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3 years ago

Which equation describes a relationship that is directly proportional?

Mathematics

1 answer:

mixer [17]3 years ago

3 0

Answer:

(C) y = 3x

Step-by-step explanation:

Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.

example of such relation can be y = kx

where k is the constant of proportionality which depicts by how much value of y will change in response to change of x.

_______________________________________________

now in the option

A and B

y= 9 , y =1/5

value of y is constant and does not depend on other variable. it value will remain same.

for y = x+4

value of y increases with x but it does not increase proportionally.

let see an example for x =1 , y = 1+4 = 5

x =2 , y = 2+4 = 6

(1,5) and (2,6) are not proportionally changing also this equation is not of form y = kx

thus, it is incorrect option.

_______________________________

here equation is form y =kx . in place of k there is 3

let see an example for x =1 , y = 3*1 = 3

x =2 , y = 3*2 = 6

(1,3) and (2,6) are proportionally changing (1/3 = 2/6) also this equation is of form y = kx

thus, it is correct option.

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Which ratio is greater? 3 : 4 or 5:6

olga55 [171]

Answer:

5:6 is greater than 3:4.

4 0

3 years ago

A circular pool with a 10 foot diameter is surrounded by a deck. What is the area of the deck which surrounds the pool? use 3.14

zavuch27 [327]

Answer:

146.5 sq. feet.

Step-by-step explanation:

Area of the deck = Large Square (with 15 ft side) - Circular Pool (with radius 10/2=5)

Large Square area = $s^2=(15)^2=225$

Circular Pool area = $\pi r^2=\pi (5)^2=\pi (25)\\=25(3.14)\\=78.5$

Thus, area of deck surrounding pool = $225-78.5=146.5$ sq. feet

7 0

4 years ago

Read 2 more answers

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

Select an appropriate display for each situation. Justify your reasoning.

Igoryamba

A good display to use for his situation is a bar chart. It will show the number of students that like each flavor so they are easy to compare.

5 0

3 years ago

As I was sitting on a dock, I noticed that the wavelength of the waves were about 6 m long. The crest

torisob [31]

Answer:

IT IS C I BET YOU 6 AND 8

Step-by-step explanation:

7 0

3 years ago