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3 years ago

Given: 3x < -6.

Mathematics

2 answers:

nexus9112 [7]3 years ago

5 0

A. {x | x < -2}

I think sorry if I'm wrong.

In-s [12.5K]3 years ago

3 0

3x < -6
x < -6/3
x < -2
Therefore, the solution set is {x | x < -2}.

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Graph the direct variation y=−1.5x. Using the graph, find:

Mariana [72]

Y=-3

-3=-1.5x
you substitiue y value, then you divide both sides by -1.5 and you get 2 for x.
(2,-3)

y=4.5
4.5=-1.5x
you substitute y value, then again you divide both sides by -1.5 and you get 3.
(3,4.5)

y=6
6=-1.5x
same thing for this last one. then once again divide by -1.5 and you get -4.
(-4,6)

7 0

3 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 c)

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

This becomes the solution m=α±βi where α=0 and β=2

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

Where A and B 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

3 years ago

Kedar earns a monthly salary if $2,200 plus a 3.75% commission on the amount of his sales at a men's clothing store. What would

ryzh [129]

Monthly salary of Kedar = $2000
Percentage commission on the amount of his sales = 3.75%
Amount of money for which clothing sold by Kedar = $4500
Amount of interest earned by Kedar this month = (3.75/100) * 4500
= 3.75 * 45
= 168.75 dollars
So
The total amount earned by Kedar this month = (2200 + 168.75) dollars
= 2368.75 dollars
So Kedar earned a total amount of $2368.75 this month.I hope the procedure is absolutely clear to you.

7 0

3 years ago

Which of the following is an arithmetic sequence?

Mashcka [7]

The following answer would be D because I’m guessing and I need the answers too sorry

6 0

3 years ago

Simplify the following expression completely using distribution and combining like terms

coldgirl [10]

Hey there!

6 (2 - 3g) - 10

= 12 - 18g- 10

= 12 - 10 - 18g

= 2 - 18g

Hope it helps ya!

4 0

3 years ago

Read 2 more answers