find the the ratio write the answer as a fraction and as a decimal rounded to four decimal places.​

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

Answer:

$22.05

Step-by-step explanation:

If a product has a sales commission, then one must divide the commission percent by (100) to convert the percent to a decimal. Then multiply the result by the price of the product to find the amount of money that will be given as a commission.

Applying this knowledge to the given problem, one must divide (9%) by (100) to convert to decimal form,

9% / 100 = 0.09

Now multiply the result by the price of the product (245) to find the amount given away in commission,

0.09 * 245 = 22.05

Answer:

I need help in math too so

Answer:

120 units²

Step-by-step explanation:

A= [tex]\frac{a+b}{2}[/tex]×h

A= [tex]\frac{15+15}{2}[/tex]×8

A= [tex]\frac{30}{2}[/tex]×8

A= 15×8

A= 120

Answer:

[tex]64(in)^{3} [/tex]

Step-by-step explanation:

The volume of a box is equal to the length l times the width w times the height h.

[tex](lenght) \times (width) \times (height)[/tex]

Substitute the values of the length l=8, the width w=2, and the height h=4 into the formula.

[tex]8 \times 2 \times 4[/tex]

Multiply 8 by 2.

[tex]16 \times 4[/tex]

Multiply 16 by 4.

[tex]64 {in}^{3} [/tex]

Hence, the volume of the rectangle prism is 64(in)³.

Answer:

Step-by-step explanation:

Given dimensions:

Volume of the prism is:

Answer:

26. $46.75

27. $4.80

28. $32.00

29. $3.60

Answer:

5/6

Step-by-step explanation:

Answer:

The answer is 5/6

Step-by-step explanation:

4        5           20             2

-   x   -       =      -      =       -

5       6            30             3

Answer:

one

Step-by-step explanation:

Answer:

The graph shows a proportional relationship because t=50, and that pattern follows.

Step-by-step explanation:

The graph shows a proportional relationship because t=50, and that pattern follows.

The graph represent a proportional relationship between the variables d and t as distance in miles, d a car travels is proportional to the time in hours t.

The speed of a body is the rate at which it covers the total distance in the time taken. The speed of the body is given as,

[tex]s=\dfrac{d}{t}[/tex]

Here, (d) is the distance travelled by the body and (t) is the time taken by the body to cover that distance.

The graph shows the distance in miles, d, a car travels in hours. Rewrite the above formula, ​considering it for the car,

[tex]s=\dfrac{d}{t}\\t\times s={d}[/tex]

In this formula, distance in miles, d, is directly proportional to the time taken by car in hours.

It is because as the car moves, the time start to pass and so the distance car start to cover the distance. In more time, the car will cover more distance with same speed.

Thus, the graph represent a proportional relationship between the variables d and t as distance in miles, d a car travels is proportional to the time in hours t.

Learn more about the speed here:

https://brainly.com/question/359790

#SPJ2

Answer: 8000?

Step-by-step explanation:

If your asking the area of his land, 800 yards

Total of 180 I guess? What are you trying to askkk?

Answer:

1.2

I t is the answer

Answer:

( 4, 11 ) , ( - 4, 27 )

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = - 2x + 19

x² - 2x + 3 = - 2x + 19

x² - 16 = 0

( x + 4 )( x - 4 ) = 0

[tex]x_{1}[/tex] = - 4

[tex]x_{2}[/tex] = 4

f(x) = [tex]y_{1}[/tex] = - 2( - 4 ) + 19 = 27

[tex]y_{1}[/tex] = 27

f(x) = [tex]y_{2}[/tex] = - 2( 4 ) + 19 = 11

[tex]y_{2}[/tex] = 11

( 4, 11 ) , ( - 4, 27 )

Answer:

24

Step-by-step explanation:

85.77-62.396 estimated by rounding each number to the nearest whole number is 24. I got this by first rounding 85.77 to 86. I then rounded 62.396 to 62. Next, I did 86-62= 24.

So, the answer is 24.

Answer:

23.000

Step-by-step explanation:

8-6=2

5-2=3

So you know that 23.000 is the roaded answer, you can just ignore the digits behind the decimal point in order to round

Answer:

1

3814697265625

Decimal Form:

2.62144 ⋅ 10 / 13

Step-by-step explanation:

Answer:

296

Step-by-step explanation:

Answer:

plz rate 5star accept my efforts

+ thanks :)

Answer:

go make me a sandwhich you witch

Step-by-step explanation:

Answer:

D. 12

Step-by-step explanation:

93/3 = 31

155/5 = 31

248/8 = 31

In every case, you see that the number of pages is 31 times the number of hours.

For 372 pages, the number of hours is 372/31 = 12

Check: 372/12 = 31

Answer: D. 12

Answer:

6 hours.

Step-by-step explanation:

To find how many hours it would take to drive a 240 mile distance at a constant speed of 40 miles per hour, you'd divide 240 by 40 and the result of that is 6.

Answer:

6 hours

Explanation:

240/40= 6

Answer:

15x9 is 130 but, what u mean by divided by 2 fraction?

Step-by-step explanation:

135/ 2 this is correct unless you want a mixed fraction which is 67 and 1/2

Answer:

C. 0.10

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Goes to the city playoffs

Event B: Goes to the state playoffs.

In Littletown, the probability that a baseball team goes to the city playoffs is 0.20.

This means that [tex]P(A) = 0.2[/tex]

The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.50.

This means that [tex]P(B|A) = 0.5[/tex]

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1[/tex]

The correct answer is given by option C.

Answer:

y=0x+6

Step-by-step explanation:

slope intercept form is: y=mx+b

Answer:

112 teaspoons of crushed garlic

Step-by-step explanation:

56•2=112

9514 1404 393

Answer:

  e. no solution

Step-by-step explanation:

You would be looking for factors of +5 that have a sum of -4. There are none (no solution). None of the values offered in the answer choices have a product of +5.

__

The discriminant of the quadratic is (-4)² -4(1)(5) = -4, so the roots are complex.

Step-by-step explanation:

We need to find the area of the shaded region. We see that the region next to that has a central angle of 120°. Also we know that angle in a straight line is 180° . So the measure of central angle of that shaded region will be 180° - 120° = 60° . Now we can use the formula of area of sector to find out the area of the shaded region.

[tex]\tt\to Area = \dfrac{\Theta}{360^o}\times \pi r^2 \\\\\tt\to Area = \dfrac{60^o}{360^o}\times \pi (8cm)^2 \\\\\tt\to Area =\dfrac{\pi \times 64}{6}cm^2\\\\\to\boxed{\orange{\tt Area_{(Shaded)}= 10.66\pi cm^2}}[/tex]

Answer:

D. 2

Step-by-step explanation:

The only possible outcomes that Janessa could possibly calculate would be 5 and 6. This is because a single die has 6 possible outcomes. If Janessa's friends rolled a 3 and a 4, and Janessa needs to roll something higher, then the only higher possible outcomes would be a 5 or a 6. Meaning that Janessa can only use a total of 2 desired outcomes for her to actually win the game.

Answer:

sorry i need more points

Step-by-step explanation:

Take an arbitrary interval [a, b], where a < b.

Compute the arc length L of y = f(x) over [a, b] :

[tex]L=\displaystyle\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm dx[/tex]

Now comptue the area A under the curve y = f(x) over [a, b] :

[tex]A=\displaystyle\int_a^bf(x)\,\mathrm dx[/tex]

We have

f (x) = 1/4 e ⁻ˣ + e ˣ   →   f ' (x) = -1/4 e ⁻ˣ + e ˣ

Then

√(1 + (f ' (x))²) = √(1 + (-1/4 e ⁻ˣ + e ˣ)²)

… = √(1 + 1/16 e ⁻²ˣ - 1/2 + e ²ˣ)

… = √(1/16 e ⁻²ˣ + 1/2 + e ²ˣ)

… = 1/4 √(e ⁻²ˣ + 8 + 16e ²ˣ)

… = 1/4 √((e ⁻ˣ + 4 e ˣ)²)

… = 1/4 (e ⁻ˣ + 4 e ˣ)

… = 1/4 e ⁻ˣ + e ˣ

… = f (x)

so both A = L for any choice of interval [a, b].

It is true that the arc length on any interval has the same value as the area under the curve.

The function is given as:

[tex]f(x) = \frac 14e^{-x} + e^x[/tex]

Differentiate the function

[tex]f'(x) = -\frac 14e^{-x} + e^x[/tex]

On any interval, the following must be true

[tex]f(x) =f'(x)[/tex]

and

[tex]f(x) = \sqrt{1 + (f'(x))^2}[/tex]

So, we have:

[tex]f(x) = \sqrt{1 + (-\frac 14e^{-x} + e^x)^2}[/tex]

Expand the exponents

[tex]f(x) = \sqrt{1 + (\frac{1}{16}e^{-2x} - \frac 12 + e^{2x})}[/tex]

Remove the bracket

[tex]f(x) = \sqrt{1 + \frac{1}{16}e^{-2x} - \frac 12 + e^{2x}}[/tex]

Evaluate the like terms

[tex]f(x) = \sqrt{\frac{1}{16}e^{-2x} + \frac 12 + e^{2x}}[/tex]

Multiply by 16/16

[tex]f(x) = \sqrt{\frac{16}{16}(\frac{1}{16}e^{-2x} + \frac 12 + e^{2x})}[/tex]

So, we have:

[tex]f(x) = \sqrt{\frac{1}{16}(e^{-2x} + 8 + 16e^{2x})}[/tex]

Take the square root of 1/16

[tex]f(x) = \frac{1}{4}\sqrt{e^{-2x} + 8 + 16e^{2x}}[/tex]

Express the radical as a perfect square

[tex]f(x) = \frac{1}{4}\sqrt{(e^{-x} + 4e^{x})^2}[/tex]

Evaluate the exponents

[tex]f(x) = \frac{1}{4} * (e^{-x} + 4e^{x})[/tex]

Evaluate the products

[tex]f(x) = \frac{1}{4}e^{-x} + e^{x}[/tex]

Hence, it has been proved that  the arc length on any interval has the same value as the area under the curve.

Read more about areas at:

https://brainly.com/question/24487155

The calculated quadratic function for the height of the rocket is "[tex]h = 64t - 16.085t^2[/tex]" and the further calculation of the given points can be defined as follows:

For point A):

Rocket Initial velocity (u) [tex]= 64 \ \frac{feet}{sec}[/tex]

Considering gravity's acceleration of 32.17 feet/sec2

The rocket's height can be expressed as follows:

[tex]h = ut - \frac{1}{2} \times 32.17 \times t^2 \\\\h = 64 - 16.085 \times t^2 \\\\h = 64t - 16.085t^2[/tex]

For point B):

A y-axis indicates its rocket's height in feet, whereas the x-axis represents the duration in seconds.

Please find the attached file.

For point C):

Find out more information about the velocity here:

brainly.com/question/25749514