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3 years ago

Raj is visiting the United States and needs to convert 2000 rupees to US dollars

Mathematics

2 answers:

Stells [14]3 years ago

7 0

Answer:

After converting Raj will have $31.88 USD

Step-by-step explanation:

1 unit rupee = 0.01594 USD

It is given that,

Raj is visiting the United States and needs to convert 2000 rupees to US dollars

<u>Convert 2000 rupees to USD</u>

To find USD we have to multiply rupees with 0.01594

USD = 2000*0.01594

USD = $31.88

Therefore Raj will have $31.88 USD

seropon [69]3 years ago

6 0

Answer:

$31.88 USD

Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

Sketch the region of integration and convert the polar integral into cartesian integral or sum of cartesian integral. Don't eval

sashaice [31]

Answer: The transformed integral is

$\int_0^{\pi/6}\int_0^{2\sec\theta}r^5\sin^2\theta dr d\theta=\int_0^2\int_0^{\frac{1}{\sqrt{4}}x}y^2(x^2+y^2).$

The region of integration is a triangle delimited by the $x$ axis, the vertical line $x=2$ , and the line $y=\frac{1}{\sqrt{3}}x$ .

Step-by-step explanation: For this integral we have:

1. $0$ and

2. $0$ .

The first condition says that the region of integrarion is within the "slice" of the xy plane between the polar angle of $\theta=0$ and $\theta=\frac{\pi}{6}$ in the first quadrant. To make sense of the second condition we will convert to the Cartesian coordinates. Remember that

3. $x=r\cos\theta$

4. $y=r\sin\theta$

5. $r=\sqrt{x^2+y^2}$

6. $\theta=\arctan\frac{y}{x}\quad \text{only in the first quadrant}$

Using 2. (squaring it), along with 5. we obtain

$0$

Now using 3. to express $\cos^2\theta=\frac{x^2}{r^2}=\frac{x^2}{x^2+y^2}$ we obtain

$0$

The left inequality $0$ just says that we start from the origin. The right inequality, after cancelling $x^2+y^2$ , yields $1$ . Since we are in the first quadrant $x$ has to be positive so this inequality can be rewritten as (taking the square root) $x$ . So the region is a triangle delimited by the slice of the first quadrant between $\theta=0$ and $\theta=\frac{\pi}{6}$ and by the vertical line $x=2$ (see figure).

In other words, this triangle is delimited by the x axis, by the vertical line x=2 and by the line $\frac{y}=\tan\frac{\pi}{6}x=\frac{1}{\sqrt{3}}x.$ This helps us to define the boundaries of integration: we have $0$ (from the origin up to x=2) and $0$ (from the x axis i.e. y=0 up to the line mentioned before).

Next we transform the area element. In cartesian coordinates it is $dxdy$ while in polar coordinates it is $rdrd\theta$ so we have $r^5\sin^2\thetadrd\theta=r^4\sin^2\theta dxdy.$

Next we use 4. to express the sine: $r^4\sin^2\theta dxdy=r^4\frac{y^2}{r^2}dxdy=r^2y^2dxdy$ .

Finally, we use 5. $r^2y^2dxdy=y^2(x^2+y^2)dxdy$ .

Therefore, the transformed integral is

$\int_0^{\pi/6}\int_0^{2\sec\theta}r^5\sin^2\theta dr d\theta=\int_0^2\int_0^{\frac{1}{\sqrt{4}}x}y^2(x^2+y^2).$

5 0

2 years ago

Two families stayed at the same hotel in identical rooms. The first family stayed for 5 nights and paid extra to use a rollaway

Vesna [10]

Part A: The system of equations that can be used is

5h + 2b = 413

3h + b = 243

Part B: The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24

Step-by-step explanation:

Two families stayed at the same hotel in identical rooms

The first family stayed for 5 nights and paid extra to use a roll away bed for 2 of the nights.
Their total bill was $413
The second family stayed for 3 nights and used a roll away bed for 1 night.
Their total bill was $243

We need to write a system of equations that can be used to find, h, the cost per night of renting a room at the hotel, and b, the cost per night of using a roll away bed at the hotel and find the values of h and b using the elimination method

Part A:

∵ The first family stayed for 5 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 5h

∵ The first family paid extra to use a roll away bed for 2 of the nights

∵ The cost of the roll away bed per night is $b

∴ The cost of the two nights = 2b

∵ Their total bill was $413

∴ 5h + 2b = 413 ⇒ (1)

∵ The second family stayed for 3 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 3h

∵ The first family paid extra to use a roll away bed for 1 of the night

∵ The cost of the roll away bed per night is $b

∴ The cost of the two nights = b

∵ Their total bill was $243

∴ 3h + b = 243 ⇒ (2)

The system of equations that can be used is

5h + 2b = 413

3h + b = 243

Bart B:

∵ 5h + 2b = 413 ⇒ (1)

∵ 3h + b = 243 ⇒ (2)

- Multiply equation (2) by -2 to eliminate b

∴ -6h - 2b = -486 ⇒ (3)

- Add equations (1) and (3)

∴ -h = -73

- Multiply both sides by -1

∴ h = 73

Substitute the value of h in equations (1) or (2) to find b

∵ 3(73) + b = 243

∴ 219 + b = 243

- Subtract 219 from both sides

∴ b = 24

The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

7 0

2 years ago