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2 years ago

Help pls. Due 10/4/18

Mathematics

2 answers:

andreev551 [17]2 years ago

8 0

15+ -80=-65

you get -65 because what ever sign the bigger number has is what sign you will use.

Hopefully that was helpful to you.

luda_lava [24]2 years ago

7 0

Write down

15-80

Solve it by adding 15 to -80

The final answer is -65

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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

2 years ago

Zara filled up her car with 15 gallons of gas. If Zara paid $33.00, what was the price per gallon of gas?

djyliett [7]

Answer:

$2.20 per gallon.

Step-by-step explanation:

That is 33/15 = $2.20 per gallon.

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2 years ago

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nikdorinn [45]

Answer:

w = 8 inches

Step-by-step explanation:

P = 2w + 2l

l = 3 + w

38 = 2w + 2(3 + w)

38 = 2w + 6 + 2w

38 - 6 = 4w

32 = 4w

w = 32 : 4

w = 8 inches

l = 3 + w

l = 3inches + 8inches

l = 11 inches

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2 years ago

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Please answer quickly thanks :)))

soldi70 [24.7K]

From least to greatest: |6.99|,|-7.09|,|7.15|,|-7.18|,|-7.21|. This is becauase every value will be positive because of the absolute value

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soldier1979 [14.2K]

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