1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lyudmila [28]
3 years ago
12

Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely wit

h x. In the function, the relationship between x and y should be neither inverse variation nor direct variation. Describe the graph of each function and give a real world example for each.
Mathematics
1 answer:
skelet666 [1.2K]3 years ago
3 0
<span>A) First function, y varies directly with x.

1) function: y = (3/4)x

2) graph: it is a straight line that passes through the origin and has slope 3/4. The slope means that the rate of change of the function is 3 units per every 4 units the x-value incresase or, what is the same 0.75 units per incresase unit of x - value.

3) real world example

 A recipe of a cake instructs to use 3 cups of sugar for every 4 cups of flour. So, how much flour you need if you have 12 cups of sugar?

y = (3/4)x , so if x = 3, y = (3/4)*12 = 3*12/4 = 9.

So, given that the variation is direct you multiply the number of cups of sugar times the constant rate, 3/4, to get the number of cups of flour in relation with the given amount of sugar.

B) The second function: y varies inversely with x.

Inverse variation => y*x = constant or y = constant / x.

Tnat means that if x increase y will decrease in the same factor that x increases.

1) function: y = 12 / x

2) graph: the form of this graph is called hyperbola, it is a decreasing line from left to right. It has two asymptotes, the y-axis (x =0) and the x-axis (y = 0). That means that x and y can never be zero.

As the x-value approaches 0, the y value approaches positive or negative infinity;  as the y-values approaches 0 the x-values approaches to positive or negative infinity.

If you take the positive values, the graph is a decreasing curve in the first quadrant (x and y are positive).

If you take the negative values, the graphs is a decreasing curve in the third quadrant (x and y are negative)

3)  real world example.

The relatioship between velocity and time in a uniform motion.

If the distance run by an object is constant, as the velocity increases the time decreases in the same factor.

Suppse a distant of 100  km between cities A and B.

How long will it take to travel from A to B at 50 km/ h and 25 km/h ?:

100 km = velocity * time

at 50 km/h: 100 km = 50 km/h * t => t =  [100 km ] / [50 km/h] = 2 hours

at 25 km/h: 100 kg = 25 km/h * t => t = [ 100 km ] / [25 km/h] = 4 hours.

 C) Third case, the relationship between x and y should is neither inverse variation nor direct variation.

Of course, there are infinite type of functions that are neither inverse variation nor direct variation: linear (that do not passe through the origin), quadratic, exponential, logarithmical, trigonometric sine, ...

1) example of function: y = 30 + 2x

2) graph: it is a straigh line with y-intercept 30 and slope 2.

3) real world example:

The cost of producing chairs consists of 30 dollars of rent for the facility plus 2 dollar to produce each chair, so the total cost y is 30 + 2x.
</span>
You might be interested in
Will mark brainlest! <br>formula of (x+1)cube <br>​
ANTONII [103]

Answer:

(x+1)^3=x^3+3x^2+3x+1

6 0
2 years ago
Read 2 more answers
You flip a coin three times. What is the probability that you get heads all three times? Answer as a simplified fraction use the
Ratling [72]

Answer:

50% chance each time

each tim

6 0
2 years ago
Read 2 more answers
The number of donuts produced by a machine is directly proportional to the time the machine runs . The machine produces 380 donu
mrs_skeptik [129]

Answer:

855 donuts

Step-by-step explanation:

380/20 = 19 donuts per minute

19 × 45 = 855

5 0
3 years ago
Which integral gives the area of the region in the first quadrant bounded by the graphs of y^2 = x − 1, x = 0, y = 0, and y = 2?
r-ruslan [8.4K]
Weird that the only choices are given as integrals with respect to x. (Integration along the y axis would be way easier, but whatever)

The fourth option should do it.
5 0
2 years ago
The value of the figure's surface area is equal to the value of the figure's volume find the value of x. the picture is of recta
emmasim [6.3K]
Surface are of a rectangular prism = 2(l x w + l x h + w x h) = 2(10 x 3 + 10x + 3x) = 2(30 + 13x) = 60 + 26x

Volume of a rectangular prism = l x w x h = 10 * 3 * x = 30x

Since surface area = volume
60 + 26x = 30x
4x = 60
x = 15 in
7 0
3 years ago
Other questions:
  • How do I do vertex in quadratics?How do I graph the quadratic?
    10·1 answer
  • The quotient of y and 2 is greater than -21
    12·1 answer
  • The average wind speed at the weather station of a certain city is 34.4 miles per hour. The
    6·2 answers
  • A student bought a book for $7 and a pen. The total cost was $9. Which of the following equations can be used to find the cost o
    10·2 answers
  • What is the exact value of cos(–60º)?
    12·2 answers
  • The amount of money that college students spend on rent each month is usually between $300 and $600. However, there are a few st
    6·2 answers
  • What is the slope of the line through (-1,2) and (-3,2)
    6·1 answer
  • 2. Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the
    6·1 answer
  • The length of segment AE is 5 centimeters.
    11·1 answer
  • 5th grade math. Correct answer will be marked brainliest.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!