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3 years ago

14

Express 14/6 as a mixed number in simplest form

2 answers:

motikmotik3 years ago

6 0

I think the answer is 2 1/3

kenny6666 [7]3 years ago

3 0

The number is 7/3 or 2 1/3

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2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

3 0

3 years ago

Enter the sum of numbers as a product of their GCF.

frutty [35]

Their GCF is 6 and the sum is 66

Step-by-step explanation:

8 0

3 years ago

4x^2 +3x-11y+17

masha68 [24]

Answer:

1) 4x^2, 3x, -11y, 17 (4 terms)

2) 4, 3, -11, 17 (4 coefficients)

3) none

Step-by-step explanation:

3 0

3 years ago

Find the sum of 2x2 + 3x - 4, 8 - 3x, and -5x2 + 2.

inessss [21]

2x^2 +3x -4 +8 -3x -5x^2 +2
-3x^2 + 6

Answer is C) -3x^2 + 6

3 0

3 years ago

Read 2 more answers

The ordered pair (-4, -5) is a solution of the following system of equations 2x+y=13 19x+13y=15

liberstina [14]

Answer:

Step-by-step explanation

672

8 0

3 years ago