Find the area and the circumference of a circle with radius 4m. Use the value 3.14 for π, and do not round your answers. Be sure to include the correct units in your answers. 4m Area: Circumference:

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Convert point Q to polar coordinates (accounting for correct direction):

[tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(-5)^2+(-5\sqrt{3})^2}=\sqrt{25+75}=\sqrt{100}=10\\\\\theta=\tan^{-1}\biggr(\frac{-5\sqrt{3}}{-5}\biggr)=\tan^{-1}\bigr(\sqrt{3}\bigr)=\frac{4\pi}{3}[/tex]

Thus, the answer is [tex]\displaystyle \biggr(10,\frac{4\pi}{3}\biggr)[/tex], or A

Problem 2

Make polar substitutions:

[tex]x^2+y^2-2x+8y=0\\\\r^2-2r\cos\theta+8r\sin\theta=0\\\\r^2=2r\cos\theta-8r\sin\theta\\\\r=2\cos\theta-8\sin\theta\\\\r=-8\sin\theta+2\cos\theta[/tex]

Hence, the answer is C

Problem 3

Eliminate the parameter:

[tex]x=t+3\\x-3=t\\\\y=t^2+2t\\y=(x-3)^2+2(x-3)\\y=x^2-6x+9+2x-6\\y=x^2-4x+3[/tex]

Hence, the answer is C

Problem 4

Identify [tex]z_1[/tex] and [tex]z_2[/tex] and add the complex numbers:

[tex]z_1+z_2=(-3+5i)+(-5-2i)=-3+5i-5-2i=-8+3i[/tex]

Thus, the correct answer is S

Problem 5

Use the formula for multiplying complex numbers in polar form:

[tex]z_1z_2=r_1r_2(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))\\z_1z_2=(5)(15)(\cos(240^\circ+135^\circ)+i\sin(240^\circ+135^\circ))\\z_1z_2=75(\cos375^\circ+i\sin375^\circ)\\z_1z_2=75(\cos15^\circ+i\sin15^\circ)[/tex]

Hence, the answer is A

Problem 6

Determine when the ball first hits the ground:

[tex]y=-\frac{1}{2}gt^2+(v\sin\theta)t+y_0\\0=-\frac{1}{2}(32)t^2+(58\sin19^\circ)t+1.9\\0=-16t^2+(58\sin19^\circ)t+1.9\\t\approx1.273[/tex]

Determine the horizontal distance covered by the ball:

[tex]x=(v\cos\theta)t\\x=(58\cos19^\circ)(1.273)\\x\approx69.811[/tex]

Hence, the best answer is C

Problem 7

The equation is in the form of [tex]r=a\cos(n\theta)[/tex] where [tex]a[/tex] is the length of each petal and the curve has a horizontal pole. If [tex]n[/tex] is odd, then there are [tex]n[/tex] petals, but if [tex]n[/tex] is even, then there are [tex]2n[/tex] petals.

From our given equation, there are clearly 4 petals since [tex]n[/tex] is even, and each petal length is 4 units. Hence, the first graph is correct.

Answer:

35.70

Step-by-step explanation:

because 15% of 42 is 6.3 and 6.3 - 42 = 35.70

Answer:

8 dimes and 3 nickels

Step-by-step explanation:

If we change $0.95 to $0.9 + $0.05, we get 9 dimes and 1 nickel. However, that is only 10 coins. We can then try 8 dimes and 3 nickels. When you add them up, they equal $0.95. Also, there are 11 coins in total. Therefore, 8 dimes and 3 nickels is the answer.

I hope this helps and please mark me as brainliest!

Answer:

24 for estimate, the accurate is 25.2

Step-by-step explanation:

surveyed total = 30

9 = run 5> days a week

84 = total members

9/30 = percent of members who run 5> days a week

9/30 => 3/10

percent of members who run 5> days a week * total members = number of members who run 5> days a week

3/10 x 84 = 25.2 members

84 = 80

3/10 x 80 = 24

24, a reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week.

Answer:

70

Step-by-step explanation:

23+47

Answer:

Step-by-step explanation:

Brainlest me please

#a

Take one coordinate and solve

So

Take another

So

Hence k=4

#b

Graph attached

#c

Turn to vertex form

Compare to vertex form

So

#d

At no intervals of x the graph decreases negatively

Because

#d

So if y be 0

x intercepts are

Zeros are

Answer:

518,317 > 518,246 > 518,197

Answer:

The median is 9

The Range is 13-5=8

The mean is 5+5+9+11+13/5=43/5=8 3/5=8.6

Answer:

5th month

Step-by-step explanation:

the relationship between the second and third month is that the 2nd month's salary was multiplied 4 to get the third month's salary

therefore the salaries for the next months will be

4th month=Gh¢12800.00

5th month=Gh¢51,200.00 which exceeds 20,000

Answer:

A True

Step-by-step explanation:

[tex]4^{3} x ^{3} + 5^{3} [/tex]

Answer:

18000 m

Step-by-step explanation:

Hey there!

In order to solve this problem, we need to first know how many minutes are in an hour

As you know, there are 60 minutes in an hour so this means in 1 hour, he will climb 9000 meters two times

So 9000 two times is 18000,

Meaning, in 1 hour, Sam will climb 18000 m

Answer:

18,000m in an hour

Step-by-step explanation:

We know this because if its 9000 m in 30 minutes, we can do 9000 x 2 and get 18,000m for an hour.

Answer:

10, 41, 42

Step-by-step explanation:

(n)+(4n+1)+(5n-8)=93 because triangle perimeter

10n-7=93

10n=100

n=10

Answer: 10 cm, 41 cm, and 42 cm

Step-by-step explanation:

       We can set up an equation knowing the perimeter to solve for the lengths of each side. Then, we will plug the value of n into the different expressions that represent each side.

   Perimeter of a triangle:

P = side a + side b + side c

   Plug in our known values:

93 cm = (n) + (4n + 1) + (5n - 8)

   Simplify and combine like terms:

93 cm = n + 4n + 1 + 5n - 8

93 cm = n + 4n + 5n + 1 - 8

93 cm = 10n -7

   Add 7 to both sides of the equation:

100 cm = 10n

   Divide both sides of the equation by 10:

10 cm = n

n = 10 cm

        -

   Solve for the lengths of each side:

n = 10 cm

4n + 1 = 4(10) + 1 = 40 + 1 = 41 cm

5n - 8 = 5(10) - 8 = 50 - 8 = 42 cm

Answer:

y  = 60.3

Step-by-step explanation:

Using it's concept, it is found that there is a [tex]\frac{2}{9}[/tex] experimental probability that the next client to get a haircut Cameron's salon will have blond hair.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these number of outcomes are taken from previous trials.

In this problem, 4 out of 18 clients had blond hair, hence the probability is given by:

P(blond) = 4/18 = 2/9

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

  YZ = 28

Step-by-step explanation:

A proportion involving the known and unknown sides is ...

  TR/ST = ZY/SZ

__

This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...

  SZ +ZT = ST . . . . . . . segment sum theorem

  SZ + 5 = 40 . . . . with given values

  SZ = 35 . . . . . subtract 5

__

So, the proportion with values filled in is ...

  (3x -7)/40 = (2x +2)/35

  7(3x -7) = 8(2x +2) . . . . . . . multiply by 280

  21x -49 = 16x +16 . . . . . . . eliminate parentheses

  5x = 65 . . . . . . . . . . add 49 -16x

  x = 13 . . . . . . . . divide by 5

  YZ = 2x +2 = 2(13) +2

  YZ = 28

_____

Additional comment

RT = 3x -7 = 3(13) -7 = 32

Answer: Attributed to the increase in VAT, the change in cost of a car worth RS 15000+VAT is Rs 375.

Step-by-step explanation:

Answer:

x²+14x+33<0.

Step-by-step explanation:

1) according to the condition x=-11 and x=-3 are zeros of the function y=ax²+bx+c;

2) if -3;-11 are zeros, then (-3)*(-11)=c ( already a=1; b=14). Then

3) x²+14x+33<0.

Answer: n+6

-1 + 7 = 6

So therefore, the answer is n+6

Hope this helped

Answer:

Step-by-step explanation:

To solve this problem, first, you have to do is isolate it on one side of the equation.

First, remove parentheses.

→ n-1+7

Add the numbers from left to right.

→ -1+7=6

→ n+6

I hope this helps you! Let me know if my answer is wrong or not.

Answer: 12-2r

Step-by-step explanation:

3r+12-5r

= -2r+12 or 12-2r

Answer:

-2r + 12

Step-by-step explanation:

simplify 3(r + 4) - 5r

3(r + 4) - 5r <== distribute first

3(r) + 3(4) - 5r

3r + 12 - 5r <== combine like terms

-2r + 12 <== final answer

Hope this helps!

Answer:

(a) The total expenditures per household in the year 2008 were approximately $3,080.

(b) The spending reached $2875 per household in 2006.

Step-by-step explanation:

Note: This question is not complete, and the part c is not another question but the same question as part a. The complete question is therefore provided before answering the question as follows:

Out of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2574e^(0.0359x) models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003.

(a) Estimate out-of-pocket household spending on health care in 2008.

(b) Determine the year when spending reached $2875 per household

The explanation to the answer is now given as follows:

(a) Estimate out-of-pocket household spending on health care in 2008.

Given;

f(x) = 2574e^(0.0359x) ........................ (1)

Since x = 0 corresponds to 2003; by counting from 2003 to 2008, it implies that x = 5 corresponds to 2008.

Substituting x = 5 into equation (1) to estimate out-of-pocket household spending on health care in 2008, we have:

f(6) = 2574e^(0.0359 * 5)

f(6) = 2574 * 1.19661890406748

f(6) = 3,080.09705906969

Rounding to the nearest dollar as needed, we have:

f(6) = $3,080

Therefore, the total expenditures per household in the year 2008 were approximately $3,080.

(b) Determine the year when spending reached $2875 per household

This can be determined using equation (1) in part a by equating f(x) to $2875 solve for x as follows:

2875 = 2574e^(0.0359x)

2875 /2574 = e^(0.0359x)

1.11693861693862 = e^(0.0359x)

Taking the natural log of both sides, we have:

ln(1.11693861693862) = ln(e^(0.0359x))

0.110591565075382 = 0.0359x

x = 0.110591565075382 / 0.0359

x = 3.0805449881722

Approximating to a whole number, we have:

x = 3

Since x = 0 corresponds to 2003; by counting from 2003, x = 3 corresponds to 2006.

Therefore, the spending reached $2875 per household in 2006.

Answer:

6656 cm²

Step-by-step explanation:

6656 cm² is the required answer

The true statement is that most insurance plans encourage the use of In-Network doctors by offering lower costs on most services they perform.

An HMO is regarded as an acronym that is used for “Health Maintenance Organization”. It is know to be  companies  that has been given the power to solely to manage the provision of health care services to the people.

The use of the in-network option is one that tends to save money. The Providers in your network are known to have a form of agreements with your insurance company that tends to make one to save money.

Lean more about insurance plans from

https://brainly.com/question/1941778

Answer: B-Insurance plans encourage the use of in-network doctors by offering lower costs on most services they perform.

Answer:

12 feet

Step-by-step explanation:

3 times 4 is 12

you would multiply by 4 because of the 4 sides of the window

option A

hope it helps...!!

Answer:

The weight of an object is the force of gravity exerted on that object. The mass of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity.[1] That's why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth.

Step-by-step explanation:

Answer:

your mother

Step-by-step explanation:

The logical answer would be your mother because 9.8m/s^2 x 55 would equal your mother weight,  539 squared pounds.

Answer:

742

Step-by-step explanation:

the sum of -1000 and 848

= -1000+848

= -152

Subtract the sum of -1000 and 848 from 590

= 590-(-152)

= 590+152

= 742

you didn't show the pic

hope you understood...!!!

The inner diameter of the washer is 7/10 inch, this value is gotten by multiplying the path by 2 and subtracting the result from the outer diameter

Given Data

The inner diameter

= Outer Diameter - 2*Path Distance

= 1 - 2*3/20

= 1- 6/20

= 1- 3/10

= 1/1 - 3/10

Find the LCM we have 10

= 10-3/10

= 7/10 inch

Learn more about shapes here:

https://brainly.com/question/25965491

Answer:

8.5

put numbers least to greatest and find the median by crossing numbers out front from back.

Answer:

Step-by-step explanation I can answer if you pin in the pic below