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2 years ago

6

There are 20 machines at the gym and Manuel wants to perform exercises on 5 different machines while he is there. How many diffe

rent ways can he select the machines to use?
31008

1860480

100

15504

2 answers:

sasho [114]2 years ago

7 0

Total machines: 20

Required: on 5 <u>different</u> machines

Selection of machines is persons choice and not arranged specifically, thus we will use Combination.

⇒ 20C5

⇒ 20!/5!(20-5)!

⇒ 15504

Brut [27]2 years ago

3 0

n=20
r=5

Use combination

total ways

$\\ \rm\dashrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}$

$\\ \rm\dashrightarrow ^{20}C_5$

$\\ \rm\dashrightarrow \dfrac{20!}{5!15!}$

$\\ \rm\dashrightarrow \dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(15!}$

$\\ \rm\dashrightarrow 15504$

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3 years ago

I need help remembering the steps to solve a polynomial equation

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3 years ago

A,B and C are the vertices of one triangle.

dsp73

Answer:

Step-by-step explanation:

Given: The triangle with coordinate A(4,6), B(2,-2) and C(-2,-4). D is the mid point of AB and E is the mid point of AC.

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4 0

3 years ago

Read 2 more answers

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

harina [27]

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$L_x=8+8\lambda x=0\implies 1+\lambda x=0$
$L_y=8+8\lambda y=0\implies 1+\lambda y=0$
$L_z=4+8\lambda z=0\implies 1+2\lambda z=0$
$L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9$

$yL_x=y+\lambda xy=0$
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$\implies yL_x-xL_y=y-x=0\implies y=x$

$2zL_x=2z+2\lambda xz=0$
$xL_z=x+2\lambda xz=0$
$\implies 2zL_x-xL_z=2z-x=0\implies x=2z$

$2zL_y=2z+2\lambda yz=0$
$yL_z=y+2\lambda yz=0$
$\implies 2zL_y-yL_z=2z-y=0\implies y=2z$

$x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1$

$z=\pm1\implies y=x=\pm2$

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5 0

3 years ago

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andreev551 [17]

Answer:

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Take the time derivative (d/dt) of the entire given expression and apply chain rule on d/dt ( 2px ). Since both "p" and "x" are only functions of time "t":

d/dt

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Use the given values x=2, p=6, and dp/dt=1.5 to determine dx/dt

4*1.5 + 4*dx/dt + 2*(2*1.5+6*dx/dt)=0

6+4dx/dt + 2*(3+6dx/dt)=0

6+4dx/dt + 6+12dx/dt=0

12+16dx/dt=0

12=-16dx/dt

dx/dt= 12/-16

= -0.75

7 0

3 years ago