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4vir4ik [10]
3 years ago
7

X^5(1-x)^6 How to find the critical points

Mathematics
2 answers:
Lana71 [14]3 years ago
7 0
y=x^5(1-x)^6\\
y'=5x^4(1-x)^6+x^5\cdot6(1-x)^5\cdot(-1)\\
y'=x^4(1-x)^5(5(1-x)-6x)\\
y'=x^4(1-x)^5(5-5x-6x)\\
y'=x^4(1-x)^5(5-11x)\\\\
x^4(1-x)^5(5-11x)=0\\
\boxed{x=0 \vee x=1 \vee x=\dfrac{5}{11}}
Ksenya-84 [330]3 years ago
4 0
Critical points are when the derivative is equal to zero
F(x)=x^{ 5 }(1-x)^{ 6 }\\ F'(x)=x^{ 5 }*-6(1-x)^{ 5 }+5x^{ 4 }(1-x)^{ 6 }\\ F'(x)=-6x^{ 5 }(1-x)^{ 5 }+5x^{ 4 }(1-x)^{ 6 }\\ -6x^{ 5 }(1-x)^{ 5 }+5x^{ 4 }(1-x)^{ 6 }=0\\ (x^{ 4 }(1-x)^{ 5 })(-6x+5(1-x))=0\\ (x^{ 4 }(1-x)^{ 5 })(5-11x)=0\\ \\ (x^{ 4 }(1-x)^{ 5 })=0\\ x=0\ and\ 1\\ \\ (5-11x)=0\\ x=\frac { 5 }{ 11 } \\ \\ \boxed { Critical\ Points\ at\ x=\frac { 5 }{ 11 }\ ,0,\ and\ 1 }

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Sonny substituted 5 for x in the proportion startfraction 16 over x endfraction = startfraction 48 over 15 endfraction and cross
frez [133]

The cross products of the proportion are equal.

According to the question, Sonny's equation can be written as follows.

16/x = 48/15

Now, the variable x is replaced by the constant 5. So the equation can now be written as follows.

16/5 = 48/15

When two fractions are equal to one another as shown above, the constants are cross multiplied with one another in order to form an equation.

16*15= 48*5

The values of both the products are equal which is 240.

Therefore, because the cross products of the proportion are equal.

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4 0
2 years ago
If i only do 8/9 assignments what will my grade be if it was 100%
Pie

Answer:

Im not sure that really makes sense but I think your grade would be 90% if you did 8/9 or somewhere around that

Step-by-step explanation:

3 0
3 years ago
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In the band, there are 2 vocalists and 5 musicians. What is the ratio of musicians to vocalists
AfilCa [17]

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Step-by-step explanation:

It sounds like they want the ratio to be given in that order.

Hope that helps!

3 0
3 years ago
I got this wrong on a test and I can't understand it. Can someone explain? I figured out it was compound interest, but I dont kn
Oliga [24]
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A= 500(1.0325)¹² ==> 500(1+0.0325)¹² ==> 500(1+3.25%)¹²
The mistake is:
Either she has a yearly interest of 3.25% & she wrote 12 instead of 3 (years)
OR
She got a quarterly interest of 3.25% and in this case she should have divided 3.25& by 12 (4 quarter a year ==> 12 quarter for 3 years) by keeping as exponent the number 12 (right)

1)Now the Amount of A (as she wrote it) =500(1.0325)¹² = 734
2) If she wrote 12 instead of 3, and after correction A=500(1.0325)³ =550
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3 0
3 years ago
The Bowen family's pancake recipe uses 2 teaspoons of baking powder for every
Veseljchak [2.6K]

Answer:

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Step-by-step explanation:

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Hope this helps!

5 0
3 years ago
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