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3 years ago

Simplify by combining like terms -6x equals 12 + 8y + 16x

Mathematics

1 answer:

garik1379 [7]3 years ago

8 0

Answer:

The simplified expression is 22 x + 8 y + 12 = 0

Step-by-step explanation:

Here, the given expression is : - 6x = 12 + 8y + 16 x

Like Terms: The terms which have the same coefficient variable in any given expression are called Like Terms.

In the given expression the only pair of like terms is (-6 x, and 16 x)

Solving the given expression , we get:

- 6x = 12 + 8y + 16 x

⇒12 + 8y + (16 x + 6 x) = 0

or, 12 + 8 y + 22 x = 0

Hence, the simplified expression is 22x +8y + 12 = 0

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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

qwelly [4]

Answer:

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

Step-by-step explanation:

x and y are differentiable functions of t, and we are given the equation:

$xy=6$

First, let's differentiate both sides of the equation with respect to t. So:

$\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]$

By the Product Rule and rewriting:

$\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0$

Therefore:

$\displaystyle y\frac{dx}{dt}+x\frac{dy}{dt}=0$

We want to find dy/dt when x = 4 and dx/dt = 11.

Using our original equation, find y when x = 4:

$\displaystyle (4)y=6\Rightarrow y=\frac{3}{2}$

Therefore:

$\displaystyle \frac{3}{2}\left(11\right)+(4)\frac{dy}{dt}=0$

Solve for dy/dt:

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

We want to find dx/dt when x = 1 and dy/dt = -9.

Again, using our original equation, find y when x = 1:

$(1)y=6\Rightarrow y=6$

Therefore:

$\displaystyle (6)\frac{dx}{dt}+(1)\left(-9)=0$

Solve for dx/dt:

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

5 0

3 years ago

find the quadratic equation if its solutions are 1.5 and -.25, and the equation coefficients are not decimals.

denpristay [2]

If a quadratic equation has solutions $x_1$ and $x_2$ , then we can write it as

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$\left(x-\dfrac{3}{2}\right)\left(x+\dfrac{1}{4}\right) = x^2-\dfrac{5}{4}x-\dfrac{3}{8}$

If we don't want decimal coefficient, we can multiply the whole expression by 8:

$8x^2-10x-3$

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