All Answers 358087 Answers

1) F + (N - 1)*D=Nth Term, where F=First term, D=Common difference and N=Number of terms.

-1 + (8 - 1)*D =20, solve for D

-1 + 7D = 20

7D = 20 + 1

7D =21 divide both sides by 7

D = 21 / 7

D = 3 Common difference

2)

(F + L) / 2*N, where F=First term, L=Last term and N=Number of terms.

Sum = (-7 - 115) / 2*13

Sum =( -122 / 2) * 13

Sum = -61 * 13

Sum = -793

Solve for x:
3 x^2 + 5 x = 0

Divide both sides by 3:
x^2 + (5 x)/3 = 0

Add 25/36 to both sides:
x^2 + (5 x)/3 + 25/36 = 25/36

Write the left hand side as a square:
(x + 5/6)^2 = 25/36

Take the square root of both sides:
x + 5/6 = 5/6 or x + 5/6 = -5/6

Subtract 5/6 from both sides:
x = 0 or x + 5/6 = -5/6

Subtract 5/6 from both sides:
Answer: | x = 0     or     x = -5/3

if i need 5000 coins and i get 10 every 5 minutes how much minutes dose it take to get 5000 coins?

10 / 5 = 2 coins per minute

5,000 / 2 = 2,500 minutes, or 2,500 / 60 = 41 2/3 hours, or [41 2/3] / 24 =1 day and 17 2/3 hours.

OR:

5,000 / 10 =500 "5-minute" intervals

500 x 5 =2,500 minutes - same as above.

Use all of the numbers.

I think it's 41.6 minutes. 500 x 10 = 5000 coins.

5 x 500 = 2,500

2,500/60=41.6

(rounded to one decimal point)

5/6 x -2 =

-10 / 6 =-1 2/3

how to subtract 10% from amount 324?

Two ways:

1-

10% means: 10 / 100 =0.10

0.10 x 324 =32.40

324 - 32.40 =291.60 First way.

2-

100% - 10% =90%

90% means: 90 /100 =0.90

0.90 x 324 =291.60 Second way.

70(13)^3/4 = 70 x 6.846325..... =479.24......

Look it up on YouTube under "The Monty Hall problem".

Like so:

\(y = \frac{3x-7}{x+1} \text{ Solve for x }\\ y(x+1)=3x-7\\x(y-3)=-(y+7)\\x = -\frac{y+7}{y-3} \text{ swap y and x and replace y by f^{-1}(x) }\\f^{-1}(x)=-\frac{x+7}{x-3}\)

This question was asked and answered here: https://web2.0calc.com/questions/i-need-some-help_8#r1 

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Nvm, i solved it. answer is (3,10)

22+222=244

277+53=330

\(22+222=244\)

No solve(a^2+b^2)=c^2,c^2=3^2={{a=r1, b=-sqrt(9-(r1^2)), c=-3, a=r2, b=sqrt(9-(r2^2)), c=-3}, {a=r3, b=-sqrt(9-(r3^2)), c=3, a=r4, b=sqrt(9-(r4^2)), c=3}}

Well, Mr. BB I am impressed that you know a Latin phrase.  Are you fluent in pîg Latin?  I bet you are!  I know a Latin phrase that instantly brings you to anyone’s mind.  Persona non grata

Like usual, and seemingly always, Mr. BB, you are wrong. Lancelot Link’s metaphorical comment definitely relates by a logical sequence to the kinematic equation it follows. I can explain this, but (again) we are back to wasting time and annoying the pîg. 

In this in this instance, I will try, because I love Lancelot, and truly appreciate his humor and wisdom, and the unique way he blends them to convey knowledge and information.  I don’t expect you to understand this or acknowledge it if you do. But I’m sure there a few on here who will understand and appreciate Lancelot’s teaching methods.

 Lancelot attached this comment to the end of a systematic series of related equations expressed in the form of hypotheticals to demonstrate macro logic from micro observations.  The hypothetical depicted above is not likely to be a casual observational experience in the real world. For this experiment to have any accuracy, one needs careful observation and high-precision timing devices.  In a related hypothetical, the observer notes the travel time from the top to the bottom of a window and derives the starting height of the object. Again, no one in the real world can casually measure this objects travel time in tenths of seconds.  

Lancelot’s opera metaphor extends to general observations. When one has a macro view, a tool is needed for the micro view. Here, this tool is opera glasses.   To understand the (Italian) opera one needs to understand the Italian language.   This is also true for physics. One needs to understand the language of physics: how gravity, velocity, distance, and time relate to each other.

Plus, the thought of a chimp watching an opera, while hanging from a rafter or sitting in a chandelier, is just plain funny to most humans and we genetically enhanced chimps.   

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One final note:  The phrases Non sequitur and Non- sequitur are different.  When used as a noun, it should not have a hyphen. Using a hyphen makes it a phrasal adjective. This is a major change in the meaning.  If you wish to point out potential esoteric communication errors, you really should have higher standards.   

Find  c  if  f( g(x) )  =  g( f(x) )  for all  x  .

f(x)  =  2x + 7                          To find  f( g(x)  ) , replace every instance of  x  with  g(x)  .

f( g(x) )  =  2( g(x) ) + 7             Since  g(x)  =  3x + c  , we can write...

f( g(x) )  =  2( 3x + c ) + 7

g(x)  =  3x + c                         To find  g( f(x) ) , replace every instance of  x  with  f(x)  .

g( f(x) )  =  3( f(x) ) + c              Since  f(x)  =  2x + 7  , we can write...

g( f(x) )  =  3( 2x + 7 ) + c

We want to know what  c  is when

f( g(x) )  =  g( f(x) )                                   Substitute the functions in.

2( 3x + c ) + 7  =  3( 2x + 7 ) + c

6x + 2c + 7  =  6x + 21 + c                    Subtract  6x  from both sides.

2c + 7  =  21 + c                                    Subtract  c  from both sides, and subtract  7  from both sides.

c  =  14

nagito komaeda 

Yes it is

arc tan is the same as inverse tan :)

A cup has a base radius of 3cm,
a height of 15cm and a top radius of 5cm,
calculate the volume
i got 769.69ml, just wanna know if im right or not

Volume cup:  \(V = \frac13 \pi \cdot 5^2 \cdot H - \frac13 \pi \cdot 3^2 \cdot ( H - 15 ) \)

Height H of the cone: \(\frac{H-15}{3} = \frac{H}{5}\)

\(\begin{array}{|rcll|} \hline \frac{H-15}{3} &=& \frac{H}{5} \\ 5\cdot(H-15) &=& 3H \\ 5H-75 &=& 3H \\ 2H &=& 75 \\ H &=& \frac{75}{2} \\ \mathbf{H} &\mathbf{=}& \mathbf{37.5} \\\\ H-15 &=& 37.5 - 15 \\ \mathbf{H-15} &\mathbf{=}& \mathbf{22.5} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline V &=& \frac13 \pi \cdot 5^2 \cdot H - \frac13 \pi \cdot 3^2 \cdot ( H - 15 ) \\\\ &=& \frac13 \pi \cdot 5^2 \cdot 37.5 - \frac13 \pi \cdot 3^2 \cdot 22.5 \\\\ &=& \frac13 \pi \cdot ( 5^2 \cdot 37.5 - 3^2 \cdot 22.5 ) \\\\ &=& \frac13 \pi \cdot ( 25 \cdot 37.5 - 9 \cdot 22.5 ) \\\\ &=& \frac13 \pi \cdot ( 937.5 - 202.5 ) \\\\ &=& \frac13 \pi \cdot 735 \\\\ &=& 245 \pi \\ &=& 769.690200129 \ cm^3 \\ \mathbf{V} &\mathbf{=}& \mathbf{769.69\ldots \ ml} \\ \hline \end{array}\)

The function f(x,y) accepts an ordered pair as input and gives another ordered pair as output.
It is defined according to the following rules:
If x > 4, f(x,y) = (x - 4,y).
If x less equal 4 but y > 4, f(x,y) = (x,y - 4).
Otherwise, f(x,y) = (x + 5, y + 6).
A robot starts by moving to the point (1,1).
Every time it arrives at a point (x,y),
it applies f to that point and then moves to f(x,y).
If the robot runs forever,
how many different points will it visit?

What is the velocity of an object dropped from a height of 190 m when it hits the ground?

u=0

v=?

a=9.8m/s^2

t=?

s=190m

v=u+at

s=ut+0.5at^2

v^2=u^2+2as

using the last formua

v^2=0+2*9.8*190

v^2=3724

v=61m/s

how do i do a definite integration ex integrate y = (1/50) x^2 between 0 and 160

\(\displaystyle\int_0^{160}\;\frac{1}{50}x^2\;dx\\~\\ =\displaystyle\frac{1}{50}\int_0^{160}\;x^2\;dx\\~\\ =\displaystyle\frac{1}{50}\left[\;\frac{x^3}{3}\right]_0^{160}\\~\\ =\displaystyle\left[\;\frac{x^3}{150}\right]_0^{160}\\~\\ =\displaystyle\left[\;\frac{160^3}{150}-0\right]\\~\\ =27306\frac{2}{3} \)