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3 years ago

Help Me5k = 6k + 4 - 6

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

6 0

Answer:

k = 2

Step-by-step explanation:

5k = 6k + 4 - 6

We can simplify this by solving 4 - 6 (replacing it with -2 !)

5k = 6k - 2

Now we can subtract 5k from both sides.

0 = k - 2

Finally, we can add 2 to both sides. This gets rid of the negative 2 on the right.

2 = k

Just reversing it...

k = 2

Answer: k = 2

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3 years ago

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3 years ago

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1 year ago

Read 2 more answers

Y varies directly with X and has a constant rate of change of 6. When the value of Y is 11, then the value of X could be _____.

Bogdan [553]

Answer: The correct option is (B) less than 2.

Step-by-step explanation: Given that Y varies directly with X and has a constant rate of change of 6.

We are to find the possible value of X when the value of Y is 11.

Since Y varies directly with X, so we can write

$Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}$

Since the rate of change is constant and is equal to 6, so we must have

$k=6.$

So, from equation (i), we have

$Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)$

Now, when Y = 11, then from equation (ii), we get

$Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=\dfrac{11}{6}$

Thus, the value of X is less than 2 when Y = 11.

Option (B) is CORRECT.

8 0

3 years ago

Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7

Nutka1998 [239]

As a Bernoulli equation:

$x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6$

Let $z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}$ . The ODE becomes

$-x^2\dfrac{\mathrm dz}{\mathrm dx}-6xz=6$
$x^6\dfrac{\mathrm dz}{\mathrm dx}+6x^5z=-6x^4$
$\dfrac{\mathrm d}{\mathrm dx}[x^6z]=-6x^4$
$x^6z=-6\displaystyle\int x^4\,\mathrm dx$
$x^6z=-\dfrac65x^5+C$
$z=-\dfrac6{5x}+\dfrac C{x^6}$
$y^{-1}=-\dfrac6{5x}+\dfrac C{x^6}$
$y=\dfrac1{\frac C{x^6}-\frac6{5x}}$
$y=\dfrac{5x^6}{C-6x^5}$

With $y(3)=6$ , we get

$6=\dfrac{5(3)^6}{C-6(3)^5}\implies C=\dfrac{4131}2$

so the solution is

$y=\dfrac{5x^6}{\frac{4131}2-6x^5}=\dfrac{10x^6}{4131-12x^5}$

which is valid as long as the denominator is not zero, which is the case for all $x\neq\sqrt[5]{\dfrac{4131}{12}}$ .

8 0

3 years ago