What is the value of w?
w
36°

Answer:

13.  [tex]x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]

14.  [tex]r=3\cos(\theta)-2\sin(\theta)[/tex]

Step-by-step explanation:

Question 13

Conversion from Polar equation to rectangular equation:

[tex]x=r \cos(\theta) \implies \cos(\theta)=\dfrac{x}{r}[/tex]

[tex]y=r \sin(\theta) \implies \sin(\theta)=\dfrac{y}{r}[/tex]

[tex]x^2+y^2=r^2 \implies r=\sqrt{x^2+y^2}[/tex]

Given:

[tex]r=3-2\cos(\theta)[/tex]

[tex]\textsf{Substitute }\cos(\theta)=\dfrac{x}{r}:[/tex]

[tex]\implies r=3-\dfrac{2x}{r}[/tex]

Multiply both sides by r:

[tex]\implies r^2=3r-2x[/tex]

[tex]\implies r^2+2x-3r=0[/tex]

[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }r=\sqrt{x^2+y^2}:[/tex]

[tex]\implies x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]

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Question 14

Conversion from Rectangular equation to polar equation:

[tex]x=r \cos(\theta)[/tex]

[tex]y=r \sin(\theta)[/tex]

[tex]x^2+y^2=r^2 \implies r^2\cos^2(\theta)+r^2\sin^2(\theta)=r^2[/tex]

Given:

[tex]x^2+y^2-3x+2y=0[/tex]

[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }x=r \cos(\theta)\:\textsf{and }y=r \sin(\theta):[/tex]

[tex]\implies r^2-3r\cos(\theta)+2r\sin(\theta)=0[/tex]

Factor out common term r:

[tex]\implies r(r-3\cos(\theta)+2\sin(\theta))=0[/tex]

Divide both sides by r:

[tex]\implies r-3\cos(\theta)+2\sin(\theta)=0[/tex]

Rewrite to make r the subject:

Answer:

Sammis work is correct

Step-by-step explanation:

when handling equations such as 107d= 1,733.4

you see that d is being multiplied to 107 to equal the total,

so to find the answer to d you would divide 107 by the total to get your value of d

Answer:the last one

Step-by-step explanation:

Answer:

b) Quad ABCD must be a rectangle and could be a rhombus

Step-by-step explanation:

:)

The measure of variability that describes the values in the box plot is: C. interquartile range, because: C. the data distribution is symmetric.

A symmetric data distribution is depicted on a box plot when the median is in the middle of the rectangular box, and the whiskers are of almost the same length at both sides of the box. Such data distribution is said to be normally distributed.

A normally distributed data distribution is symmetric.

Interquartile range is a measure of variability in a box plot, which is the range of the rectangular box.

Therefore, the measure of variability that describes the values in the box plot is: C. interquartile range, because: C. the data distribution is symmetric.

Learn more about Symmetric Data Distribution on:

https://brainly.com/question/304810

The simulation of the gender of a child by the couple is an illustration of probability.

The number of trials (n) is given as:

n = 90

The chance of getting each gender is equal.

So, we have:

P(Boy) = 0.5

P(Girl) = 0.5

The simulation would be based on numbers 0 to 9. Such that:

Notice that each gender have the same amount of digits i.e. 5

This is so because they both have equal chance

Read more about probability at:

brainly.com/question/251701

Answer:

Ace of Diamonds, King of Hearts, Two of Spades ( hope this helps)

The amount of juice by Benito is an illustration of volumes

The amount of juice made is 900 milliliters

The question is incomplete, as the figure and the dimensions are not given.

So, I will give a general solution

Assume the following parameters

The amount of juice would be:

V = πr^2h

This gives

V = 3.14 * 4^2 * 18

Evaluate

V = 904.32

Approximate

V = 900

Hence, the amount of juice made is 900 milliliters

Read more about volume at:

https://brainly.com/question/1972490

Answer:

B and C

Step-by-step explanation:

Answer:

-15/-3,-5/-1

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

the outer left side is also 50 ft.

in inner (upper) left side is also 13 ft.

the bottom line is 10+20+11 = 41 ft

this is all possible because all the angles are clearly right angles (90°).

so, the perimeter is

2×(10+20+11) + 2×50 + 2×13 = 82 + 100 + 26 = 208 ft

Answer:

R=3.38627

Step-by-step explanation:

Answer:

17.5 %

Step-by-step explanation:

5.6 is 17.5 percent of 32

Check the picture below.

The straw is placed diagonally in the rectangular prism, therefore, the length of the straw is √109 inches

Diagonal of a rectangular prism = √(l² + w² + h²)

Where,

Therefore,

l = 6 inches

w = 3 inches

h = 8 inches

diagonal = √(6² + 3² + 8²)

diagonal = √36 + 9 + 64

diagonal = √109 inches

learn more rectangular prism here:https://brainly.com/question/21888893

Answer:

36:24

Step-by-step explanation:

The second number was :24, and you started out with 6:4.

To get the 24, you would have to multiply the 4 by 6 to get the 24.

So, multiply the first number 6, as well by 6.

6 x 6 = 36

36:24

:)

Answer: 36

Step-by-step explanation: 6:4 = __:24

1. 4 goes into 24, 6 times because 4x6=24 so you have to multiply 6 to 6 and 6x6=36.

Answer:

Scale: 100 meters per 1 meter

Actual: 316 per unknown meters(our scale)

So order our units:-

_______   _______ =  _______, solve for x;

1/100 = x/316

*316      *316

3.16 = x, 3.16 rounded = 3.20 is the scale.

Answer:

See below ↓

Step-by-step explanation:

We need to check the different time intervals to find the max. height

   2. t = 2

⇒ Clearly as she is diving, her maximum height will be her initial height which is 12 feet

⇒ To achieve this, it takes her 0 seconds [initial height = no time needed]

Taking f(x) = 0 [surface of water → just touching/hit the water]

⇒ After 1 second, she is 12 feet above the water

⇒ The diving board is 12 feet above the water

Answer:

2x < 10 would show that even 'if' x would make 2 larger, it still wouldn't match up to 10. But in this case, 2 would turn into 10. 10 = 10.

Answer:

18 +2

Step-by-step explanation:

it's like 3x you just add each side 3 then you will get the answer. and the (+2) stays the same.

Apply Pythagorean theorem

So

Answer:

√(122)

Step-by-step explanation:

Pythagoras Theorem:  a² + b² = c²

(where a and be are the legs, and c is the hypotenuse, of a right triangle)

First, find the length of the hypotenuse of the triangle with legs of 9 and 5 units:

⇒ 5² + 9² = c²

⇒ 25 + 81 = c²

⇒ c² = 106

⇒ c = √(106)

Therefore √(106) is the longest leg of the other triangle.

So we can now use this measurement to find x (the hypotenuse) of the other triangle:

⇒ 4² + √(106)² = c²

⇒ 16+ 106 = c²

⇒ c² = 122

⇒ c = √(122)

Answer:

2,8,14,20...… the 49th term is 294.

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

294

Step-by-step explanation:

formula

an=a1 +(n-1)d

n= unknown term

d= difference between each term

8=a1

14=a2

20=a3

a49=8+(49-1)×(6)

a49= 8+ 48 ×(6)

a49= 8+ 288

a49= 294

Using proportions, it is found that it takes [tex]3.5 \times 10^{23}[/tex] meter sticks to equal the mass of the moon.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, one meter stick has a mass of 0.2 kg. How many meter sticks are needed for a mass of [tex]7 \times 10^{22} \text{kg}[/tex]? The rule of three is given by:

One meter stick - 0.2 kg

x meter sticks - [tex]7 \times 10^{22} \text{kg}[/tex]

Applying cross multiplication:

[tex]0.2x = 7 \times 10^{22}[/tex]

[tex]x = \frac{7 \times 10^{22}}{0.2}[/tex]

[tex]x = 35 \times 10^{22}[/tex]

[tex]x = 3.5 \times 10^{23}[/tex]

It takes [tex]3.5 \times 10^{23}[/tex] meter sticks to equal the mass of the moon.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

22 feet

Step-by-step explanation:

Area of circle = pi(r²)

the square root of 121 is 11, so r = 11

d = 2r

d = 22

Answer:

125x^15

Step-by-step explanation:

Hope this helps! :)

P = 2 x (5,5 + 3,5) = 18 cm

P = is the circumference of the figure

Answer:

the answer should be 18 cm

you can either do 2 × (length + width)

2 × (5.5 + 3.5)

2 × 9 = 18

or

5.5 + 5.5 = 11

3.5 + 3.5 = 7

11 + 7 = 18

either way it's 18, I hope this helps

Using proportions, it is found that there are c + 0.25n cents in n nickels and c cents.

A proportion is a fraction of a total amount. To solve problems involving proportions, such as this one, multiplications of the amounts and their values are made.

In this problem, we consider that each nickel has 0.25 cents, hence, there are c + 0.25n cents in n nickels and c cents.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

c+0.25n cents is the answer.

Answer:

335.69

Step-by-step explanation:

If the exchange rate of USD to Kuwaiti Dinar is 0.2879, multiply the amount of USD by the exchange rate to get the answer.

$1,166 x 0.2879 = 335.6914

335.6914 rounded to the nearest hundredth (two decimal places) is 335.69

So, it is A, 335.69 dinar.

335.69 dinar Sharon will get in exchange for $1,166 option (a) 335.69 is correct.

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

We have a total amount that will need to convert = $1,166

Exchange rate of us dollars to kuwaiti dinar = 1 : 0.2879

It means $1 converted into 0.2879 dinar

The amount $1,166 in kuwaiti dinar = 1166×0.2879

= 335.69 dinar

Thus, 335.69 dinar Sharon will get in exchange for $1,166 option (a) 335.69 is correct.

Learn more about the ratio here:

brainly.com/question/13419413

Answer:

1% of 100 = 1

Step-by-step explanation:

simple and easy :D hope this helps