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2 years ago

Sam is using the expression M/8n in class. What is the value of this expression when m = 4 and n = 1/2

Mathematics

1 answer:

vichka [17]2 years ago

4 0

Answer:

Step-by-step explanation:

m/8n > 4/8(1/2) ( since its 1/2 all you need to do is change the fraction to whole number which is 1/2 = 0.5)

The given will become 4/4 then simplest form is 1

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

6 0

3 years ago

if we write a 3 in front of a two-digit number, the new three digit number will be 24 more than 7 tines the origional two digit

JulsSmile [24]

Here we have a simple algebra problem, we will see that the original number was 46.

<h3>How to find the equation we need to solve:</h3>

We know that we start with a 2 digit number, it can be written as:

a*10 + b

Where a and b are decimal numbers. (from 0 to 9).

If we add a 3 "in front of it", we are adding:

3*100 + a*10 + b

And this is 24 more than 7 times the original number, so we have:

3*100 + a*10 + b = 24 + 7*(a*10 + b)

Now we can solve that:

300 + a*10 + b = 24 + a*70 + b*7

300 - 24 + a*10 - a*70 + b - b*7 = 0

276 - a*60 - b*6 = 0

276 = a*60 + b*6

This part is tricky, here you need to remember that a and b can only be integers from 0 to 9, so you can try with different integer values for b and see if a is also an integer for that value, for example taking b = 6 we get:

276 = a*60 + 6*6 = a*60 + 36

276 - 36 = a*60

240/60 = a = 4

So if b = 6, then a = 4, so both are integers in the wanted range.

From this, we can conclude that the original number is 46.

If you want to learn more about algebra, you can read:

brainly.com/question/4344214

4 0

3 years ago

This figure is

Ratling [72]

Solution

The perimeter of the 1/4 of the circle is = (pi/2 + 2)r

Here pi = 3.14, r = 3

Now plug in the values in to the above formula.

=(3.14/2 + 2) 3

= (1.57 + 2) 3

= 3.57*3

Perimeter of the circle = 10.71 cm.

The answer is C) 10.7 cm

4 0

4 years ago

Find the side length of x (trigonometry)

MrRa [10]

Answer:

x=12.124

Step-by-step explanation:

here 7 and x are the legs of the triangle where as 14 is hypotenuse because it is opposite opposite to 90 degree.

using pythagoras theorem

a^2 + b^2 = c^2

here and b are legs and c is hypotenuse

7^2 + x^2 = 14^2

49 + x^2 = 196

x^2 =196-49

x^2 =147

x= $\sqrt{147}$

x=12.1243

x=12.124 (after converting to the nearest hundredth)

3 0

3 years ago

What is 5 divided by 8.1

stellarik [79]

.6172839506
as a fraction this is 50/81

3 0

4 years ago

Read 2 more answers