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3 years ago

Write the fraction in simplest form. 16/24

Mathematics

2 answers:

hammer [34]3 years ago

8 0

It is 2/3 because 16 divided by 8 is 2 and 24 divided by 8 is 3

slavikrds [6]3 years ago

7 0

Hi , the answer is 2/3 , because ;
16 divided by 8 equals 2
24 divided by 8 equals 3
We basically find a number that is divisible , in this case 8 is the number because 8 times 2 equals 16 and 8 times 3 equals 24 .

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73%

Step-by-step explanation:

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3 years ago

All of these ODEs model a system with a spring, mass and dashpot.

Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

$a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

This differential equation will have a characteristic equation of the form:

$a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

If the discriminant is greater than zero, the solution is over-damped

If the discriminant is less than zero, the solution is under-damped

If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

$-3y''-3y+3y=0$

Which has characteristic equation of the form:

$-3r^2-3r+3=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=-3\\b=-3\\c=3$

So:

$Disc=(-3)^2-4(-3)(3)=9-(-36)=45$

In this case:

$Disc=45>0$

Therefore the solution is over-damped.

Now, given the differential equation:

$-2y''-4y'+1y=0$

Which has characteristic equation of the form:

$-2r^2-4r+1=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=-2\\b=-4\\c=1$

So:

$Disc=(-4)^2-4(-2)(1)=16+8=24$

In this case:

$Disc=24>0$

Therefore the solution is over-damped.

Finally, given the differential equation:

$1y''+7y'+5y=0$

Which has characteristic equation of the form:

$1r^2+7r+5=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=1\\b=7\\c=5$

So:

$Disc=(7)^2-4(1)(5)=49-20=29$

In this case:

$Disc=29>0$

Therefore the solution is over-damped.

6 0

3 years ago

What is the slope of a line perpendicular to the line whose equation is

jonny [76]

Answer:

$- \frac{1}{2}$

Step-by-step explanation:

How do we find the line that's perpendicular to another?

We find the negative reciprocal. So for example if our slope is 2, the negative reciprocal would be $- \frac{1}{2}$ .

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3 years ago

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mojhsa [17]

CPI in 1960 = 29.6

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Growth (%) in CPI = $\frac{\text{CPI in 1980 - CPI in 1960}}{\text{CPI in 1960}}$ × 100

⇒ Growth (%) in CPI = $\frac{82.4-29.6}{29.6}$ × 100

⇒ Growth (%) in CPI = 178.3783.. %

⇒ Growth (%) in CPI = 178.4%

Now, we know that price of frozen chicken pie in 1960 = $0.28

Also, we know that over 1960 to 1980, frozen chicken pie price grew at the same rate as CPI

Hence, Price of Chicken Pie in 1980 = Price of Chicken Pie in 1960 × (1 + Growth in CPI)

⇒ Price of Chicken Pie in 1980 = 0.28 × (1 + 178.4%)

⇒ Price of Chicken Pie in 1980 = 0.28 + (0.28 × 178.4%)

⇒ Price of Chicken Pie in 1980 = 0.28 + 0.49952

⇒ Price of Chicken Pie in 1980 = 0.28 + 0.50

⇒ Price of Chicken Pie in 1980 = $0.78

Hence, price of chicken pie in 1980 would be ~$0.78

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3 years ago

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