.5=-5cos(2\pi t)\\\Rightarrow 0.3=cos(2\pi t)[/tex]

Taking the inverse:

[tex]cos^{-1}(0.3) = 2\pi t[/tex]

[tex]\Rightarrow 2\pi t=72.54^\circ[/tex]

We know that [tex]2\pi\ radians = 360^\circ[/tex]

Putting the value above:

[tex]\Rightarrow 360t=72.54^\circ\\\Rightarrow t = \dfrac{72.54}{360}\\\Rightarrow t =\bold{0.20}\ seconds[/tex]

So, after 0.20 seconds, the pendulum reaches 3.5 cm from the place it was released.

Answer:

1.  B

2. A

3. C

4. A

I hope this helps!

Answer:

Question 1

The greatest number of treasure chest you can fill = 23

Step-by-step explanation:

Gold coins = 46

Diamonds = 115

Rubies = 184

To determine the greatest number of treasure chests you can fill, find the highest common factors of 46, 115 and 184

46 = 1, 2, 23, 46.

125 = 1, 5, 23, 115

184 = 1,2,4,8,23,46,92,184

The highest common factors of 46, 115 and 184 is 23

The greatest number of treasure chest you can fill = 23

Number of gold coins in each chest = 46/23

= 2

Number of diamonds in each chest = 115 / 23

= 5

Number of rubies in each chest = 184 /23

= 8

Question 2

Nickels = 246

Dimes = 312

Quarters = 204

Find the highest common factor of 246, 312, 204

246 = 1, 2, 3, 6, 41, 82, 123, 246

312 = 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.

204 = 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The highest common factor of 246, 312, 204 is 6

How many are in your group?

6 members

There are 6 members in your group that each person got the same exact amount of each coin with no coins remaining.

Number of nickels each person receive = 246 / 6

= 41

Number of dimes each person receive = 312 / 6

= 52

Number of quarters each person receive = 204 / 6

= 34

Step-by-step explanation:

find distance of AC first

ac= √(y2-y1)²+(x2-x1)²

since there is no y we will consider it zero

so Ac= √(16-(-8))²

ac=24

ab is 1/3 of ac so it means

24*1/3=8

so ab is 8 units

The location of point B on the number line is 0.

Given that,
on the number line, point b is between points a and c. the distance between points a and b is 1/3 of ac.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
AB = 1/3 AC
AB = 1/3 (16 - (-8))
AB = 1/3 (16 + 8)
AB = 1/3 * 24
AB = 24 / 3
AB = 8
B - A = 8
B - (-8) = 8
B + 8 = 8
B = 8 - 8
B = 0

Thus, location of the point B on the number line is at 0.

Learn more about number line here:

brainly.com/question/17683084

#SPJ2

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[tex] \frac{2}{3} + \frac{4}{3} = \frac{6}{3} = 2 \\ [/tex]

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Answer:

its the one on the bottom left.

it has the proper demision just look at the sides and they match up

Hope This Helps!!!

Answer: The net which can represent the solid figure given in image 1 is the net in image 4.

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

2x-5x+20=-7+5x-21

-3x-5x=-7-21-20

-8x=-48

x=6

Answer:

x=6

Step-by-step explanation:

2x-5x+20=5× -28

-3x+20=5x-28

-8x=-48

x=6

check:

2x-5(2)=-30-28

12-10=2

2=2

Answer:

k = 8

Step-by-step explanation:

8(10 - k) = 2k

First, distribute within the parenthesis,

80 - 8k = 2k

Add 8k to both sides of the equation

80 = 10k

Divide both sides by 10 to get your answer

8 = k

I hope this helps :)

Answer:

Aspect Ratio:13:5

Answer: 52 inches

Step-by-step explanation:

The aspect ration is the ratio between the sides which is 6.5:2.5 or 13:5.

Now we know the shorter side is 20 inches, and our aspect ratio basically means shorter side is 5x and longer side is 13x. well putting 5x=20, we get x=4. So the longer side, 13x, is 52 inches.

20 different pizzas

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

Explanation:

Consider 3 slots to fill. I'll label them slot A, B, C.

There are 6 choices for slot A, then 5 choices for B, and 4 for C. We count down by one each time since we cannot reuse a topping.

There would be 6*5*4 = 30*4 = 120 permutations if order mattered.

However, order doesn't matter with pizza toppings. So we must divide by 3*2*1 = 6 (this is the number of ways to arrange any group of 3 things)

We get 120/6 = 20 as the final answer

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

Alternatively, you can use the nCr combination formula following these steps.

n C r = (n!)/(r!(n-r)!)

6 C 3 = (6!)/(3!*(6-3)!)

6 C 3 = (6!)/(3!*3!)

6 C 3 = (6*5*4*3!)/(3!*3!)

6 C 3 = (6*5*4)/(3!)

6 C 3 = (6*5*4)/(3*2*1)

6 C 3 = (120)/(6)

6 C 3 = 20 different pizzas possible

As the third to the last line shows, we have 6*5*4 up top and 3*2*1 down below. This matches exactly what was discussed in the previous section.

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

Yet another alternative is to use Pascal's Triangle (see below) and we locate the row that has 1,6,... at the start. We circle the fourth item of this row that corresponds to 6C3 = 20

Answer:

4 months

300 off of 5th month

Step-by-step explanation:

$3500-800= 2,700

2,700-500=2,200

4 months or 500 x 4= 2,000

2,000 - 2, 200= 200

Answer:

x = -2

Step-by-step explanation:

2x + 4 = 0

2x= -4

x=-2

Equation: [tex]2x+4=0[/tex]

Subtract 4 from both sides:

[tex]2x+4-4=0-4\\2x=-4[/tex]

Divide both sides by 2:

[tex]\frac{2x}{2}=\frac{-4}{2}[/tex]

Simplify:

[tex]\frac{-4}{2}=-2\\x=-2[/tex]

Therefore, your answer would be x = -2.

-TestedHyperr

Answer:

The answer is B

Step-by-step explanation:

Answer:

197 in^2

Step-by-step explanation:

See attached image

Step-by-step explanation:

total weight = 81 + 97+69+75+74+96+86+53 = 613kg

2 people will have to wait

Answer:

The equation of a line that passes through the point (-5,7) and has a slope of -2/5 would be y = -2/5x + 5

Step-by-step explanation:

In the math term y = mx + b, "m" represents slope. So you can just substitute it for -2/5. "b" represents the y-intercept. 5 is the only number that works, so you just substitute "b" for 5.

Answer:

In this case, the area is more useful to find out how much the paint covers.

This is, because the circumference is the perimeter of the table whilst the area is the whole region of the table.

So to find out the area of this table, we must use the formula for the area of a regular circle.

A = π[tex]r^{2}[/tex]

Where 'π' represents pi(22/7 or 3.14), and 'r' represents the radius which is being squared.

But, if we see the information that we have, we can see that it gives the diameter and not the radius.

So in order to find out our radius, we must perform 1/2 of the diameter(1/2 x diameter) to find the radi.

30(diameter) x 1/2

= 15 is the radius.

Now we substitute this value into our equation, since it's the only information we need.

A = π[tex]r^{2}[/tex]

A = 3.14(15^2)

A = 3.14(225)

A = 706.5 square inches of paint is needed to cover the table.

Answer:

answer of this question is A

Answer:

A.       2

      ----------

     3x^3 y^5 z

B.         49k^8 m^6

         --------------------

                  81

C.          a^9 b^3

           ---------------

              27c^12

D.         -125y^9

          --------------

                 x^6

Step-by-step explanation:

A.

12x^2 y^-4                2

-----------------  =     -----------

18x^5 yz               3x³y^5z

B.

 (9k^2 m)^-2        -81k^-4 m^-2               49k^12 m^8           49k^8 m^6

---------------     =   ----------------------     =    ---------------------   =   --------------

(7k^6m^4)            -49k^-12 m^-8              81k^4 m^2                    81

C.

 ( 4a² b² )³                 64 a^9 b^6                   a^9 b^3

-------------------    =   -------------------------   =       -------------

( 12a^-1 bc^4 )³          1728 b^3 c^12                27c^12

D.

( -5x^-2 y³ )³   =   -125 x^-6 y^9   =       -125y^9

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

                                                                  x^6

I hope this helps!

Answer:

60%

Step-by-step explanation:

The total is 90 students, and 54/90 is 0.6. 0.6 is equal to 60%!

Answer:

y=-5x+25

That is the answe in slope intercept form

Answer:

Combined means to add so you are going to add anything over 1 because it says longer than 1

1 1/4  has 2 marks so you add 1 1/4 + 1 1/4 =

they have like denominators so you can add them together

1 + 1 = 2 and 1/4 + 1/4 = 2/4 which can be reduced to 1/2

so your answer is 2 1/2

Step-by-step explanation:

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

Explanation:

For these type of problems, it helps to do a grid so you can line up the digits.

Check out the diagram below to see what I mean.

The 3 from "3x1" means we have 3 in the units digit

The first "1" from "1x0.1" means we have 1 in the tenths digit

The 4 in 4x0.001 means we have a 4 in the thousandths digit

There's a 0 in the hundredths digit as just a gap or placeholder so to speak. We can think of it as 0x0.01

Answer:

No

Step-by-step explanation:

Since a is in absolute value symbols, you would be adding a positive number to 1, and therefore cannot have a number lower than 0.

For example, say a = -3. We would get 1 + |-3| = 4.

Answer:

No

Step-by-step explanation:

Because the vertical lines mean the absolute value of a.

-  a negative value of a like -2 in vertical lines  has absolute value 2.

If a = 0 then absolute value = 0.

So 1+|a|   will always be positive.

Answer:

Each pretzel had cost $6.30

Step-by-step explanation:

You would have to subtract 22.00 - 15.70 and that would be your answer ($6.30)

Answer:

Each pretzel cost $2.10

Step-by-step explanation:

First,

Take your original amount and subtract it by your remanding amount:

22 - 15.70 = 6.30

Then, divide by three, since we bought three pretzels:

6.30 / 3 = 2.10       or       6.30 ÷ 3 = 2.10

So, each pretzel cost $2.10

Answer:

D.) the solution is 9

Step-by-step explanation:

9x9 = 81

Answer:

7

Step-by-step explanation:

average = 19 + 9 +(-9)+6+10 / 5

=> 35/5 = 7