factor this polynomial completely x^2-10x+25

For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = \lim_{z\to\frac\pi4}\frac1{(3-1)!} \frac{d^{3-1}}{dz^{3-1}}\left[e^z\cos(z)\right][/tex]

We have

[tex]\dfrac{d^2}{dz^2}[e^z\cos(z)] = -2e^z \sin(z)[/tex]

and so

[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = - \lim_{z\to\frac\pi4} e^z \sin(z) = -\frac{e^{\pi/4}}{\sqrt2}[/tex]

Then by the residue theorem,

[tex]\displaystyle \int_C \frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3} \, dz = 2\pi j \left(-\frac{e^{\pi/4}}{\sqrt2}\right) = \boxed{-\sqrt2\,\pi e^{\pi/4} j}[/tex]

For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:

[tex]\displaystyle \mathrm{Res}\left(\frac{\cosh(2z)}{(z-2j)^2\left(z-\frac j2\right)^2}, z=\frac j2\right) = \lim_{z\to\frac j2}\frac1{(2-1)!} \frac{d^{2-1}}{dz^{2-1}}\left[\frac{\cosh(2z)}{(z-2j)^2}\right] = \frac{16\cos(1)-24\sin(1)}{27}j[/tex]

The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.

Answer:

8, 2.

Step-by-step explanation:

2*4 is 8 so I think line them up together and 12/6 is 2

Answer:

a. A(x) = 3x² - 8x + 5

b. x = ⁸/₃

Step-by-step explanation:

a.

A(x) = shaded area

A(x) = (2x - 3)² - (x - 2)²

= 4x² - 12x + 9 - (x² - 4x + 4)

= 4x² - x² - 12x + 4x + 9 - 4

= 3x² - 8x + 5

b.

ΔABF area = ⁵/₄ cm²

A(x) = 4(⁵/₄)

= 5

Substitution:

3x² - 8x + 5 = A(x) = 5

3x² - 8x + 5 = 5

3x² - 8x = 0

x(3x - 8) = 0

3x - 8 = 0

x = ⁸/₃

x = 0

Since x > 2, x = 0 is not valid;

So, x = ⁸/₃

Answer:

40% of airline A's flights were on time

Step-by-step explanation:

0.4=40% .the top row indicates that it was airline A. the left column indicates that it was on time.

Answer:

B

Step-by-step explanation:

happy holidays

Answer:

d. 7, -14, 28, -56, 112

Step-by-step explanation:

f(2) = -2(7) = -14

f(3) = -2(-14) = 28

f(4) = -2(28) = -56

f(5) = -2(-56) = 112

Answer:

First Option, log 3x is equivalent to the expression shown

Answer:

x<-3

Step-by-step explanation:

I will set it up.

Let a = adults

Let s = seniors

The first equation is a + s = 325.

The second equation is 9a + 7s = 2504.

Here is your system of equations:

{a + s = 325

{9a + 7s = 2504

Take it from here.

Answer:

a-2=a-2

Step-by-step explanation:

Here it is, you just have to notice that the numerator has common factors alternated. You will then collect the same parentheses and simplify with the denominator.

Answer:

Step-by-step explanation:

Parentheses are missing in your problem statement if you intend to simplify ...

  [tex]\dfrac{3a^2-ac+2c-6a}{3a-c}\\\\=\dfrac{a(3a-c) -2(3a-c)}{3a-c}\qquad\text{factor pairs of terms}\\\\=\dfrac{(a-2)(3a-c)}{(3a-c)}\\\\=\boxed{a-2}\qquad\text{cancel common factors}[/tex]

The "steps" are ...

Answer:

c

Step-by-step explanation:

each shape has one more side than the other

the last shape in the pattern so far has 5

the shape at letter c has 6

therefore it is c

Answer:

14

Step-by-step explanation:

because both sides need to be equal so if u plug in the 14 in x it gives you the same number for both sides 107.

Using the t-distribution, it is found that:

a)

The null hypothesis is: [tex]H_0: \mu \geq 60[/tex]

The alternative hypothesis is: [tex]H_1: \mu < 60[/tex]

b) t = -1.47

c) 0.0878.

d) Do not reject the null hypothesis.

e) Not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.

Item a:

At the null hypothesis, it is tested if the mean is not less than 60 seconds, that is:

[tex]H_0: \mu \geq 60[/tex]

At the alternative hypothesis, it is tested if the mean is less than 60 seconds, that is:

[tex]H_1: \mu < 60[/tex]

Item b:

We can find the standard deviation for the sample, hence, the t-distribution is used to solve this question.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

With the help of a calculator to find the sample mean and the standard deviation, the values of the parameters are:

[tex]\overline{x} = 55.8, \mu = 60, s = 9.04, n = 10[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{55.8 - 60}{\frac{9.04}{\sqrt{10}}}[/tex]

[tex]t = -1.47[/tex]

Item c:

The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -1.47.

Item d:

The p-value is of 0.0878 > 0.05, hence, we do not reject the null hypothesis.

Item e:

Since the null hypothesis is not rejected, there is not enough evidence to conclude that the average maximum amount of time people can hold their breath is less than 60 seconds.

A similar problem is given at brainly.com/question/24826023

Answer:

11 hours

Step-by-step explanation:

8t + 7 > 89

8t > 81 : subtract 7 from both sides

t > 10.125 : divide by 8 for both sides

t = 11 : estimate

Trey has to work 11 hours because 10 hours would only give him $87.

Answer:

5/7

Step-by-step explanation:

3/4-1/28

21/28-1/28

20/28

simplify

5/7

Answer:

The answer is going to be A

Step-by-step explanation:

Answer:

x = 35

Step-by-step explanation:

First, set both equations equal to each other because it is the same angle (congruent)

6x - 20 = 4x + 50

-4x and +20 to both sides of the equation and you end up with:

2x = 70

divide both sides by 2 and:

x = 35

Answer:

Image below!

Step-by-step explanation:

Plotting [tex]\underline{y=2x+3}[/tex]

Step 1: determine the y-intercept

[tex](0,3)[/tex]

Step 2: Move 2 units up, and 1 unit left (keep repeating this process until you have reached the limit of the graph)

Step 3: Go to the other side of the graph of the first point (y-intercept)

When you've completed this process, it should look like this:

Answer:

Elevator 1 is 12 feet above ground level, and Elevator 2 is 15 feet below the position of Elevator 1. We are given that Elevator 1 is "+12 feet" and Elevator 2 is "-15 feet" meaning 15 feet below that of Elevator 1 (because they said it was where it was at Elevator 1 ground level prior), so this should be your answer "A".

Step-by-step explanation:

1 a

Stacy sold 15 children tickets and 30 adult tickets.

The tickets are $7 for adults and $4 for children.

She sells twice as many adult tickets as children tickets and bring in a total of $270.

Therefore,

let

number of children ticket sold = x

number of adult ticket sold = 2x

7(2x) + 4(x) = 270

14x + 4x = 270

18x = 270

x = 270 / 18

x = 15

The number of children ticket sold = 15

The number of adult ticket sold = 15 × 2 = 30

learn more about algebra here: https://brainly.com/question/14569336?referrer=searchResults

Answer:

Ayo

Step-by-step explanation:

Thanks bro

Answer:

x = 9

Step-by-step explanation:

75 - 6x = 4x - 15

We want to arrive at an answer that looks like

x = a number,

so we want x on the left side and numbers on the right side.

Remember that whichever operation we do to one side of the equation, we must do to both sides.

Since there is a 75 on the left side, and it is being added to -6x, subtract 75 from both sides.

75 - 75 - 6x = 4x - 15 - 75

Simplify both sides.

-6x = 4x - 90

Since there is a 4x on the right side, and it is being added to -90, subtract 4x from both sides.

-6x - 4x = 4x - 4x - 90

Simplify both sides.

-10x = -90

We want x, but x is being multiplied by -10, so we divide both sides by -10.

[tex] \dfrac{-10x}{-10} = \dfrac{-90}{-10} [/tex]

Simplify both sides.

x = 9

Answer:

x

Step-by-step explanation:

Since the x- terms are opposites , that is 3x and - 3x , then when the 2 equations are added the x- term will be eliminated.

Answer:

The answer is 4.2,

Hope that helped. x

Step-by-step explanation:

3 x 7 (3*7) = 21

21 divided by 5 = 4.2.

Answer:

4.2

Step-by-step explanation:

Using PEMDAS,

We know that to solve (3*7) divided by 5, we will need to solve what is in the parenthesis.

So, we need to figure out what is 7*3, which is 21.

This is what we have right now:

21 divided by 5

The next step is dividing,

In the end, the answer is 4.2, hope this helped!

Answer:

1000

Step-by-step explanation:

So the taken chocolate weight equals to the original 1 box of chocolate.

Thus there are 200 x 5 = 1000g.

The orginal chocolate has 1000g each.

Area = length x width

Area of square = 8 x 8 = 64 square inches

Area of rectangle = 24 x 20 = 480 square inches

Area of rectangle surrounding the square = 480 - 64 = 416 square inches

Answer: 416 square inches

Answer:

225 children tickets, 450 adult tickets and 500 student tickets were sold

Answer:

For part a multiply the pound amount by 16. Your work would look something like this... (not actual answer) 10 pounds x 16= 160 ounces. So 10 pounds= 160 ounces!

For part B

0.15 gallons=1.2 pints

Example: .15 x 4= .6

.6 x 2= 1.2 pints

1.2 x 20 seconds= 24 pints!

Hope this helps

Step-by-step explanation:

:)

Answer:

Part A: 52 oz

Part B: 24 pints

Step-by-step explanation:

Part A:

Since 1 pound = 16 ounces, the number of ounces is 16 times the number of pounds. To convert pounds to ounces, multiply the pounds by 16.

3 1/4 lb × 16 oz/lb =

= 13/4 × 16 oz

= 13 × 4 oz

= 52 oz

Answer: 52 oz

Part B:

We need to convert from gallons to pints.

1 gallon = 4 quarts

1 quart = 2 pints

That means that 1 gallon = 8 pints.

0.15 gallon/second × 8 pints/gallon =

= 1.2 pints/second

The tap dispenses 1.2 pints/second.

Now we calculate the number of pints dispensed in 20 seconds.

1.2 pints/second × 20 seconds = 24 pints

Answer: 24 pints

Answer:

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Answer:

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Step-by-step explanation: Hope it Helpss :D

Using the slope of the linear function, it is found that:

A linear function is modeled by:

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

In which:

In this problem:

Two of the points are: (0,0) and (2,1).

[tex]m = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]

Then, applying the interpretation:

To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622

Answer:

hes correct. the slope is 0.5 and it grows 0.5 inches everyday

Step-by-step explanation:

ΔPQR has:  PM is a median

So: MR = QM = 3 cm

ANSWER:  MR = 3 cm

Ok done. Thank to me :>