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3 years ago

6

What is the 100th term of the arithmetic sequence 3, 8, 13, 18

1 answer:

Marina CMI [18]3 years ago

3 0

Equation y=5x-2
500-2 =498

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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

When 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, what is the value of q? Show your work please.

Strike441 [17]

= 2x^2 - 20x + 49 = 2(x^2 - 10x + 49/2)

y= 2((x-5)^2 - 25 + 49/2) = 2((x-5)^2 - 1/2) = 2(x-5)^2 - 1

q =5, r=-1, p=2

Vertex = (q,r) = (5,-1)

hope it helps plz mark as brainliest

5 0

3 years ago

Eyan bought 234 pounds of apples for $1.32 per pound, 112 pounds of peaches for $1.20 per pound, and some tomatoes, all from a g

9966 [12]

Answer:

the money spend on tomatoes is $4.20

Step-by-step explanation:

The computation of the money spend on tomatoes is shown below

Let the money spend on tomatoes be x

So

$2 \frac{3}{4} \times \$1.32 + 1\frac{1}{2} \times \$1.20 + x = \$9.63\\\\$

$3.63 + $1.80 + x = $9.63

x = $9.63 - $3.63 + $1.80

= $4.20

Hence, the money spend on tomatoes is $4.20

4 0

3 years ago

maxonik [38]

A. Plz mark brainliest, I need points.

7 0

3 years ago

Helppppp!! im confused lol

Lady bird [3.3K]

Answer:

a

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers