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Korvikt [17]
3 years ago
9

In how many ways can i arrange the 6 letters a, b, c, d, e, f?

Mathematics
1 answer:
Ivanshal [37]3 years ago
7 0
If there are no restrictions, there can be; 

6 ways x 6 ways x 6 ways x 6 ways x 6 ways x 6 ways = 6^6 ways for the letters a, b, c, d, e and f to be arranged. 

However, if you want to arrange them so that each letter is used only once; 

6 ways x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 6! ways 

Hope I helped :) 
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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justi
stealth61 [152]
Applying our power rule gets us our first derivative,

\rm f'(x)=6\frac13x^{-2/3}+3\cdot\frac43x^{1/3}

simplifying a little bit,

\rm f'(x)=2x^{-2/3}+4x^{1/3}

looking for critical points,

\rm 0=2x^{-2/3}+4x^{1/3}

We can apply more factoring.
I hope this next step isn't too confusing.
We want to factor out the smallest power of x from both terms,
and also the 2 from each.

0=2x^{-2/3}\left(1+2x\right)

When you divide x^(-2/3) out of x^(1/3),
it leaves you with x^(3/3) or simply x.

Then apply your Zero-Factor Property,

\rm 0=2x^{-2/3}\qquad\qquad\qquad 0=(1+2x)

and solve for x in each case to find your critical points.

Apply your First Derivative Test to further classify these points. You should end up finding that x=-1/2 is an relative extreme value, while x=0 is not.

Let's come back to this,

\rm f'(x)=2x^{-2/3}+4x^{1/3}

and take our second derivative.

\rm f''(x)=-\frac43x^{-5/3}+\frac43x^{-2/3}

Looking for inflection points,

\rm 0=-\frac43x^{-5/3}+\frac43x^{-2/3}

Again, pulling out the smaller power of x, and fractional part,

\rm 0=-\frac43x^{-5/3}\left(1-x\right)

And again, apply your Zero-Factor Property, setting each factor to zero and solving for x in each case. You should find that x=0 and x=1 are possible inflection points.

Applying your Second Derivative Test should verify that both points are in fact inflection points, locations where the function changes concavity.
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4 years ago
Frida applied the steps below to find the product of (–1.2)(–9.4). Step 1: (–1.2)(–9.4) = (–9.4)(–1.2) Step 2: = (–9.4)(–1) + (–
lozanna [386]
Check on go gle it might help
5 0
3 years ago
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Solve for the smallest value of $x$ such that $24x^2 + 17x - 20 = 0.$ Express your answer as a simplified common fraction.
Gala2k [10]
X=5/8 or x=-4/3 
here is the work if needed...
24x^2+17x-20=0
Step one: Factor left side of equation.
(8x-5)(3x-4)=0
Step two: Set factor equal to 0.
8x-5=0 or 3x-4=0
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4 0
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A sphere has a radius r=12 inches. What is it’s approximate volume
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Step-by-step explanation:

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To make ribbon and bow for a hat, Stacey needs 5/6 yard of black ribbon and 2/3 yard of red ribbon. how much total ribbon does s
larisa86 [58]
First make the denominators of the fractions the same by multiplying.

\frac{2}{3} × \frac{2}{2}
=\frac{4}{6}

Now we just need to add the fractions together

\frac{5}{6} +  \frac{4}{6}
= \frac{9}{6}

9/6 would be the answer, but it can be simplified further, then converted into decimal form.

\frac{9}{6} ÷ \frac{3}{3}
=\frac{3}{2}
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Your final answer is 1.5 yards of ribbon are needed.
7 0
4 years ago
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