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LUCKY_DIMON [66]

4 years ago

9

Write an algebraic expression to model each situation.

1 answer:

Masja [62]4 years ago

6 0

25-1.5x ? i hope this helps

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Find two numbers the quotient is between. Then estimate the quotient 284 divided by 5

Pavel [41]

The quotient is 284 divided by 5, or

284
----- If you mult. numerator and denominator by 2, you get 578/10, or 57.8.
5

Try the numbers 550 and 600 (because 574 is between them). Now divide 550 and 600 by 10; the results will be 55 and 60. The actual value of 284/5 is between 55 and 60: 57.8 (which you can verify with a calculator).

4 0

4 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in <em>c)</em>

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where <em>A</em> and <em>B</em> are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

4 years ago

Drag the numbers to order them from greatest to least, with the greatest at the top.

Savatey [412]

10pi

9.92749....

square root of 101

0.99853....

6 0

3 years ago

Read 2 more answers

Help me please :))) this is my last question on a final

djverab [1.8K]

I'll help you. :)))) Your answer is 6
25

8 0

4 years ago

If John read 8 pages in 10 minutes, how many pages can he read in 70<br> minutes?

loris [4]

Answer:

56 pages

Step-by-step explanation:

7 0

3 years ago