Find the volume: in cm 7cm high 3cm wide 2 cm long

Answers

Answer 1
v=l×w×h
so 7×3×2=42 cm3
Answer 2
The answer is 42 cm cubed



Related Questions

What is 40 kilometers per hour in meters per hour

Answers

40 km - meters is 40 * 1000 whch is 40000 meters per hour
1 kilometer= 1000 meters
1000*40
=40000 meters

Hope this helps!
-Benjamin

a full-time employee who works 40 hours per week earns 29.85 per hour estimate the person's annual income

Answers

There are 52 weeks in a year. The question is asking how much is the annual salary.
their annual income would be around 62,088

40h x $29.85 = $1,194 per week 
then take $1,194 x 52 (because there are 52 weeks in a year) = $62,088 annual income

Jonathan's Antiques purchased an old wooden sled at an auction for $210. Jonathan wants to mark up the sled 60% of the selling price. What would be the selling price of the sled?

Answers

well, if the selling price was 210, and that's the 100%, then if he adds 60% to that, the new price will be 160% of 210... well, if 210 is the 100%, what's 160% of that?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 210&100\\ x&160 \end{array}\implies \cfrac{210}{x}=\cfrac{100}{160}[/tex]

solve for "x".

A drawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. What is the least number of socks you must choose, without looking, to be certain that you have chosen two brown socks?

Answers

The only time you can be so certain that you have picked 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have picked 2 brown socks, you must pick all 12 white socks and all 18 black socks and only then you can pick 2 brown socks without looking. Therefore the total number of socks that should be picked is:

Total number of socks = 12 white socks + 18 black socks + 2 brown socks

Total number of socks = 32 socks

A total picking of 32 socks is required to be certain without looking that 2 brown have already been chosen.

Find the decimal notation for 84.3%

Answers

to turn a percent into a decimal, move the decimal point 2 places to the left

84.3% = 0.843

2ax+1=ax+5 solve for x

Answers

You solve to get ax=4 so x=4/a
x=4/a

If you need a better understanding just ask

tan 2θ; cos θ = 8 17 , θ in Quadrant I

Answers

Final answer:

We first found sin θ using the Pythagorean identity, then found tan θ, and finally used the double-angle formula for tan to find tan 2θ.

Explanation:

To find the value of tan 2θ when cos θ = 8/17 and θ is in Quadrant I, you need first to find the value of sin θ. Since we are in Quadrant I, both cos and sin are positive. You can use the Pythagorean Identity for sin, cos, and tan, which states sin² θ + cos² θ = 1, to find sin θ. Substituting the given value of cos θ in this identity, we can find that sin θ = sqrt(1 - (8/17)²) = 15/17.

With sin and cos known, we can now find tan θ using the formula tan θ = sin θ/cos θ which gives tan θ = (15/17)/(8/17) = 15/8.

Finally, to find tan 2θ, use the Double-Angle formula for the tangent, which states tan 2θ = 2 tan θ / (1 - tan² θ). Substituting tan θ = 15/8 into this formula, we get tan 2θ = 2 * (15/8) / (1 - (15/8)²).

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To find tan 2θ, given cos θ is 8/17 and θ is in the first quadrant, first find sin θ using the Pythagorean identity, then use the double-angle formula where tan 2θ equals 2 tan θ divided by 1 minus tan squared θ, yielding -2.

To find tan 2θ given that cos θ is 8/17 and θ is in the first quadrant, we first need to find the value of sin θ. Since θ is in the first quadrant, all trigonometric functions are positive. Using the Pythagorean identity, we have:

sin θ = √(1 - cos² θ)

Substituting cos θ = 8/17:

sin θ = √(1 - (8/17)²) = √(1 - 64/289) = √(225/289) = 15/17.

Next, we use the double-angle formula for tangent:

tan 2θ = (2 tan θ) / (1 - tan² θ)

To find tan θ, we use:

tan θ = sin θ / cos θ = (15/17) / (8/17) = 15/8

Now, substitute tan θ into the double-angle formula:

tan 2θ = (2 × 15/8) / (1 - (15/8)²)

= (30/8) / (1 - 225/64)

= (30/8) / (-161/64) = -1920/1288 = -15/7.5 = -2

The complete question is :

Given that [tex]\(\cos \theta = \frac{8}{17}\)[/tex] with [tex]\(\theta\)[/tex] in the first quadrant, determine [tex]\(\tan 2\theta\).[/tex]


The total cost to rent a row boat is $14 times the number of hours the boat is used. Write an equation to model this situation if c = total cost and h = number of hours.

Answers

c = 14h

this would give you the total cost by multiplying 14 by the number of hours

A map of Brasilia has a scale of 1 inch to 5 miles. If the city is 2 7/16 inches across on the map, what is the distance across the actual city? a.) 10 1/2 mi b.) 8 3/16 mi c.) 12 3/16 mi d.) 8 1/4 mi

Answers

The answer is c because that is what the website said with the exact same question , I hope you don't need to show your work but the correct answer is c

Answer:

[tex]12\frac{3}{16} \text{inches}[/tex]

Step-by-step explanation:

Given : The city is [tex]2 \frac{7}{16}[/tex] inches across on the map

To Find:On the map, what is the distance across the actual city?

Solution:

Distance on map = [tex]2 \frac{7}{16}=\frac{39}{16} inches[/tex]

Scale: 1 inch = 5 miles

So, [tex]\frac{39}{16} inches=\frac{39}{16} \times 5[/tex]

[tex]\frac{39}{16} inches=\frac{195}{16} =12\frac{3}{16} [/tex]

Thus ,the distance across the actual city is [tex]12\frac{3}{16} inches[/tex]

So, option C is correct.

Tom predicted that the Giants would score three 3-point field goals, score two 6-point touchdowns, and score 1 extra point. If Tom were correct, what would the Giants' score be at the end of the game?

Answers

3x3 = 9

2x6 = 12

12+9 = 21+1 =22

 score would be 22 points

Answer:

The Giants' score will be 22 points.

Step-by-step explanation:

Consider the provided information.

It is given that tom predicted that the Giants would score three 3-point field goals. Which can be written as:

3 × 3 = 9

Total score by field goals is 9 points.

If he score two 6-point touchdowns, this can be written as:

2 × 6 = 12

Total score by touchdown is 6 points.

And 1 extra point.

Now add all the points as shown below:

Total score is: 9 + 12 + 1 = 22 points

Hence, the Giants' score will be 22 points.

Miriam’s study group received test scores of 96, 81, 82, 99, 94, 92, 95, 82, and 80. Find the mean and median scores.

Answers

Answer:

The mean is  

✔ 89

The median is  

✔ 92

The mean of Miriam's test scores is 89 and the median is 92.

What is mean?

"It is the average of a data set. "

What is median?

"It is the middle value in a list ordered from smallest to largest."

For given question,

Total number of test scores = 9

The sum of all the test scores would be,

96 + 81 + 82 + 99 + 94 + 92 + 95 + 82 + 80 = 801

So, the mean would be,

[tex]\bar{X}=\frac{801}{9} \\\\\bar{X}=89[/tex]

So, the mean of Miriam's test scores is 89.

If we arrange the test scores in ascending order then it would be,

80, 81, 82, 82, 92, 94, 95, 96, 99

The middle value is 92

So, the median is 92.

Therefore, the mean of Miriam's test scores is 89 and the median is 92.

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By what factor will the rate of the reaction change if the ph decreases from 5.50 to 2.00? express your answer numerically using two significant figures.

Answers

a. Rate law expression: [tex]\(\text{rate} = kxyz\)[/tex]

b. [tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]

**Part A: Rate Law Expression**

Given that the reaction is first order in [tex]\( (IO_3)^- \)[/tex], first order in [tex]\( (SO_3)^{2-} \)[/tex], and first order in [tex]\( H^+ \)[/tex], the rate law for the reaction can be expressed as:

[tex]\[ \text{rate} = k \cdot [(IO_3)^-]^1 \cdot [(SO_3)^{2-}]^1 \cdot [H^+]^1 \][/tex]

Simplifying this, we get:

[tex]\[ \text{rate} = kxyz \][/tex]

Here, [tex]\( x \), \( y \), and \( z \)[/tex] are the concentrations of [tex]\( (IO_3)^- \), \( (SO_3)^{2-} \), and \( H^+ \)[/tex], respectively. [tex]\( k \)[/tex] is the rate constant.

**Part B: Rate Change with pH**

The pH of a solution is a measure of its hydrogen ion concentration [tex](\( [H^+] \))[/tex]. As the reaction is first order in [tex]\( H^+ \)[/tex], a change in pH will directly impact the rate. The relationship between pH and [tex]\( [H^+] \)[/tex] is logarithmic:

[tex]\[ \text{pH} = -\log[H^+] \][/tex]

To calculate the rate change factor when the pH decreases from 5.50 to 2.00, we need to consider the relationship between pH and [tex]\( [H^+] \)[/tex]:

[tex]\[ \text{pH} = -\log[H^+] \][/tex]

1. **At pH 5.50:**

  [tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-5.50} \][/tex]

2. **At pH 2.00:**

  [tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-2.00} \][/tex]

Now, calculate the rate factor:

[tex]\[ \text{Rate factor} = \frac{\text{rate at pH 2.00}}{\text{rate at pH 5.50}} = \frac{[H^+]_{\text{pH 2.00}}}{[H^+]_{\text{pH 5.50}}}\][/tex]

[tex]\[ \text{Rate factor} = \frac{10^{-2.00}}{10^{-5.50}} \][/tex]

[tex]\[ \text{Rate factor} \approx \frac{0.01}{3.16 \times 10^{-6}} \][/tex]

[tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]

Expressing the answer numerically using two significant figures, the rate change factor is approximately [tex]\(3.2 \times 10^3\).[/tex]

The question probable maybe:

Part A:

The reaction is found to be first order in [tex](IO_3)^-[/tex], first order in [tex](SO_3)^2^-[/tex], and first order in H^+.
If [[tex](IO_3)^-[/tex]] = x, [[tex](SO_3)^2^-[/tex]] = y and [[tex]H^+[/tex]]=z, what is the rate law for the reaction in terms of x, y, and z and the rate constant k?
Express the rate in terms of k, x, y, and (e.g., kxy^3z^2).

▸ View Available Hint(s)

rate= kx^1y^1z

Part B:

By what factor will the rate of the reaction change if the ph decreases from 5.50 to 2.00? express your answer numerically using two significant figures.

What is 46 2/3% of 28

Answers

2/3 is the same as 66.6666.....
so 46 2/3 will be the same as 46.666 multiply by 28 divided by 100
answer=13.06

Answer:

46 2/3% of 28 is 13.06

Step-by-step explanation:

Hello,

thank you very much for asking this here in brainly, I think I can help you with this one

Let's remember

[tex]a\frac{b}{c} =\frac{(a*c)+b}{c}\\[/tex]

Step 1

[tex]46\frac{2}{3} =\frac{(46*3)+2}{3} =\frac{140}{3} =46.67[/tex]

so 46 2/3% =46.67%

Step 2

using a rule of three

define the relationships

if

28⇒ 100%

x?  ⇒46.67%

[tex]\frac{28}{100}=\frac{x}{46.67} \\[/tex]

isolating x

[tex]\frac{28}{100}=\frac{x}{46.67}  \\x=\frac{28*46.67}{100}\\x=\frac{1306.67}{100} \\x=13.06[/tex]

46 2/3% of 28 is 13.06

I hope it helps, have a great day

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2

Answers

Let x =lenght, y = width, and z =height 
The volume of the box is equal to V = xyz 
Subject to the surface area 
S = 2xy + 2xz + 2yz = 64 
= 2(xy + xz + yz) 
= 2[xy + x(64/xy) + y(64/xy)] 
S(x,y)= 2(xy + 64/y + 64/x) 
Then 
Mx(x, y) = y = 64/x^2 
My(x, y) = x = 64/y^2 
y^2 = 64/x 
(64/x^2)^2 = 64 
4096/x^4 = 64/x 
x^3 = 4096/64 
x^3 = 64 
x = 4 
y = 64/x^2 
y = 4 
z= 64/yx 
z= 64/16 
z = 4 

Therefor the dimensions are cube 4.

Ethel is arranging rides so that 27 members go bowling. Some people can ride in a van that belonges to the center where they meet the rest must ride in cars if 12 can go in the van and 5 can go in each car how many cars will they need?

Answers

Answer: Three cars will be needed.

This is because the only possible combination of cars and vans that add up to the total seating of 27 people is one van (12 seats) and three cars (15 seats).

12+15=27 seats total.

Answer:

Number of cars needed=3

Step-by-step explanation:

Ethel is arranging rides for 27 members.

If 12 can go in the van and 5 can go in each car.

Let c cars are needed

Then, 12+5c=27

5c=27-12

5c= 15

c= 15/5

c=3

Hence, number of cars needed equals:

3

pie =????????????????????.??

Answers

Hello there!

I can assume you mean "Pi".

Pi is an irrational number that has an infinity decimal, also known as a terminating decimal, which means to repeat infinitely.

The summarized form of Pi is 3.14, but since you have multiple units, I can assume you want the extended form.

Here it is:
3.14159265359

I hope this helps!

If you have 18 out of 20 homework sections completed what percentage do you have

Answers

You have 90% of the homework sections completed
The word 'percent' can mean 'for every 100' or 'per 100'. And we can imagine 100% as being a whole of something.

In the question, we have 20 homework sections. 20 can be thought as the 100%. We word 'per' in 'percent' can be sought of as a division operator or the fraction line that separates the numerator and denominator.

So, we can think 18 out of 20 as [tex]\frac{18}{20}[/tex]

First simplify the fraction.

[tex]\frac{18}{20} = \frac{9}{10}[/tex]

Convert the fraction into a decimal.
We can convert a fraction into a decimal by dividing the numerator by the denominator.

9 / 10 = 0.9

Now convert the decimal into a percent by moving the decimal point two places to the right and making the decimal point into a % sign.

0.9 = 90%

So, 90% is the answer.


A two pound box of fruit snacks contains 24 packets. Find the unit rate in packets per pound

Answers

24/2=12

The unit rate is 12 packets per pound.

Hope this helps!

Answer:

12

Step-by-step explanation:

Given that a two pound box of fruit snacks contains 24 packets

We have to find the unit rate per pound

This is a question of direct variation.

[tex]2 pounds = 24 packets\\1 pount= 12 packet[/tex]

i.e. unit rate is 12 packets per pound

If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters

Answers

Matrix A ={ 2 8}{4 -2}, so a-b+c+d = 2-4+8+(-2) = 4


Answer: a-b+c+d =4


Step-by-step explanation:

The given system of equation is

[tex]2x+8y=7\\4x-2y=9[/tex]

from this we have the following matrices

[tex]A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}[/tex]

the given matrix A =[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}[/tex]

On comparing Matrix  [tex]A_1[/tex] with Matrix A

[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}[/tex]

we have the following values

a=2 ,b=4,c=8,d=-2

Thus a-b+c+d =2-4+8+(-2)=4

The average yearly temperature T in degrees for Newport, Oregon is given by: |T−55|≤10 Find the average temperature range in degrees.

Answers

| T - 55 | < = 10

-10 < = T - 55 < = 10
-10 + 55 < = T - 55 + 55 < = 10 + 55
45 < = T < = 65

the average temp ranges are between (and including) 45 degrees to 65 degrees

The average temperature range in Newport, Oregon is between 45 and 65 degrees.

The average yearly temperature T in degrees for Newport, Oregon is given by: |T−55|≤10. This means that the temperature T is within 10 degrees of 55 degrees. To find the average temperature range, we consider the range between 55+10 = 65 degrees and 55-10 = 45 degrees.

Therefore, the average temperature range in Newport, Oregon is 45 to 65 degrees.

How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?

Answers

Answer:

[tex]\displaystyle b = 11[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Functions

Function Notation

Calculus

Integration

IntegralsDefinite IntegralsIntegration Constant C

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

g(x) = 4x

Interval [1, b]

A = 240

Step 2: Solve for b

Substitute in variables [Area of a Region Formula]:                                   [tex]\displaystyle \int\limits^b_1 {4x} \, dx = 240[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle 4\int\limits^b_1 {x} \, dx = 240[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                     [tex]\displaystyle 4(\frac{x^2}{2}) \bigg| \limits^b_1 = 240[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle 4(\frac{b^2}{2} - \frac{1}{2}) = 240[/tex][Distributive Property] Distribute 4:                                                             [tex]\displaystyle 2b^2 - 2 = 240[/tex][Addition Property of Equality] Add 2 on both sides:                                 [tex]\displaystyle 2b^2 = 242[/tex][Division Property of Equality] Divide 2 on both sides:                               [tex]\displaystyle b^2 = 121[/tex][Equality Property] Square root both sides:                                                 [tex]\displaystyle b = \pm 11[/tex]Choose:                                                                                                         [tex]\displaystyle b = 11[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Mrs white wants to crochet beach hits and baby afghans for a church fund raising bazaar. she needs 7 hours to make a hat and 4 hours to make an Afghan and she has 68 hours available. she wants to make no more than 14 items and no more than 11 afghans. the bazaar will sell hats for $21 each and the afphans for $9 each. How many of each should she make to maximize the income for the bazaar?

Answers

This is a maximization problem so we apply derivatives here to determine the unknown variables in the problem. 

In this problem, we represent x as the number of hats made, and y as the number of Afghans made by Mrs White. 
Equation 1 relating to the time it takes to make these is expressed:

7x + 4y = 68
Another equation that represents inequality to the number of hats and Afghans respectively is expressed: 
x<= 14
y<=11

the third equation expresses the income from selling these items expressed as 
P = 21 x + 9y 
we subtitute 1 to 3

P = 9(68-7x)/4 + 21x = 153-15.75x + 21 x = 153 -5.25x 

So by trial and errror, x and y should be integers, we get two cases of which x and y should be

1) x = 4 ; y = 10
2) x = 8 ; y = 3


Subsituting to 3,  P1 = 174$ while P2is equal to $195, Answer then is 8 hats and 3 Afghans in total.

You are planning a study and are considering taking an srs of either 300 or 700 observations. explain how the sampling distribution would differ for these two scenarios.

Answers

This question has following choices to choose the answer from:

The larger sample would have a center closer to the true population parameter.

The larger sample would have less sampling variability.

The smaller sample would have less sampling variability.

The statistics of the smaller sample have more chance for bias than those of the larger sample.

 

I believe that the correct answer from the 4 choices would be the last one:

"The statistics of the smaller sample have more chance for bias than those of the larger sample."

This is because in a smaller sample, there is a high probability that not all parts or portion of the sample population is represented hence resulting in bias. This is especially true for distribution types of data wherein extreme values exist. Following that bias would already be effect on the center and the sampling variability. So bias always comes first.

How much do you need to invest in an account earning an annual interest rate of 2.938% compounded weekly, so that your money will grow to $7,880.00 in 50 weeks?

Answers

bearing in mind the compounding is weekly on an APR, so the compounding cycle is 52, since there are 52 weeks in a year

however, the maturity term in years, is just 50/52, since is 50weeks from 52 in a year, so is 50/52 years, which is just a fraction of a year

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$7,880\\ P=\textit{original amount deposited}\\ r=rate\to 2.938\%\to \frac{2.938}{100}\to &0.02938\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\to &52\\ t=years\to \frac{50}{52}\to &\frac{25}{26} \end{cases} \\\\\\ 7880=P\left(1+\frac{0.02938}{52}\right)^{52\cdot \frac{25}{26}}[/tex]

solve for P

The senate in a certain state is compromised of 58 republicans, 39 democrats, and 3 independents. How many committees can be formed if each committee must have 3Republicans and 2 ​Democrats?

Answers

Defining C(n,r) as the number of combinations (order does not count) to choose r objects from n, where C(n,r)=n!/(r!(n-r)!)
there are 
C(58,3) ways to choose 3 from 58 republicans, 
and
C(39,2) ways to choose 2 from 39 democrats.
So the committee has
(C(58,3)*(C(39,2)) variants, or
58!/(3!55!) * 39!/(2!37!)
=30856*741
=22864296

Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 60 cents each and the key chains cost $2 each. She must purchase at least 36.gifts but has to spend less than $40. Let x represent the amount of key chains and y represent the amount of magnets. Model the scenario with a system of inequalities.

Answers

x + y > = 36 (thats greater then or equal)
2x + 0.6y < 40

Answer:

[tex]x+y\geq 36[/tex]

[tex]2x+0.6y<40[/tex]

Step-by-step explanation:

The magnets are on sale for 60 cents each.

The key chains cost $2 each.

Katie must purchase at least 36 gifts but has to spend less than $40.

Now let x represent the amount of key chains.

Let y represent the amount of magnets.

So, the system of inequalities that form are:

[tex]x+y\geq 36[/tex]

And

[tex]2x+0.6y<40[/tex]

How much times does 7 go into 48??

Answers

7 goes into 48, 6 times.
7 * 6 = 42.
If you did 7 * 7 it equals 49 which goes over 48, so it would not work. Therefor your answer is 6.
7 can go into 48  6 times because 7 times 6 = 42 and 7*7=49 so 6 times

Please help. Find the cube root of -27 that graphs in the first quadrant.
3(cos?+isin?) Use degree measure.

Answers

[tex]z = r (cos \theta + i sin \theta) \\ \\ \sqrt[3]{z} = \sqrt[3]{r}(cos \frac{\theta +360k}{3} +i sin \frac{\theta +360k}{3} ) , k = 0,1,2[/tex]

Now find r and theta for -27
[tex]-27 = 27(-1 +0i) = 27(cos 180 + i sin 180)[/tex]

r = 27 , theta = 180

[tex]\sqrt[3]{-27} = \sqrt[3]{27} (cos \frac{180 +360k}{3} +i sin \frac{180 +360k}{3} ) [/tex]
[tex]= 3(cos 60 + i sin 60) , k =0 \\ \\ = 3 (cos 180 + i sin 180) , k =1 \\ \\ =3(cos 300+i sin 300), k =2[/tex]
Final answer:

The cube root of -27 is -3, which cannot be graphed in the first quadrant of the complex plane. When considering complex roots, the angles of these roots do not lie in the first quadrant either, contradicting the given requirement.

Explanation:

The cube root of -27 that graphs in the first quadrant in complex form can be represented as 3(cos Θ + i sin Θ), where Θ is the angle in degrees. To find a cube root that lies in the first quadrant, we look for an angle Θ whose cosine is positive and sine is positive, which corresponds to angles between 0° and 90°. However, the cube root of -27 is actually a negative real number, which is -3.

Since we cannot graph a negative real number (-3) in the first quadrant of the complex plane, which only contains positive real and imaginary numbers, the question seems to be a bit contradictory. Nonetheless, if we interpret the cube root in terms of complex numbers, we find that the complex roots of -27 are -3, 3ε², and 3ε⁴, where ε² = e²πi/3 and ε⁴ = e⁴πi/3, correspond to angles of 120° and 240° respectively, which do not lie in the first quadrant.

Find the Taylor series for
f(x), centered at the given value of a.

f(x) = sin(x), a = π

Written as a summation?

Radius of convergence?

Answers

The Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).

To find the Taylor series for [tex]\( f(x) = \sin(x) \)[/tex] centered at [tex]\( a = \pi \),[/tex] we first need to find the derivatives of \( \sin(x) \) and evaluate them at \( x = \pi \). Then, we'll write out the Taylor series using the formula:

[tex]\[ f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \cdots \][/tex]

Let's find the derivatives of [tex]\( \sin(x) \)[/tex] and evaluate them at [tex]\( x = \pi \):[/tex]

1. [tex]\( f(x) = \sin(x) \)[/tex]

2. [tex]\( f' (x) = \cos(x) \)[/tex]

3.[tex]\( f''(x) = -\sin(x) \)[/tex]

4.[tex]\( f'''(x) = -\cos(x) \)[/tex]

Now, evaluate these derivatives at \( x = \pi \):

1. [tex]\( f(\pi) = \sin(\pi) = 0 \)[/tex]

2. [tex]\( f'(\pi) = \cos(\pi) = -1 \)[/tex]

3.[tex]\( f''(\pi) = -\sin(\pi) = 0 \)[/tex]

4. [tex]\( f'''(\pi) = -\cos(\pi) = 1 \)[/tex]

Now, plug these values into the Taylor series formula:

[tex]\[ \sin(x) = 0 - 1(x - \pi) + \frac{0}{2!}(x - \pi)^2 + \frac{1}{3!}(x - \pi)^3 + \cdots \][/tex]

Simplify:

[tex]\[ \sin(x) = -\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

So, the Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:

[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).

An employment agency specializing in temporary construction help pays heavy equipment operators $ 134 per day and general laborers $ 92 per day. If thirty-eight people were hired and the payroll was $ 4756 , how many heavy equipment operators were​ employed? How many​ laborers?

Answers

x=heavy equipment

y= general labor

x+y=38

x=38-y

134x + 92y=4756

134(38-y)+92y =4756

5092-134y+92y=4756

-42y = -336

y = -336/-42 = 8

x=38-8=30

check 30*134 =4020

8*92 = 736

4020+736 = 4756


 8 general laborers

30 heavy equipment operators

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