Find all the zeros of f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12

Answer:

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Step-by-step explanation:

The objective of this question is to solve:

[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]

Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:

Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:

i.e.

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]

To Replace:

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]

[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]

[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]

Thus;

[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0

[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]

∴

In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:

[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]

By Factorization:

[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]

[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]

However;

The root [tex]\lambda = -6 \pm i[/tex] yield;

[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]

[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]

The root [tex]\lambda = 3[/tex] yield;

[tex]y_3(x) = c_3 e^{3x}[/tex]

∴

The general solution is:

[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]

Using Euler's Identity ;

[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]

[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

9514 1404 393

Answer:

  19

Step-by-step explanation:

If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...

  55 +35 = 90 . . . minutes

That is, it is the number already in transit when they leave, plus the number that start while they are traveling.

That's 90/5 +1* = 19 ferries.

_____

The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.

The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.

__

* the +1 is because the number of points defining intervals is 1 more than the number of intervals.

Answer:

2x-1

Step-by-step explanation:

Answer:

a. y = -½x

b. y = -½x + 3

c. 2y = -x - 4

e. x + 2y = 8

Step-by-step explanation:

Parallel lines have the same slope. Therefore, the lines that will be parallel to the given line on the graph would have the same slope as the line of the graph.

First, find the slope of the line on the graph:

[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Use the coordinates of any two points on the line. Let's use (-4, 0) and (0, -2)

[tex] m = \frac{-2 - 0}{0 -(-4)} = \frac{-2}{4} = -\frac{1}{2} [/tex]

Slope of the line on the graph is -½.

Check each given line equation, ensure they are in the slope-intercept form and find out if the value of their slope is the same as -½.

Slope-intercept form is given as y = mx + b, where, m = slope.

Option 1: y = -½x

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 2: y = -½x + 3

The slope of this line is also -½, therefore it is parallel to the line on the graph.

Option 3: 2y = -x - 4

Rewrite in slope-intercept form.

y = -x/2 - 4/2

y = -½x - 2

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 4: y = 2x - 5.

The slope of this line is 2, therefore it is NOT parallel to the line on the graph.

Option 5: x + 2y = 8

Rewrite in slope-intercept form.

2y = 8 - x

y = 8/2 - x/2

y = 4 - ½x

The slope of this line is -½, therefore it is parallel to the line on the graph.

Answer:

3.20

Step-by-step explanation:

Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.

Answer:

20

Step-by-step explanation:

20 - 3

Sarah is 3 years older so 23 is going to be subtracted.

Answer: Which question?

Step-by-step explanation:

Answer:

could you give a picture of the problem. cause I may be able to help but I cant really understand the question with what you typed

Answer:

D

Step-by-step explanation:

just took this test

/~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~

Answer:

−x2+g+3x−5 (I think)

Step-by-step explanation:

Answer:

2143

Step-by-step explanation:

Answer:

3,1

Step-by-step explanation:

Answer:

In 5 hours, the migrating bird will frly 215 miles.

Step-by-step explanation:

Since the bird flys 688 miles in 16 hours we need to find the unit rate. So i divided 16 by the 16 hours which gave me 1, so i also divided 688 by 16 and i got 43. So the bird flys 43 miles in a hour. We are not done yet because we need to find how many miles in 5 hours. So we multiply the 43 miles by 5 and got 215, and i also multiplied the 1 hour bye 5 and got 5. Last but not least, the migrating bird will fly 215 miles in 5 hours. I hope that this will help you out.

Answer:

hope it is helpful

Step-by-step explanation:

mark as branlist

^ ^

Answer:

7⅓ cups of water

Step-by-step explanation:

Water-salt mixture ratio = ¾ cup of salt to 5½ cups of water (¾ : 5½)

To maintain this water to salt ratio, if you intend to use 1 cup of salt, the number of water you need to add can be calculated as follows:

¾ cup of salt : 5½ cups of water = 1 cup of salt : x cups of water

¾ : 5½ = 1 : x

[tex] \frac{\frac{3}{4}}{5\frac{1}{2}}. = \frac{1}{x} [/tex]

[tex] \frac{\frac{3}{4}}{\frac{11}{2}} = \frac{1}{x} [/tex]

[tex] \frac{3}{4}*{\frac{2}{11} = \frac{1}{x} [/tex]

[tex] \frac{3}{2}*{\frac{1}{11} = \frac{1}{x} [/tex]

[tex] \frac{3*1}{2*11} = \frac{1}{x} [/tex]

[tex] \frac{3}{22} = \frac{1}{x} [/tex]

Cross multiply

[tex] 3x = 22 [/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{22}{3} [/tex]

[tex] x = 7\frac{1}{3} [/tex]

Number of cups of water to add to 1 cup if salt is 7⅓ cups.

Answer:

8units

Step-by-step explanation:

Given parameters:

  Area of triangle  = 32units²

   Base  = 8units

Unknown:

height x of the triangle = ?

Solution:

The area of a triangle is given as;

    Area = [tex]\frac{1}{2}[/tex] x base x height

 Input the parameters and solve for the height;

     32  = [tex]\frac{1}{2}[/tex] x 8 x h

     32 = 4h

      h = 8

height of the triangle is 8units

Answer:

I might be stupid but 5 feet and 8 inches...im not positive tho. good luck

Answer && Step-by-step explanation:

just do 16-11, we also know there are 12 inches in a foot so do 12-4

5 feet, 8 inches is the answer

Answer: 17 / 990

Step-by-step explanation:

To obtain the probability of the question above :

Find the count of number pairs whose difference gives is 15 in the range (1 to 100).

Also find the count of all distinct number pair differences

Number pair which have a difference of 15 = 85

Total distinct number pair differences = 4950

Probability = required outcome / Total possible outcomes

P(difference of 15) = 85/4950 = 17/990

Answer:

Hundreds & 100

Step-by-step explanation:

Answer: 615

Step-by-step explanation:

Answer:

[tex]\huge\boxed{y=-x-1}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

[tex]m[/tex] - slope

[tex]b[/tex] - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

[tex](x_1;\ y_1)[/tex] - point on a line

========================================

We have

[tex]m=-1;\ (-4;\ 3)\to x_1=-4;\ y_1=3[/tex]

substitute

[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)\\\\y-3=-x-4\qquad|\text{add 3 to both sides}\\\\y-3+3=-x-4+3\\\\y=-x-1[/tex]

Answer: they didn’t give the exact answer.

Step-by-step explanation: they rounded to the nearest.

Answer:

12i + 9

Step-by-step explanation:

Since sqrt of negative numbers cannot exist, they are numbers followed by the letter I.

sqrt -16=4i

sqrt -64=8i

3 and 6 cannot be grouped with them, so you would add these two

3+6=9

8i+4i=12

I believe this would be the answer:

12i + 9.

Answer:

18-32i

Step-by-step explanation:

(3+sqrt(16i)(6-sqrt(64i)

= 18-32i

Answer:

154.44

Step-by-step explanation:

What is 13% of 396?

Y is 13% of 396

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 13% * 396

Converting percent to decimal:

p = 13%/100 = 0.13

Y = 0.13 * 396  

Y = 51.48

Now multiply by 3 (amount of continuous years)

51.48 * 3

=154.44

Hope it helps!

Answer: -7.7%

Step-by- A P E X

Answer:

4/3 per minute

Step-by-step explanation:

Complete Question

Researchers investigated whether the proportion of American teenagers with some level of hearing loss was different in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol [tex]\pi __{05-06}}[/tex] denote the population proportion of American teenagers with some level of hearing loss in 2005–2006 and similarly for [tex]\pi__{{88-94}}[/tex]. A 95% confidence interval for the parameter [tex]\pi__{{05-06}} }- \pi__{{88-94}}[/tex] turns out to be (0.0015, 0.0467).

Required:

What is an appropriate conclusion to draw?

Answer:

The appropriate conclusion is  

The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006

Step-by-step explanation:

Generally the appropriate conclusion is

The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006.

This because the confidence intervals are very close to zero , i.e both the upper limit and the lower limit are close to zero  and if we are take 0.05 as our level of significance we see that the both values of the confidence level are small to be significant

Answer:

Its A

Step-by-step explanation:

I got it right on EDGE 2021

Answer:

The answer is actually the last one

Step-by-step explanation:

I just did it. The other answer isn't even the right question.

Answer:

f(5) = 35

Step-by-step explanation:

In any function f(x), x is the input and f(x) is the output

Example:

f(x) = 2x + 3, find f(a)

That means we need to find value of f(x) at x = a, so substitute x by a

f(a) = 2(a) + 3 = 2a + 3

f(a) = 2a + 3

Let us use the same way to solve our question

∵ f(x) = x² + 2x

→ We need to find f(5), so substitute x by 5

∴ f(5) = (5)² + 2(5)

∴ f(5) = 25 + 10

→ Do addition

∴ f(5) = 35