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3 years ago

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The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a mo

ving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they’re useful. Research on the Internet, if needed.

1 answer:

valentinak56 [21]3 years ago

3 0

Answer:

Step-by-step explanation:

y = kx represents a proportional relationship between x and y

where,

k is the constant of proportionality

Given:

d = st

Where,

d = distance

s = speed

t = time

The constant of proportionality of the quantities d, s and t is speed(s)

Speed(s) remains constant at a given time and distance

The equation can be written in different forms below:

d = st

S = d/t

t = d/s

Real world example of proportional relationships

• F=ma

Where,

F=Force

m=mass

a=acceleration

F=ma is used to calculate force

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Answer:

The pairs of integer having two real solution for $ax^{2} -6x+c = 0$ are

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$a = 2, c = 3$
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Step-by-step explanation:

Given

$ax^{2} -6x+c = 0$

Now we will solve the equation by putting all the 6 pairs so we get the following

$-3x^{2} -6x-5 = 0$ for $a = -3 , c=-5$

$-4x^{2} -6x+5 = 0$ for $a = -4 , c=5$

$1x^{2} -6x+6 = 0$ for $a = 1 , c=6$

$2x^{2} -6x+3 = 0$ for $a = 2 , c=3$

$3x^{2} -6x+3 = 0$ for $a = 3 , c=3$

$5x^{2} -6x+4 = 0$ for $a = 5 , c=4$

The above all are Quadratic equations inn general form $ax^{2} +bx+c=0$

where we have a,b and c constant values

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for $a = -3 , c=-5$ we have

$Discriminant =-24$ which is less than 0 ∴ not a real solution.

for $a = -4 , c=5$ we have

$Discriminant = 116$ which is greater than 0 ∴ a real solution.

for $a = 1 , c=6$ we have

$Discriminant =12$ which is greater than 0 ∴ a real solution.

for $a = 2 , c=3$ we have

$Discriminant =12$ which is greater than 0 ∴ a real solution.

for $a = 3 , c=3$ we have

$Discriminant =0$ which is equal to 0 ∴ a real solution.

for $a = 5 , c=4$ we have

$Discriminant =-44$ which is less than 0 ∴ not a real solution.

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