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kramer
3 years ago
14

Simplify (x+4)(x^2-6x

Mathematics
1 answer:
lesya [120]3 years ago
4 0

Answer:

The answer is x^3 - 2x^2 - 24x

Step-by-step explanation:

(x+4)(x^2-6x)

= (x+4)(x^2 + -6x)

= (x)(x^2) + (x)(-6x) + (4)(x^2) + (4)(-6x)

=x^3 - 6x^2 + 4x^2 - 24x

=x^3 - 2x^2 - 24x

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At what point does the curve have maximum curvature? y = 9 ln(x) (x, y) =
Andrews [41]

y = 9ln(x) 
<span>y' = 9x^-1 =9/x</span>
y'' = -9x^-2 =-9/x^2

curvature k = |y''| / (1 + (y')^2)^(3/2) 

<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2) 
= (9/x^2) / (1 + 81/x^2)^(3/2) 
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)] 
= 9x(x^2 + 81)^(-3/2). 

To maximize the curvature, </span>

we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2) 
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2] 
...= 9(81 - 2x^2)/(x^2 + 81)^(5/2) 

Setting k' = 0 yields x = ±9/√2. 

Since k' < 0 for x < -9/√2 and k' > 0 for x > -9/√2 (and less than 9/√2), 
we have a minimum at x = -9/√2. 

Since k' > 0 for x < 9/√2 (and greater than 9/√2) and k' < 0 for x > 9/√2, 
we have a maximum at x = 9/√2. </span>

x=9/√2=6.36

<span>y=9 ln(x)=9ln(6.36)=16.66</span>  

the answer is
(x,y)=(6.36,16.66)
7 0
3 years ago
In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
ra1l [238]
Easy!
You take the total number of students (55) then you remove the people that only like math and remove the people that only like English and remove the people that like none of them and what’s left is how many like both subjects.

55-15-18-5=17 students that like both subjects!

6 0
2 years ago
-4x+ 8x2 – 2x3 + 5<br> this is algebra
Serggg [28]

Answer:

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Step-by-step explanation:

use Khan academy it's very helpful

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Nesterboy [21]

Answer:

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Step-by-step explanation:

8 0
2 years ago
The two segments formed as a result of a bisector will always be
hjlf

Answer:

two equal parts .

Step-by-step explanation:

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