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3 years ago

Which expression represents the number of possible combinations of n items taken rat a time

Mathematics

1 answer:

Likurg_2 [28]3 years ago

8 0

Answer:

nCr = n! / (r!)(n-r!).

Step-by-step explanation:

That would be nCr = n! / (r!)(n-r!).

A quick way of working these out is as follows:

Take 7C4:

this is 7*6*5*4/4*3*2*1 Cancelling out the 4 and 3*2:

= 7*5

= 35.

15C12 = 15C(15-12)

= 15C3

= 15*14*13 / 3*2*1

= 5*7*13

= 455.

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Ahhh help please find the perimeter

spin [16.1K]

Answer:

12 $x^{2}$ + 6y

Step-by-step explanation:

3 0

3 years ago

The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = x, y,

suter [353]

Answer:

$\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

Step-by-step explanation:

The straight line path between point (a,b,c) and (l,m,n) is parametric by the expression

$r(t)=(1-t)(a,b,c) +t(l,m,n)\\$

since we are giving point (4,0,0) and (4,3,4), the parametric equation is giving below

$r(t)=(1-t)(4,0,0) +t(4,3,4)\\$

using the dot product system of multiplication, we have

$r(t)=(4,3t,4t) \\$

t is between 0,1.

Next we define the line integral for work done which is express as

$\int\limits^a_b {F.} \,dr\\$

First we define the general expression for the force

$f(x,y,z)=\frac{K(x,y,z)}{(x^{2}+y^{2}+z^{2})^{3/2}} \\$

If we substitute our parametric equation we arrive at

$F(r(t))=\frac{K(4,3t,4t)}{(4^{2}+(3t)^{2}+(4t)^{2})^{3/2}}\\F(r(t))=\frac{K(4,3t,4t)}{(16+34t^{2})^{3/2}}\\$

also we need to find the expression for <em>dr</em>

$r(t)=(4,3t,4t)\\dr=(0,3,4)dt\\$

Now we substitute into the integral expression

$\int\limits^1_0 {\frac{k(4,3t,4t)}{(16+34t^{2})^{3/2}}} \, .(0,3,4)dt$

using dot product we arrive at

$\int\limits^1_0 {\frac{25kt}{{(16+34t^{2})^{3/2}} } \,$

let make a simple substitution so we can simplify the integral,

let assume $u=16+34t^{2}\\$

$\frac{du}{dt}=68t\\ dt=\frac{du}{68t} \\$

and changing setting the new upper and lower limit, we have

$\frac{25k}{68} \int\limits^a_b {\frac{1}{u\frac{3}{2} } } \, du\\a=50\\b=16\\$

by simple integral we arrive at

$-\frac{25k}{34}[\frac{1}{u^{1/2}}] ^{50}_{16} \\\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

Hence the workdone is

$\frac{25k}{34}[\frac{1}{4}-\frac{1}{50^{1/2}}] \\$

3 0

3 years ago

Which of the following is equivalent to i⁹

mote1985 [20]

The correct answer is letter F

4 0

3 years ago

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How to round 1,199,495 to the nearest hundredth

ollegr [7]

The next bigger hundredth is 1,199,495.01 .
The next smaller hundredth is 1,199,494.99 .
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6 0

4 years ago

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The table below shows the birth weight and the weight for the first three weeks of a baby whale. Determine the slope and y-inter

Licemer1 [7]

Answer:

Step-by-step explanation:

The slope is 1400. And the y intercept is 5000 because when x=0 y=5000. And if you multiply 1400 by 4 and then add 5000 you get 10,600 lbs for the weight at 4 weeks.

8 0

3 years ago