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3 years ago

How many yards carpeting is needed to cover a 60 feet length room and 40 feet width

Mathematics

1 answer:

Bad White [126]3 years ago

5 0

Answer:

$266$ $\frac{2}{3}$ $yards$

Step-by-step explanation:

1. Approach

First, convert the dimensions of the room from feet to yards. Remember, the conversion rate between feet and yards is, $3feet=1yard$ . Next, find the area of the room by multiplying the length by the width.

2. Convert the unit of measurement

The measurement unit is given in feet, one must convert it into yards. The conversion rate between yards and feet is, $3feet=1yard$ .

$60feet=20yards\\\\40feet=13\frac{1}{3}yards$

3. Find the area of the room

Now multiply the length by the width to find the area of the room.

$20yards*13\frac{1}{3}yrads\\\\= 20 * \frac{40}{3}\\\\=\frac{800}{3}\\\\= 266\frac{2}{3}_{.}yards^{2}$

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mr Goodwill [35]

Answer:

{x = 7 ,y = 5

Step-by-step explanation:

Solve the following system:

{3 x + 3 y = 36 | (equation 1)

8 x - 5 y = 31 | (equation 2)

Swap equation 1 with equation 2:

{8 x - 5 y = 31 | (equation 1)

3 x + 3 y = 36 | (equation 2)

Subtract 3/8 × (equation 1) from equation 2:

{8 x - 5 y = 31 | (equation 1)

0 x+(39 y)/8 = 195/8 | (equation 2)

Multiply equation 2 by 8/39:

{8 x - 5 y = 31 | (equation 1)

0 x+y = 5 | (equation 2)

Add 5 × (equation 2) to equation 1:

{8 x+0 y = 56 | (equation 1)

0 x+y = 5 | (equation 2)

Divide equation 1 by 8:

{x+0 y = 7 | (equation 1)

0 x+y = 5 | (equation 2)

Collect results:

Answer: {x = 7 ,y = 5

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3 years ago

ZanzabumX [31]

Answer:

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Step-by-step explanation:

15(6.5% * 7000)+7000=y

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3 years ago

Convert the Cartesian equation x^2 + y^2 = 16 to a polar equation.

RideAnS [48]

Answer:

Problem 1: $r=4$

Problem 2: $r=-2\sin(\theta)$

Problem 3: $r\sin(\theta)=3$

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

$x=r \cos(\theta)$

$y=r \sin(\theta)$

$\frac{y}{x}=\tan(\theta)$

So if we make those substitution into the first equation we get:

$x^2+y^2=16$

$(r\cos(\theta))^2+r\sin(\theta))^2=16$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)=16$

Factor the $r^2$ out:

$r^2(\cos^2(\theta)+\sin^2(\theta))=16$

The following is a Pythagorean Identity: $\cos^2(\theta)+\sin^2(\theta)=1$ .

We will apply this identity now:

$r^2=16$

This implies:

$r=4 \text{ or } r=-4$

We don't need both because both of include points with radius 4.

Problem 2:

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$(r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0$

Factoring out $r^2$ from first two terms:

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Apply the Pythagorean Identity I mentioned above from problem 1:

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$r^2+2r\sin(\theta)=0$

or if we factor out r:

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$r=0 \text{ or } r=-2\sin(\theta)$

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

$y=3$

$r\sin(\theta)=3$

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Answer:

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Step-by-step explanation:

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How many yards carpeting is needed to cover a 60 feet length room and 40 feet width ​

How many yards carpeting is needed to cover a 60 feet length room and 40 feet width