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3 years ago

Write a linear factorization of the function. f(x) = x^4 + 64x^2

2 answers:

6 0

we are given with the function f(x) = x^4 + 64x^2 and is asked to factor the function. The greatest common factor of the terms is x^2 . hence taking out x^2 from the set, the result is x2 *(x2 + 64).(x2 + 64) is equal to (x+8)^2 - 16x. hence the linear factorization is x^2 * ( (x+8)^2 - 16x)

Gelneren [198K]3 years ago

3 0

Hello,

y=x^4+64x&
In IR, y=x^2(x^2+64).

In C, y=x²(x+8i)(x-8i)

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A number of friends decided to go on a picnic and planned to spend rs. 96 on eatables. four of them, however, did not turn up. a

mr Goodwill [35]

The number of those who attended the picnic was 8.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = $ax^{2} + bx + c$ = 0 where a, b, c, ∈ R and a ≠ 0.

Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.

Let x represent the whole population.

Total Spending = Rs. 96

Thus, each individual's contribution is equal to 96/x.

Four people did not show up causing

others to contribute Rs. 4 extra.

So the given condition can be written as

96/(x-4) – 96/x = 4

=>96x – 96(x-4) = 4x(x-4)

=> 96x -96x + 384 = 4x2 – 16x

=> 4x2 – 16x – 384 = 0

=> x2 – 4x – 96 = 0

=> (x – 12)(x + 8) = 0

=> x = 12 or x = -8 (neglect)

So x = 12

x-4 = 8 ( because four of them did not turn up)

∴ The number of those who attended the picnic was 8.

Learn more about quadratic equations here :

brainly.com/question/15241362

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4 0

2 years ago

In the following quadratic function, I can easily determine which key feature?

Kobotan [32]

Answer is y intercept
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3 0

2 years ago

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 90.5 N , Jill pul

Radda [10]

Answer:

Fn= 174.9 N : Magnitude of the net force the people exert on the donkey.

Step-by-step explanation:

We find the components of the forces in x-y-z

Force of Jack in z =F₁z=90.5 N in direction (+z)

Force of Jill in x = F₂x= -82.3*cos45°= - 58.19 N (-x)

Force of Jill in y =F₂y=-82.3*sin45°= + 58.19 N (+y)

Force of Jane in x =F₃x=125*cos45°= + 88.4 N (+x)

Force of Jane in y =F₃y=125*sin45°= + 88.4 N (+y)

Calculating of the components of the net force the people exert on the donkey.

Fnx= F₂x+F₃x=( - 58.19+ 88.4 )N=30.2N (+x)

Fny= F₂y+F₃y=( 58.19+88.4 ) = 146.59 N (+y)

Fnz =F₁z=90.5 N (+z)

Calculating of the magnitude of the net force the people exert on the donkey.

$F_{n} =\sqrt{(F_{nx})^{2}+(F_{ny}) ^{2} +(F_{nz}) ^{2} }$

$F_{n} =\sqrt{(30.2)^{2}+( 146.59) ^{2} +(90.5) ^{2} }$

$F_{n} = 174.9 N$

7 0

3 years ago

Can someone explain to me how to find mean/median of a data set real quick?

PIT_PIT [208]

Mean is were you add up all of the numbers and how many numbers are there thats how much you divide by and median is were you line up the numbers from least to greatest then try to find the middle number <span />

3 0

3 years ago

Read 2 more answers

Determine if the following system of equations has no solutions 4x+3y= -8 -8x-6y= 16

cupoosta [38]

$\begin{cases} 4x+3y=-8\\\\ -8x-6y=16 \end{cases}~\hspace{10em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$4x+3y=-8\implies 3y=-4x-8\implies y=\cfrac{-4x-8}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3} \\\\[-0.35em] ~\dotfill\\\\ -8x-6y=16\implies -6y=8x+16\implies y=\cfrac{8x+16}{-6} \\\\\\ y=\cfrac{8}{-6}x+\cfrac{16}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3}$

one simple way to tell if both equations do ever meet or have a solution is by checking their slope, notice in this case the slopes are the same for both, meaning the lines are parallel lines, however, notice both equations are really the same, namely the 2nd equation is really the 1st one in disguise.

since both equations are equal, their graph will be of one line pancaked on top of the other, and the solutions is where they meet, hell, they meet everywhere since one is on top of the other, so infinitely many solutions.

3 0

1 year ago