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2 years ago

When multiplying signed numbers, how do you know whether the number is positive or negative?

Mathematics

1 answer:

Vanyuwa [196]2 years ago

8 0

Answer:

If the numbers have the same sign, then the answer will be positive.

If the numbers have different signs, then it will be negative.

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Find the laplace transform of f(t) = cosh kt = (e kt + e −kt)/2

iren2701 [21]

Hello there, hope I can help!

I assume you mean $L\left\{\frac{ekt+e-kt}{2}\right\}$
With that, let's begin

$\frac{ekt+e-kt}{2}=\frac{ekt}{2}+\frac{e}{2}-\frac{kt}{2} \ \textgreater \ L\left\{\frac{ekt}{2}-\frac{kt}{2}+\frac{e}{2}\right\}$

$\mathrm{Use\:the\:linearity\:property\:of\:Laplace\:Transform}$
$\mathrm{For\:functions\:}f\left(t\right),\:g\left(t\right)\mathrm{\:and\:constants\:}a,\:b$
$L\left\{a\cdot f\left(t\right)+b\cdot g\left(t\right)\right\}=a\cdot L\left\{f\left(t\right)\right\}+b\cdot L\left\{g\left(t\right)\right\}$
$\frac{ek}{2}L\left\{t\right\}+L\left\{\frac{e}{2}\right\}-\frac{k}{2}L\left\{t\right\}$

$L\left\{t\right\} \ \textgreater \ \mathrm{Use\:Laplace\:Transform\:table}: \:L\left\{t\right\}=\frac{1}{s^2} \ \textgreater \ L\left\{t\right\}=\frac{1}{s^2}$

$L\left\{\frac{e}{2}\right\} \ \textgreater \ \mathrm{Use\:Laplace\:Transform\:table}: \:L\left\{a\right\}=\frac{a}{s} \ \textgreater \ L\left\{\frac{e}{2}\right\}=\frac{\frac{e}{2}}{s} \ \textgreater \ \frac{e}{2s}$

$\frac{ek}{2}\cdot \frac{1}{s^2}+\frac{e}{2s}-\frac{k}{2}\cdot \frac{1}{s^2}$

$\frac{ek}{2}\cdot \frac{1}{s^2} \ \textgreater \ \mathrm{Multiply\:fractions}: \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d} \ \textgreater \ \frac{ek\cdot \:1}{2s^2} \ \textgreater \ \mathrm{Apply\:rule}\:1\cdot \:a=a$
$\frac{ek}{2s^2}$

$\frac{k}{2}\cdot \frac{1}{s^2} \ \textgreater \ \mathrm{Multiply\:fractions}: \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d} \ \textgreater \ \frac{k\cdot \:1}{2s^2} \ \textgreater \ \mathrm{Apply\:rule}\:1\cdot \:a=a$
$\frac{k}{2s^2}$

$\frac{ek}{2s^2}+\frac{e}{2s}-\frac{k}{2s^2}$

Hope this helps!

3 0

3 years ago

A cart weighing 200 pounds rests on an incline at an angle of 40 degrees. what is the required force to keep the cart at rest? r

MAXImum [283]

The force needed to keep the cart at rest is 149.022 pounds

<h3>Force and Motion</h3>

Given Data

Weight of cart = 200 pounds

Angle = 40 degree

The force needed to keep the cart at rest is the vertical component of the resultant force, hence we have

Fy = Mg sin θ

Substituting our given data we have

Fy = 200 sin 40

Fy = 200 *0.74511

Fy = 149.022 pounds

Learn more about force here:

brainly.com/question/12970081

7 0

2 years ago

The sum of their speeds is 180 miles per hour superman is 20mph faster than Desperado how fast is each roller coaster

madreJ [45]

Superman is 100 mph

Desperado is 80 mph

there total speed is 180 mph and Superman is 20 mph faster

8 0

3 years ago

The hypotenuse in this 45-45-90 triangle is given. How would you find the length of a leg

Viefleur [7K]

Answer:

The length of the legs of the triangle is 8 units.

Step-by-step explanation:

45-45-90 triangle

A 45-45-90 triangle is a special case of a right triangle in which both legs l have the same value and the hypothenuse is h. By the Pythagorean Theorem:

$2l^2 = h^2$

Hypothenuse of 8 V2

This means that $h = 8\sqrt{2}$

$2l^2 = h^2$

$2l^2 = (8\sqrt{2})^2$

$2l^2 = 64*2$

$l^2 = 64$

$l = \sqrt{64}$

$l = 8$

The length of the legs of the triangle is 8 units.

4 0

3 years ago

1) 2x + 8y = 20 what's the solution so confused <br> y = 2

postnew [5]

If y is equal to 2 then you can find x by putting 2 for y so you will have:
2x + 8(2) = 20
2x + 16 = 20
2x = 20 - 16
2x = 4
x = 4/2
x=2 :)))
i hope this is helpful
have a nice day

8 0

3 years ago

Read 2 more answers