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4 years ago

What is 2/3x=2y+6 in ax+by=c form?

Mathematics

1 answer:

kifflom [539]4 years ago

8 0

Answer:

2x - 6y = 18

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

$\frac{2}{3}$ x = 2y + 6

Multiply through by 3 to clear the fraction

2x = 6y + 18 ( subtract 6y from both sides )

2x - 6y = 18 ← in standard form

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Imagine a deck of 500 cards numbered from 1 to 500. If all the cards are shuffled randomly and you are asked to pick three cards

amm1812

Answer:

P = 1 / 6

Step-by-step explanation:

Given:-

- A deck has 500 cards

- Numbered from 1-500

Find:-

you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previous drawn card

Solution:-

- Suppose we draw three cards. We don't care what they actually are, irrespective of number.

- Let the three numbers be a, b, c: Such that:

a < b < c.

- The total possible combinations with 3 numbered cards will be:

a b c

b a c

a c b

b a c

b c a

c a b

- We have 6 possibilities for 3 numbered cards. So the probability of of each subsequent card being larger than the previous drawn card would be:

P = 1 / possible combinations

P = 1 / 6

6 0

4 years ago

The ground-state wave function for a particle confined to a one-dimensional box of length L is Ψ=(2/L)^1/2 Sin(πx/L). Suppose th

Hitman42 [59]

Answer:

(a) 4.98x10⁻⁵

(b) 7.89x10⁻⁶

(c) 1.89x10⁻⁴

(d) 0.5

(e) 2.9x10⁻²

Step-by-step explanation:

The probability (P) to find the particle is given by:

$P=\int_{x_{1}}^{x_{2}}(\Psi\cdot \Psi) dx = \int_{x_{1}}^{x_{2}} ((2/L)^{1/2} Sin(\pi x/L))^{2}dx$

$P = \int_{x_{1}}^{x_{2}} (2/L) Sin^{2}(\pi x/L)dx$ (1)

The solution of the intregral of equation (1) is:

$P=\frac{2}{L} [\frac{X}{2} - \frac{Sin(2\pi x/L)}{4\pi /L}]|_{x_{1}}^{x_{2}}$

(a) The probability to find the particle between x = 4.95 nm and 5.05 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{4.95}^{5.05} = 4.98 \cdot 10^{-5}$

(b) The probability to find the particle between x = 1.95 nm and 2.05 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{1.95}^{2.05} = 7.89 \cdot 10^{-6}$

(c) The probability to find the particle between x = 9.90 nm and 10.00 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{9.90}^{10.00} = 1.89 \cdot 10^{-4}$

(d) The probability to find the particle in the right half of the box, that is to say, between x = 0 nm and 50 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{50.00} = 0.5$

(e) The probability to find the particle in the central third of the box, that is to say, between x = 0 nm and 100/6 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{16.7} = 2.9 \cdot 10^{-2}$

I hope it helps you!

3 0

4 years ago

Write the equation of the giving circle center (-2,-2) radius of 6

astraxan [27]

Answer:

(x+2)²+(y+2)²=36

Step-by-step explanation:

given r=6

center is (-2,-2)

the equation becomes

(x-(-2))²+(y-(-2))² = 6²

on simplifying we get the answer

5 0

3 years ago

A baker decorates 42 cupcakes in 30 minutes.She decorates cupcakes at a constant rate.

NikAS [45]

Answer:

Step-by-step explanation:

Well the way i said it was

42-30= 12

altho i not very sure

3 0

3 years ago

A local ski resort is open for 13 weeks in the winter. Write a fraction in simplest form that represents the fraction of the yea

Rudiy27

The ski resort is open 13/52 weeks out of the year

4 0

4 years ago