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coldgirl [10]
3 years ago
14

Diana has 1 square yard of fabric she will make one pillow that requires 3/8 square yard of fabric and another pillow that requi

res 2/8 square yard of fabric Diana uses the equations shown below to explain her process to find the number of square yards of fabric she will use and the number of square yards of fabric she will have left
Mathematics
1 answer:
Scilla [17]3 years ago
4 0

Answer:

<h2>Diana uses 5/8 square yard of fabric for both pillows.</h2><h2>There remains 3/8 square yard of fabric.</h2>

Step-by-step explanation:

Givens

  • The total amount of fabric is 1 square yard.
  • One pillow requires 3/8 square yard of fabric.
  • A second pillow requires 2/8 square yard of fabric.

To find the total amount of fabric Diana used, we must sum those fractions

\frac{3}{8} +\frac{2}{8}=\frac{5}{8}

Diana uses 5/8 square yard of fabric for both pillows.

Now, we subtract to find the remaining amount of fabric

1-\frac{5}{8}=\frac{8-5}{8}=\frac{3}{8}

Therefore, there remains 3/8 square yard of fabric.

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Calculate gcd(77, 30) by using the Euclidean algorithm. Find also integers u and v such that 49u + 30v = 1. Furthermore, find su
VladimirAG [237]

Answer:

1. gcd(77,30)=1

77=2*30+17\\30=1*17+13\\17=1*13+4\\13=3*4+1\\4=4*1+0

Since 1 is the last non zero remainder appearing in these equations then, 1 is the gcd of 77 and 30.

2. u=-11, v=18

Using the Euclidean Algorithm we have that

49=1*30+19\\30=1*19+11\\19=1*11+8\\11=1*8+3\\8=2*3+2\\3=1*2+1\\2=1*2+0

Now, we express the remainder as linear combinations of 49 and 30.

1&=3-2\\ &=3-(8-2*3)=3-8+2*3\\&=(11-8)-8+2(11-8)=3*11-4*8\\&=3*11-4(19-11)=7*11-4*19\\&=7(30-19)-4*19=7*30-11*19\\&=7*30-11(49-30)=\\&=18*30-11*49

Then 1=(-11)49+18*30

3. x=18

If 30x\equiv 1\text{mod 77} then

30x=k*77+1 for some k\in \mathbb{Z}.

Then, if k=7,

30x=7*77+1=540\\x=\frac{540}{30}=18

6 0
3 years ago
jane and ken share some money in the ratio 5:3. ken's share is $16 less than jane's share. find each person's share
Vlad [161]

Answer:

10:6

Step-by-step explanation:

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3 years ago
How to find the average squared distance between the points of the unit disk and the point (1,1)
ddd [48]
The unit disk can be parameterized by the function

\mathbf p(r,\theta)=(r\cos\theta,r\sin\theta)

where 0\le r\le 1 and 0\le\theta\le2\pi. The squared distance between any point in this region (x,y)=(r\cos\theta,r\sin\theta) and the point (1, 1) is

(x-1)^2+(y-1)^2=(r\cos\theta-1)^2+(r\sin\theta-1)^2
=(r^2\cos^2\theta-2r\cos\theta+1)+(r^2\sin^2\theta-2r\sin\theta+1)
=r^2(\cos^2\theta+\sin^2\theta)-2r(\cos\theta-\sin\theta)+2
=r^2-2r(\cos\theta-\sin\theta)+2

The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.

\dfrac{\displaystyle\iint_{x^2+y^2
=\dfrac{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}[r^2-2r(\cos\theta-\sin\theta)+2]r\,\mathrm dr\,\mathrm d\theta}{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r\,\mathrm dr\,\mathrm d\theta}
=\dfrac{\frac{5\pi}2}\pi=\dfrac52
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3 years ago
Infinite algebra1,multi step equations.-18-6k=6(1+3k)
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Oh thats easy. It's a piece of cake. Just use your calculator
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Nine yards of ribbon are used to make bows. How many yards of ribbon does each bow use?
Juliette [100K]
15 inches of ribbon<span> for </span><span>each</span>
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