Vinnie is 18 years old.What type of number is Vinnie's age? Is it Rational or
Irrational?

The 107th derivative of f(x) =cos(x) is sin(x).

The derivative of y = f(x) function is the rate of change of  y  with respect to the independent variable x.

Derivative is represented by [tex]\frac{d}{dx}[/tex] and

First derivative to y is given by  [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]

Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.

[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]

Given f(x) = cos(x)

Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]

The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]

Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]

[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]

Eighth derivative if cos(x) is  cos(x)

and so on

Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x)  is -sin(x)

The second, sixth, tenth.... derivative of f(x) =cos(x)  is -cos(x)

The fourth , eighth , 12th,... derivative of f(x) =cos(x)  is cos(x)

We can say that very multiple of fourth derivative of f(x) =cos(x)  is cos(x)

We can write 107 as 104 + 3

As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)

[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]

Therefore, the 107th derivative of f(x) =cos(x) is sin(x).

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Answer:11/15

Step-by-step explanation:

you have to change them to common denominators.

i chose 15.

to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15

to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15

you now have the equation 5/15 + 6/15

to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15

Answer:

0.7333333333333333 = 11/15

Step-by-step explanation:

1/3 = 5/15

2/5 = 6/15


add them, and now you get

(5+6)/15 = 11/15

Answer:

342 ÷ 23 = 14.869565217 or 14 r 20

Check step-by-step explanation below for 2 methods to solve.

14.869565217 method right below

14 r 20 method at the bottom in bold and underlined

Hope this helps :)

Step-by-step explanation:

divisor

↓ ? <------ quotient

23 | 342 <------ dividend

remainder = r (the number that the divisor can't go into.

1) 23 goes into 34 one time, so we write the one on top.

1

23 | 342

2) 23 • 1 = 23 so then we subtract 23 from 34 and get 11.

1

23 | 342

- 23

1 1

3) Now we carry down the 2 and get 112.

1

23 | 342

- 23 ↓

1 1 2

4) 23 goes into 112 four times, so we write the four on top.

1 4

23 | 342

- 23 ↓

1 1 2

5) 23 • 14 = 92 so we subtract 92 from 112 and get 20.

1 4

23 | 342

- 23 ↓

1 1 2

- 92

20

6) 23 can't go into 20 so we add a decinal and a zero to 342 (dividend) and add a decimal to 14 too.

1 4.

23 | 342.0

- 23 ↓

1 1 2

- 92

20

7) Repeat the same steps again (Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor (if greater use it if less than take the next number). Then divide it by the divisor and write the answer on top as the quotient. Subtract the result from the digit and write the difference below. Bring down the next digit of the dividend (if present). Repeat the same process.)

1 4.8

23 | 342.0

- 23 ↓↓

1 1 2

- 92

200

- 1 84

16

8) Keep repeating and then we get 14.8695652174

*However, if the directions say to not continue and add the decimal and zero then we must put a remainer (r).*

1 4 r 20

23 | 342

- 23 ↓

1 1 2

- 92

20

Answer: this is not answer but it will help u with whoever does answer it

Step-by-step explanation:

we see here, slope is another version of finding the average rate of change. Average rate of change is finding the difference between the dependent variable (y-term) divided by the difference in the independent variable (x-term). Slope and average rate of change is exactly the same thing

The two values that serves as the root of the equation are  -1-√7 and  -1+√7

Given the quadratic equation below;

X² + 2X (-6) = 0

x^2 + 2x - 6 = 0

Using the general formula

x = -2±√2²-4(1)(-6)/2(1)

x = -2±√4+24/2

x = -2±√28/2

x =  -2±2√7/2

x = -1±√7

Hence the two values that serves as the root of the equation are  -1-√7 and  -1+√7

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Answer:

768

Step-by-step explanation:

The numbers are multiplying by 4 each time, Therefore the next number will be 768.

Answer:

the other 20%

Step-by-step explanation:

calculate 20% of 65498

Answer:

13,099.6 square miles

Step-by-step explanation:

80%*65,498=

80/100 * 65,498=

4/5 * 65,498=52,398.4 square miles of land area

65,498-52,398.4=       ==> subtract the total area of Wisconsin by the total land area to get the total area that isn't land.

65,498.0-52,398.4=13,099.6 square miles of area that isn't land

Answer:

k= -3

Step-by-step explanation:

Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.

y = kx+4

-2 = k(2)+4

To get k by itself, we first have to subtract the 4 from both sides.

-2-4 = k(2)+4-4

-6 = k(2)

Then, we can divide each side by the 2 to get our answer.

-6/2 = k(2)/2

k = -3

Answer:

k=-3

Step-by-step explanation:

The values of x satisfying the condition of the quadratic function (f o g)(x) = 17 is; (2, 4)

We are given the functions;

f(x) = 2x - 3

g(x) = x² - 6x + 18

Thus;

(f o g)(x) = 2(x² - 6x + 18) - 3

= 2x² - 12x + 36 - 3

= 2x² - 12x + 33

Now, we want to find the value of x when (f o g)(x) = 17. Thus;

2x² - 12x + 33 = 17

2x² - 12x + 16 = 0

Factorizing this gives us;

(2x - 8)(x - 2) = 0

Thus;

2x - 8 = 0 or x - 2 = 0

x = 4 or 2

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Answer:

120

Step-by-step explanation:

call the number x,

then x+1090-450

so x+640=760

x=760-640

x=120

hope this works :)

Answer:

120 is the number u thought of first

Step-by-step explanation:

1090-450=640

if we add 120 into 1090

then it will be 1210

so 1210-450=760

6/7 of people are not having a disease, the whole is 1 so the difference is:

2/3 of those having a disease is:

15 people are the 1/7 fraction of total people referred to quarantine.

The total number is:

3/5 of 105 people are male, that is:

Number of female is:

Answer:

[tex]\sf (i) \quad \dfrac{1}{7}[/tex]

[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]

[tex]\sf (iii) \quad 315\:people[/tex]

[tex]\sf (iv) \quad 126\: females[/tex]

Step-by-step explanation:

If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:

[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]

Therefore, 1/7 of people in quarantine have the disease.

We are told that 2/3 of the people who have the disease come from abroad.  Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:

[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]

Therefore, the fraction of diseased people who have come from abroad is 2/21.

We are told that 15 people who have the disease do not come from abroad.  So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad.  Remember that 1/7 of the total people have the disease.

[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]

Therefore, 1/21 of the total number of people have the disease and do not come from abroad.

Therefore, 15 people are equal to 1/21 of the total number of people:  

[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]

Therefore, the total number of people in quarantine is 315.

If 3/5 of the total are male, then 2/5 must be female.

[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]

Therefore, 126 females are in quarantine.

Answer:

2,025,000,000

Step-by-step explanation:

(3×10)⁴×(5×10)

8810000×2500

2,025000,000

1. Yes, the equation represent the proportionality relationship.

2. Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3.Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

Given a picture in that we can see a graph and 3 option.

We have to check weather that 3 option satisfy the equation and what are they.

Given equation [tex]y=\frac{2}{3}x[/tex]

1st option: Is the equation represent the proportionality relationship.

Yes, the equation represent the proportionality relationship.

If we see the proportionality rule that is

The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.

A proportionate relationship exists if an equation in a different form can be rewritten as shown above.

Here, the equation is in the form of y=kx.

Therefore, Yes, the equation represent the proportionality relationship.

2nd option: the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

The amount of change in y for a change of one unit in x is the unit rate of change of y with respect to x.

The slope is [tex]\frac{2}{3}[/tex].

Therefore, Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3rd option: The slope of the line is [tex]\frac{2}{3}[/tex]

Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

It is possible to simplify the equation of the slope to the form

y=mx+b, where m is the slope of the line and b is constant.

y is the dependent variable and x is the independent variable.

By the equation [tex]y=\frac{2}{3}x[/tex]

Therefore, Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

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Answer: $1200

Step-by-step explanation:

The equation to find out the price of the couch on sale is:

972=x*0.81

(0.81 is the same as 81% or 100% - 19%)

Then this equation can be arrange to figure out x

972=x*0.81

972/0.81=x

x=1200

Answer:

$1200

Step-by-step explanation:

Given the following question:

A couch when on a 19% discount
The new price of the couch was 972 dollars

We are trying to find the original price of the couch. To find that answer we are going to use the formula to calculate the percentage.

19% of 1200
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{19\times1200}{100}[/tex]
[tex]19\times1200=22800[/tex]
[tex]22800\div100=228[/tex]

Now check our answer by subtracting 228 from our original price 1200:

[tex]1200-228=972[/tex]
[tex]=972[/tex]

Our original price is "$1200."

Hope this helps.

Answer:

x = 21°

Step-by-step explanation:

180 - 159 = 21

Alternate angles (see image below) are equal, so x = 21

Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, y°=159°

Now, y°+x°=180° (Adjacent angles on straight line)

159°+x°=180°

x°=21°

Therefore, the value of x from the given parallel lines is 21°.

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The area of the screen to the nearest square centimeter is 0.103 m².

Given, that the length of the computer screen is = 16 inches

width of the computer screen = 10 inches

we know that 1 inch = 0.0254 m

Width = 10 inches = 10 × 0.0254 m

= 0.254 m

Length = 16 inches = 16 × 0.0254 m

= 0.4064 m

By definition,

Area =  length × width

        = 0.254 × 0.4064 m²

        = 0.103 m²

hence we get the area of the computer screen as 0.103 m²

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Answer:

(4,-4)

is the way from AtoB

Answer:57.7

Step-by-step explanation:

Answer:

a-b+8=42
a-b=42-8
a-b=36
espero t sirva

Answer:

b=34

Step-by-step explanation:

The amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.

Let the principal amount that is invested be equal to x.

So, we get that:

P = x

Now, the time period t = 3 years.

Simple interest rate = r = 3.85 %

Amount after 3 years = A = $ 6750

A = P + ( P × r × t / 100)

6750 = x + ( x × 3.85 × 3 / 100)

6750 = x + 0.1155 x

6750 = 1.1155 x

x = 6750 / 1.1155

x = 6051.098

Therefore, we get that, the amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.

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Answer:

6

Step-by-step explanation:

c is on -3 and A is on 3 -3 to 3 would be 6

Answer:

x= 5/12,y=− 5/4

​

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12

FALSE because they are two different ratios

Answer:

  x = 21

Step-by-step explanation:

You are given expressions (x+63)° and (4x)° for alternate interior angles at a transversal crossing parallel lines. You want to know the value of x.

Where a transversal crosses parallel lines, alternate interior angles are congruent. That means ...

  (4x)° = (x +63)°

  3x = 63 . . . . . . . . divide by °, subtract x

  x = 21 . . . . . . . . . divide by the coefficient of x