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3 years ago

Lashonda made $80 for 5 hours of work.

Mathematics

2 answers:

valkas [14]3 years ago

8 0

Answer:

$208

Step-by-step explanation:

well 5 hours of work = $80

so 1 hour =$16

Which means 13 hours = $208

Viefleur [7K]3 years ago

8 0

The result is 208€

Because 5 are 80

80:5=16

16•13=208

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Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago

400

Feliz [49]

Answer:

Step-by-step explanation:

7 0

3 years ago

Imagine telling a friend about your favorite coffee and donut shop. Your friend asks how much it charges for a cup of coffee and

Mama L [17]

Answer:

c + 2d = $7.00

2c + 3d = $12.00

Step-by-step explanation:

Hello!

Let:

c = # of coffees
d = # of donuts

1 coffee and 2 donuts cost $7.00

This can be repesented by 1c + 2d = $7.00, or c + 2d = $7.00

2 coffees and 3 donuts cost $12.00

This can be represented by 2c + 3d = $12.00

So, the system is :

c + 2d = $7.00

2c + 3d = $12.00

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2 years ago

Write a story that matches the expression 42x - 5

nadezda [96]

I bake 45 cupcakes everyday and every hour I sell 5 cupcakes.

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3 years ago

Read 2 more answers

Fred has $ 200 in his banking account. Which integer represents a debit of $40 dollars?

maria [59]

Answer:

(D) -40

Step-by-step explanation:

Hope it helps.

According to me it is correct.

But please if it is wrong let me know.

6 0

3 years ago