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3 years ago

Chemical equations must be properly balanced because chemical reactions follow the first law of thermodynamics.

1 answer:

7 0

I thinking it’s true. The law of conservation of matter has been satisfied. When the reactants and products of a chemical equation have the same number of atoms of all elements present, we say that an equation is balanced. All proper chemical equations are balanced.

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Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

3 years ago

Solve the Equation for y . 9x +5y = -2

ASHA 777 [7]

Answer:

$\large\boxed{y=\dfrac{-9x-2}{5}}$

Step-by-step explanation:

$9x+5y=-2\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\5y=-9x-2\qquad\text{divide both sides by 5}\\\\y=\dfrac{-9x-2}{5}$

3 0

3 years ago

Gerry has a piece of poster board that is 3 feet wide. He wants to draw columns on the poster board so that each column is 1/6 o

SashulF [63]

Answer:

A.2

Step-by-step explanation:

8 0

3 years ago

A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the

Alexus [3.1K]

4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.

Step-by-step explanation:

Number of people hold by small cars = 4

Number of people hold by large cars = 6

Let,

Number of small cars = x

Number of large cars = y

The students rented 4 times as many large cars as small cars,

y = 4x Eqn 1

which altogether can hold 56 people.

4x+6y=56 Eqn 2

4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.

Keywords: linear equations, addition

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

The parent cosine function is transformed to create the function . which graphed function has the same amplitude as function m?

Shkiper50 [21]

Based on the graph given, the option that will show the same amplitude as function m is graph D.

<h3>Which graphed function is this about?</h3>

The cosine function is seen as:

f(x) = A*cos(kx) + M

And the functions are:

A stands for amplitude,
k is angular frequency,
M is the midline.

When the function is m(x) = -2*cos(x+π).

The absolute value of the amplitude will be 2*|-2| = 4

Therefore, the option that can have the requirement above is graph D.

Learn more about cosine from

brainly.com/question/23563998

#SPJ4

8 0

1 year ago