The following polar equation describes a circle in rectangular coordinates: r=10cosθ \Locate its center on the xy-plane, and find the circle's radius.
(x0,y0)=
R=
Note: You can earn partial credit on this problem.

Answers

Answer 1

The center of the circle described by the polar equation r = 10cosθ is located at the point (x0, y0), and the radius of the circle is denoted by R.radius of the circle is 10.

To find the center of the circle, we can convert the polar equation to rectangular coordinates. Using the conversion formulas r = √(\(x^2 + y^2)\)and cosθ = x/r, we can rewrite the equation as follows:
√\((x^2 + y^2)\)= 10cosθ
√\((x^2 + y^2)\) = 10(x/r)
Squaring both sides of the equation, we get:
\(x^2 + y^2 = 100(x/r)^2x^2 + y^2 = 100(x^2/r^2)\)
Since r = √(x^2 + y^2), we can substitute r^2 in the equation:
\(x^2 + y^2 = 100(x^2/(x^2 + y^2))\)
\(x^2 + y^2 = 100x^2/(x^2 + y^2)\)
Simplifying the equation, we have:
\((x^2 + y^2)(x^2 + y^2 - 100) = 0\)
This equation represents a circle centered at the origin (0, 0) with a radius of 10. Therefore, the center of the circle described by the polar equation is at the point (0, 0), and the radius of the circle is 10.

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Related Questions

The (S,S) model has a fixed period between part ordering? True False

Answers

The given statement, The (S,S) model has a fixed period between part ordering is True.

The (S,S) model is an inventory control method developed by Haan and Van Harten in 1985, that uses a core algorithm with two basic parameters, S and S, to automate the process of ordering new parts or products. The S parameter determines the order size, while the S parameter determines the time between order placements, and both are set directly by the planner.

The cycle of ordering and delivery remains relatively fixed, meaning that the time between new orders will remain constant once the parameters are set. As a result, the (S,S) model is highly suitable for inventory control within both production and retail environments, as the number and type of items can be effectively managed when the cycle is regularly repeated.

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when the consumption schedule lies below the 45-degree reference line, saving:

Answers

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

How to explain the information

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Can someone please give me the (Answers) to this? ... please ...

Can someone please give me the (Answers) to this? ... please ...

Answers

Answer:

6:A

7;B

8;c

9;A

10:c

11;b

12:A

Answer:

6. Commander David Scott

7. They dropped at the same speed

8. Scale (I think)

9. B

10. True

11. Gravity (not sure)

12. C

17. Weaker

18. Ellipsoid (also not sure)

19. Towards the Earth’s center

20. I don’t know this

21. Center

22. B

Step-by-step explanation:

Not sure about some of them (like 19 because it feels like it can have more than one answer) but yeah the others are self-explanatory

How much half a orange how much juice would it give u

Answers

Answer:

it will give you a haft of a ornge worth of juice

Step-by-step explanation:

Answer:

There are 4 to 5 tablespoons or 1/4 to 1/3 cups of juice in one orange. To make one cup of fresh orange juice, you need three oranges. It's important to note this amount is for common oranges. Different varieties of orange, such as Valencia, navel, mandarin, or blood oranges will produce different quantities of juice

Step-by-step explanation:

hope it is helpful for you keep smiling

a) A = (-89) + (-97) + (-145) + (-111) + 245 + 97 + 1351

Answers

Answer:

1251

Step-by-step explanation:

I used a calculator: -89 - 97= -186 - 145= -331 - 111= -442 + 245= -197 + 97= -100 + 1351= 1251

In case anyone is confused, adding a negative is the same as subtracting... for example: 10 + (-1) =9 and 10 - 1 =9

Solve for c.
c= -9 - 8c

Answers

c=-9-8c

+8c

9c=-9

c=-1

Hope this helps:D!!

The letter C is equal to negative one.

c = -1

Hope this helps!

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out 5 inches squares from each corner. The length of the original piece of cardboard is 10 inches more than the width. If the volume of the box is , 2520in^(3) determine the dimensions of the original piece of cardboard.

Answers

Answer:    

29 feet in lenght, 5 feet in width and 12 feet in height

Step-by-step explanation:

that shou

ld be your answer

4
Select all the expressions that are equivalent to
-2(5x - 1) + 7(5x - 1) – 3(-5x + 1)
M. -10x – 1 + 35x - 1 + 15x + 1
P. -10x + 2 + 35x - 7 - 15x - 3
R. (5x - 1)(-2 + 7 - 3)
S. (5x - 1)(-2 + 7 + 3)
T. 40% - 8
V. 10x + 2




4Select all the expressions that are equivalent to-2(5x - 1) + 7(5x - 1) 3(-5x + 1)M. -10x 1 + 35x -

Answers

Answer:

The first answer is M. -10x - 1 + 35x - 1 + 15x + 1

maybe

what is the rate of change of f(x, y) = 3xy y2 at the point (1, 3) in the direction v = 2 i − j ?

Answers

The rate of change of f(x, y) = 3xy y2 at the point (1, 3) in the direction v = 2 i − j is (9/√5 i^ + 9/√5 j^).

The rate of change of any function is given by its gradient.

i.e.

∇f(x,y) = df(x,y)/dx i^ +df(x,y)/dy j^ +df(x,y)/dz k^

Here,

f(x,y) is given as 3xy + y²

so,

∇f(x,y) = d{3xy + y²}/dx i^ +d{3xy + y²}/dy j^ +d{3xy + y²}/dz k^

Since, the function has no z components, the k^ component will be 0.

∇f(x,y) = 3y i^ + (3x + 2y) j^

putting the given points, i.e. (1,3) we get,

∇f(x,y) = 9 i^ + 9 j^

Now for calculating the slope in the given direction

we have to divide the magnitude of the direction that is,

∇f(x,y) = (9 i^ + 9 j^)/√(2²+(-1)²)

∇f(x,y) = (9/√5 i^ + 9/√5 j^)

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Find the indicated probability. The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches?

Answers

To find the probability that the diameter of a randomly selected pencil will be less than 0.285 inches, we can use the normal distribution.

Given:

Mean (μ) = 0.30 inches

Standard Deviation (σ) = 0.01 inches

We want to find P(X < 0.285), where X represents the diameter of the pencil. To calculate this probability, we need to convert the value 0.285 into a z-score using the formula:

z = (X - μ) / σ

Substituting the given values:

z = (0.285 - 0.30) / 0.01 = -0.015 / 0.01 = -1.5

Using a standard normal distribution table or calculator, we can find the corresponding probability for a z-score of -1.5. The probability can be found as P(Z < -1.5). The table or calculator will give us the probability for P(Z ≤ -1.5). To find P(Z < -1.5), we subtract this value from 1. The probability P(Z < -1.5) is approximately 0.0668. Therefore, the probability that the diameter of a randomly selected pencil will be less than 0.285 inches is approximately 0.0668.

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1. An office manager is selecting a water delivery service. Acme H2O charges a $15 fee and $7.50 per 5-gallon jug. Best Water charges a $24 fee and $6.00 per 5-gallon jug. How many 5-gallon jugs will the office have to buy each month for the cost of Best Water to be less than that of Acme H2O? Graph your solution on a number line.

Answers

Answer:

the anwser is 45

Step-by-step explanation:

Classify by degree of polynomial:
3x3 - 6x

Answers

Answer:

polynomial of degree 3

Step-by-step explanation:

Given

3x³ - 6x

The degree of a polynomial is given by the exponent of the term with the largest exponent.

In this case 3x³ has exponent 3 and - 6x has exponent 1

Thus this is a polynomial of degree 3

Simplify the expression (5)2.

25
-10
-25
10

Answers

Answer:

10

Step-by-step explanation:

5 (2) is the same as 5 × 2 which equals 10

Answer:

10

Step-by-step explanation:

Given here,

(5)2

= 5 × 2.

= 10 (Ans)

Jimmy earns a gross income of $2,500 every two weeks. deductions from each paycheck include insurance, retirement, and taxes, which total $1,000. starting with his next paycheck, his insurance will increase by $50. what conclusion can be drawn about his income with this change?

Answers

The conclusion that can be drawn from Jimmy's income with the change in insurance is that Jimmy's net income would decrease.

What happens to net income when expenses rise ?

When expenses rise, net income will decrease. Net income is calculated by subtracting expenses from gross income, so if expenses increase, the amount of net income will decrease.

This means that with the increase in insurance by $ 50, Jimmy can expect that his net income would decrease by a total amount of $ 50 which is the amount the insurance increased by.

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hello please help thanks

hello please help thanks

Answers

Option A - Sediment

The solid substance that settles down is called sediment. This entire process is known as sedimentation. The clear water (supernatant liquid) is then poured out carefully into another beaker, leaving the sediments undisturbed. This process is known as decantation.

You want to spend less than $39 at a local fair. Admission is $24 and each ride cost $2.50. At most, how many ride can you go on? Write and solve an inequality to model this situation.

6 rides : 2.50r + 24 < 39
5 rides : 2.50r + 24 < 39
5 rides : 2.50r + 39 < 24
6 rides : 2.50 + 24r > 39

Answers

Answer:

A

Step-by-step explanation:

Answer:

6 rides: 2.50r+24 39

Step-by-step explanation:

6 rides: 2.50r+424 39

AC=x+165,AB=48 and BC=2x+139. Find x

Answers

Answer:

Assuming A, B, and C are collinear and B is between A and C then x = -2 2

Step-by-step explanation:

Assuming A, B, and C are collinear and B is beetween A and C

AB + BC  = AC

48 + 2x + 139 = x + 165

  2x + 187 = x + 165

    x = -22

Petra always keeps her 6 bedrooms in her house clean it takes her 15 minutes to clean a single room how many hours will it take her to clean all 6 bedrooms

Answers

Answer:

90 minutes(1hour 30 minutes)

Step-by-step explanation:

If 1 room=15 minutes

Then 6 rooms= ?

=6×15/1

=90 minutes

=1hour 30 minutes

Find the values of my and n ​

Find the values of my and n

Answers

m = 60 and n = 24

. . . .

. . . .

. . . .

Unit 7 polygons and quadrilaterals
Homework 7 trapezoids
** this is a 2-page document **
Directions: if each quadrilateral below is a trapezoid, find the missing measures

Unit 7 polygons and quadrilateralsHomework 7 trapezoids ** this is a 2-page document ** Directions: if

Answers

Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

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Need Helps ASAP!
Complete the statements below with the process used to achieve steps 1-4
Answers for each step:
Multiply, add, subtract, divide.

Need Helps ASAP!Complete the statements below with the process used to achieve steps 1-4Answers for each

Answers

Step 1. Multiply

Step 2. Subtract

Step 3. Add

Step 4. Divide

Molly bought a lunch
special that was
originally $14. Today it is
on sale for 20% off.
What is the sale price
of the lunch special?

Answers

Answer: $11.20

Explanation: 20% of 14 is 2.8

So $14-$2.80= $11.20

I am having trouble understanding how to even approach this question

I am having trouble understanding how to even approach this question

Answers

Given:

One friend heads north 20 miles per hour.

Other heads East 50 miles per hour.

let r be the number of hours traveled.

After t hours the distance traveled by the first friend is

\(\text{Distance 1=speed}\times time\)

Substitute speed=20 and time =t, we get

\(\text{Distance1=20t}\)

After t hours the distance traveled by the second friend is

\(\text{Distance 2 =speed}\times time\)

Substitute speed=50 and time =t, we get

\(\text{Distance 2 =}50t\)

Using the Pythagoras theorem to find the distance between two friends.

Distance between two friends is

\(\text{distance }^2=(20t)^2+(50t)^2\)

\(\text{distance }^2=20^2t^2+50^2t^2\)

\(\text{distance }^2=400r^2+2500r^2\)

\(\text{distance }^2=2900t^2\)

Taking square root on both sides, we get

\(\text{distance }=\sqrt[]{2900t^2}\)

\(\text{distance }=10\sqrt[]{29}t\)

Hence the required distance is

\(\text{distance }=10\sqrt[]{29}.t\)

I am having trouble understanding how to even approach this question

An item is regularly priced at $35. It is now priced at a discount of 40% off the regular price. What is the price now?

Answers

Answer:

15

Step-by-step explanation:

AYUDAA, con procedimiento

AYUDAA, con procedimiento

Answers

By trigonometric functions, the length of the missing side is equal to 12.072.

How to find a missing side by trigonometric functions

In this case we find the case of a geometric system formed by 11 right triangles, whose missing side shall be found by means of trigonometric functions, that is, relationships between two sides of a right triangle. For this question we need the following relationships:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

x - Side adjacent to the angle.y - Side opposite to the angle. r - Hypotenuse

Step 1

x = 8 / cos 34° - 2.5

x = 7.150

Step 2

x = (7.150 + 3.6) · cos 11°

x = 10.552

Step 3

x = √[(10.552 - 2.1 + 2.9)² - 3.8²]

x = 10.697

Step 4

x = (10.697 - 3.2) · tan 42°

x = 6.750

Step 5

y = 6.750 / sin 37°

y = 11.216

Step 6

x = (11.216 + 4.3) · sin 53°

x = 12.392

Step 7

x = √[(12.392 - 2.2)² + 1.7²]

x = 10.333

Step 8

x = 10.333 / cos 21°

x = 11.068

Step 9

x = (11.068 + 1.7) · sin 71°

x = 12.072

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How many solutions are there to the inequality x1 + x2 + x3 ≤ 11, where x1, x2, and x3 are nonnegative integers? [Hint: Introduce an auxiliary variable x4 such that x1 + x2 + x3 + x4 = 11.]

Answers

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Which equation is correct regarding the measure of ∠1? m∠1 = one-half(a – c) m∠1 = one-half(a c) m∠1 = one-half(b – d) m∠1 = one-half(b d)

Answers

Answer:

<32 - </3 5810-24

Step-by-step explanation:

32

a grand piano can weight 1 and half ton how many ounces can a grand piano weigh

Answers

1.5 tons= 48,000 ounces

questionwhich equation represents this sentence?one-half the sum of a number and four is three less than the quotient of five and the number. 12n 4

Answers

The equation that represents the sentence "one-half the sum of a number and four is three less than the quotient of five and the number" is 1/2n + 4 = 5/n - 3 (option d).

Let's break down the sentence to understand the equation.

"One-half the sum of a number and four" can be represented as 1/2(n + 4). Here, n represents the number.

"Is three less than the quotient of five and the number" can be represented as 5/n - 3.

Combining the two parts, we have:

1/2(n + 4) = 5/n - 3.

This equation states that half the sum of a number and four is equal to three less than the quotient of five and the number.

Option d) 1/2n + 4 = 5/n - 3 correctly represents this relationship. It accounts for the division of 5 by n and subtracts 3, while also adding the number n to 4 and dividing the sum by 2.

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The complete question is:

which equation represents this sentence? one-half the sum of a number and four is three less than the quotient of five and the number.

a.) 1/2n 4=3−5/n

b.) 1/2(n 4)=5/n−3

c.) 1/2(n 4)=3−5/n

d.) 1/2n 4=5/n−3

what area is this figure?

A,60ft2

B,50

C,40ft2

D,100ft2

what area is this figure?A,60ft2B,50C,40ft2D,100ft2

Answers

Answer:

The answer is 100ft2 I think

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