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3 years ago

11

Karen is solving the quadratic equation shown below x2+12x-1=0 x2+12x-1+1=0+1

1 answer:

wolverine [178]3 years ago

8 0

Answer:

first of all stay away from Karen's

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PLS PLS PLS HELP I WILL GIVE BRAINLIEST!!

Art [367]

Answer:

dcba

Step-by-step explanation:

changed it because i realized it said greatest to least

3 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 <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

The lengrh of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the funct

MrRissso [65]

Step-by-step explanation:

just multiply the 2 together to get the area

it would just be

$(5x) \times (2{x}^{2} - 4x + 13)$

use the distributive property

$10 {x}^{3} - 20 {x}^{2} + 65$

unless you want to simplify the answer, this would be the answer

simplified, it would be

$5(2{x}^{3} - 4 {x}^{2} + 13)$

7 0

2 years ago

Find the value of x.

hichkok12 [17]

<h3>Angles sum up to:</h3><h3>( n - 2 ) × 180 = ( 5 - 2 ) × 180 = 3 × 180 = 540</h3>

$x + 4x + 4x + 135 + 135 = 540$

$9x + 270 = 540$

$9x = 540 - 270 \\ 9x = 270$

$x = \frac{270}{9} = 30$

8 0

2 years ago

a runner warms up for ten minutes and then takes seven minutes to run each mile. the total time after r miles in 45 minutes. how

Alika [10]

45=10+7x
35=7x
5=x

Answer: they ran 5 miles

Hope this helps:)

6 0

3 years ago