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3 years ago

14

The first two terms of a geometric sequence are a 1 = 1/ 3 and a 2 = 1/ 6 . What is a 8 , the eighth term?

1 answer:

kupik [55]3 years ago

6 0

The answer is 1/384.

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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

What is the greatest common factor of 10x and 22x“?

BartSMP [9]

Answer:

2x

Step-by-step explanation:

x and 2 are common to both 10x and 22x, so 10x + 22x = 2x(5 + 11)

The GCF is 2x.

4 0

3 years ago

Evaluate x + y when x = - 18.2 and y = 3.6

Contact [7]

-18.2 + 3.6= -14.6 is the answer to the question

3 0

3 years ago

Read 2 more answers

Round off 787592799 to the nearest 10

timama [110]

Answer:

787592800

Step-by-step explanation:

Hi there,

If you round this answer to the nearest tens place, it would be 787592800. Since the 799 is closer to 800 rather than 790, it would round up and change the last three digits of the number instead of the usual two digits.

Hope this answer helps. Cheers.

3 0

3 years ago

Hhhhhheeeeeeeellllpppp

Leni [432]

Answer:

y = 0.35x + 2.5

Step-by-step explanation:

3 0

3 years ago