Afla suma numerelor 170 si238 572 si279 395si 123 628si 229

Describe the following variation: y/x2=5

Firdavs [7]

We are asked to describe the variation $\displaystyle{ \frac{y}{x^2}=5$ ,

that is $y=5x^2$

for x≠0, in which case x=y=0, we distinguish the following intervals:

I = (-infinity, -1]
II = (-1, 0)
III = (0, 1)
III = [1, infinity)

Case I, consider the cases (examples) x= -5, and x= -6

$5(-6)^2\ \textgreater \ 5(-5)^2$ , so we can conclude that the greater the x, the smaller the y.

Case II, consider x= -1/2 < x=-1/3

$5(-\frac{1}{2})^2= \frac{5}{4}\\\\ 5(-\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \ \frac{5}{4}$

thus, the greater the x, the smaller the y.

Case III, consider the cases (examples) x= 5, and x= 6

$5(6)^2\ \textgreater \ 5(5)^2$ , so we can conclude that the greater the x, the greater the y.

Case III, consider x= 1/3 < x=1/2

$5(\frac{1}{2})^2= \frac{5}{4}\\\\ 5(\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \ \frac{5}{4}$

thus, the greater the x, the greater the y.

Conclusion:

y=0 only if x is 0. Otherwise y>0 always:

for x<0, x and y are inversely proportional

for x>0, x and y are directly proportional.

Remark, an other possible consideration in cases could be x<0 and x>0 only.

Remark, another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.

From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.

4 0

3 years ago

A group of climbers begin climbing at an elevation of 5000 feet and ascend at a steady rate of 1500 vertical feet per hour. This

KatRina [158]

Answer:

Linear function: $y=1500x+5000$

x- Independent variable

y- Dependent variable

Step-by-step explanation:

We are given that

Climbers start climbing at an elevation of height =5000 ft

The steady rate at which climbers start climbing=1500 ft/h

We have to find the independent variable and dependent variable.

Let time taken by climbers=x hours

In 1 hour, climbers cover distance =1500 ft

In x hours , climber cover distance=1500x ft

According to question

The total distance y covered by climber in x hours

$y=1500x+5000$

This is required linear function.

We can see that

x does not depend on any other quantity.Therefore, x is independent variable .

When the value of x changes then the value of y is also change.

It means the value of y depends on the value of x.

Therefore, y is dependent variable.

8 0

4 years ago

The graph below shows the height of a kicked soccer ball f(x), in feet, depending on the distance from the kicker x, in feet: Pa

Advocard [28]

the complete question in the attached figure

part A

the x intercept 0 is the point where the ball was hit, the x intercept 20 is the point where the ball fell back to the ground, 20 feet away from the kicker.

<span>the function is increasing in the interval x∈(0, 10) and decreasing in x∈(10, 20) </span>
this means that the height is increasing in the interval (0, 10) and decreasing as x goes through the interval (10,20)
the distance from the kicker is increasing during the whole interval (0, 20)

part B

the rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases or increases in the interval

x =[A, B]

from x = 22 to x = 26-------------- > the function does not exist