Mathematics, 27.09.2019 23:00 bobthebattlebot

The differential equation dy/dx=x
i. will produce a family of quadratic functions.
ii. will produce a family of linear functions.
iii. will produce a family of exponential functions.

answer options
i only
ii only
iii only
none of these
( explain)

Answers: 1

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Answers

Dy/dx
if we find the general antiderivitive
y=(1/2)x²+C
C is a constant
so then it is quaratic
I is answer

I don't think the teacher wanted you to solve it like this so

dy/dx means the slope at x
the slope at x=x is x
might be confusing, but think a little bit
when x increases, the slope at x increases
sounds like an exponential or quadratic
when x decreases, the slope also decreses
when x becomes negative, the slope is negative,
so when x=0, slope is 0
when x>0, slope>0
when x<0, slope<0
we got a parabola
this is quadratic

it isn't exponential because the sloepe in exponential will decrease but never reach zero (only approach it)

answer is I

first option

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

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The differential equation dy/dx=x
i. will produce a family of quadratic functions.
ii....

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