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4 years ago

Solve 2√x=1-√(4x-1).

Mathematics

1 answer:

andriy [413]4 years ago

8 0

Answer: $x=\frac{1}{4}$

Step-by-step explanation:

Given

$2\sqrt{x}=1-\sqrt{4x-1}$

$\sqrt{4x-1}=1-2\sqrt{x}$

Squaring both sides

$4x-1=1+4x-4\sqrt{x}$

$4\sqrt{x}=2$

$\sqrt{x}=\frac{1}{2}$

squaring both sides

$x=\frac{1}{4}$

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Which of the following is not a property of a rectangle?

sleet_krkn [62]

The correct answer is d

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4 years ago

Find the solution of this system of equations -5x - y = -7 -6x + y = 7 ?

mojhsa [17]

You’re answer - (0,7)

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3 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

V2=u2+2as v 2 = u 2 + 2 a s Where v v is the final velocity (in m/s), u u is the initial velocity (in m/s), a a is the accelerat

allsm [11]

Answer:

Final velocity, v = 21.75 m/s

Step-by-step explanation:

Given that the relation between final velocity, initial velocity, acceleration and distance traveled is expressed as:

$v^2=u^2+2as$

Also, given that:

Initial velocity, u = 9 m/s

Acceleration, a = 7 m/ $s^2$

Distance, s = 28 m

To find:

Final velocity, v = ?

Solution:

The given relation between v, u, a and s is:

$v^2=u^2+2as$

We have the values of initial velocity, acceleration and distance traveled in the question statement. We just need to put all these values to find the value of final velocity.

Let us put all the values in the given equation and try to find final velocity, v:

$v^2=9^2+2\times 7 \times 28\\\Rightarrow v^2=81+14 \times 28\\\Rightarrow v^2=81+392\\\Rightarrow v^2=473\\\Rightarrow v=\sqrt{473}\\\Rightarrow v=21.75\ m/s$

So, the answer is:

final velocity, v = 21.75 m/s

5 0

3 years ago

A line passes through the points (0, -8) and (5, 10). What is its equation in slope-intercep

DochEvi [55]

<h2>Answer: y = ¹⁸/₅ x - 8 </h2>

Step-by-step explanation:

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (0, -8) and (5, 10), from which we can find the slope and later the equation of the line.

Finding the Slope

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

= (10 - (- 8)) ÷ (5 - 0)

= ¹⁸/₅

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-8) = ¹⁸/₅ (x - 0)

we could also transform this into the slope-intercept form ( y = mx + c)

since y - (-8) = ¹⁸/₅ (x - 0)

⇒ y + 8 = ¹⁸/₅ x

∴ y = ¹⁸/₅ x - 8

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

5 0

3 years ago