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3 years ago

Can a greatest integer function be part of a piecewise defined function?

Mathematics

1 answer:

Papessa [141]3 years ago

3 0

I think yes but don't believe me

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Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(O) = 2.8 y(t) =( Preview

Karolina [17]

Answer:

$y=\frac{4}{5}e^{t}-\frac{4}{5}e^{-\frac{2}{5}t}$

Step-by-step explanation:

The given equation 5y'' + 3y' - 2y =0 can be written as

$(5D^{2}+3D-2)y(t)=0$

Solving for complementary function we have Roots of $(5D^{2}+3D-2)$ as follows

$(5D^{2}+5D-2D-2)$

$5D(D+1)-2(D+1)=0\\\\(5D-2)(D+1)=0\\\\\therefore D=-1\\D=+2/5$

Thus the complementary function becomes

y= $y=c_{1}e^{m_{1}t}+c_{2}e^{m_{2}t}$

where

$m_{1},m_{2}$ are calculated roots

thus solution becomes

$y=c_{1}e^{-t}+c_{2}e^{\frac{2}{5}t}$

Now to solve for the coefficients we use the given boundary conditions

$y(0)=0\\\\\therefore c_{1}+c_{2}=0\\\\y'(0)=-c_{1}+\frac{2}{5}c_{2}=2.8\\\\\therefore c_{2}+\frac{2}{5}c_{2}=2.8\\\\c_{2}=2\\\\\therefore c_{1}=-2}$

hence the solution becomes

$y=-2e^-{t}+2e^{\frac{2}{5}t}$

8 0

3 years ago

(x+5) (×+5)=49. I need to know what x is, how do I solve this?

Archy [21]

$(x+5)^2=49$
squaer root both sides
x+5=+/-7
minus 5 both sides
x=-5+/-7
x=-5+7=2
x=-5-7=-12

x=2 or -12

4 0

3 years ago

16 of the 22 students in Mrs. Burnham's class passed a quiz. About what

ser-zykov [4K]

Answer:

72.73

Step-by-step explanation:

3 0

3 years ago

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Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?

Valentin [98]

Answer:

A on Edg2020

Step-by-step explanation:

6 0

3 years ago

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The radius of a semicircle is extended by 6 inches.how does the measure of the semicircles arc length change?

vivado [14]

Let x be the original radius. Given that a semicircle will have an arc length of half of a circumference and C=2pr, the arc length will be just pr.

Now the difference of arc is then going to be:

p(6+x)-px

p(6+x-x)

6p inches

So the arc will be 6p inches longer. Or if you wish to approximate...

≈18.85 inches

7 0

3 years ago