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2 years ago

Which of the following equations is an example of inverse variation between variables x and y ?

2 answers:

3 0

The option C) y = 15/x

a) y = 15 x is an example of direct variation, with proportionality constant = 15

b) is an example of linear variation (it is the equation of a straight line that does not pass through the origin)

c) y = 15/x => y*x = 15 = constant which is the characteristic of an inverse relation

d) y = x/15 is an example of an inverse relation, with proportion constant = 1/15

WINSTONCH [101]2 years ago

3 0

Answer: Y=15\x

Step-by-step explanation:

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What is the value of x in the equation 7/8x 5/6

Kay [80]

The answer would be
x = 160/147
or
x = 1 and 13/147

3 0

2 years ago

Read 2 more answers

A university is trying to determine what price to charge for tickets to football games. At a price of $ per ticket, attendance

Anika [276]

This question is incomplete, the complete question is;

A university is trying to determine what price to charge for tickets to football games. At a price of $24 per ticket, attendance averages 40,000 people per game. Every decrease of $4 adds 10,000 people to the average number. Every person at the game spends an average of $4 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

Answer:

a) price per ticket = $18

b) 55,000 will attend at that price

Step-by-step explanation:

Given that;

price of ticket = $24

so cost of ticket = 24 - x

every decrease of $4 adds 10,000 people

for $1 adds 2,500 people

Total people = 40000 + 2500x

Revenue function = people × cost + people × 4

R(x) = (40000 + 2500x)(24 - x) + (40000 + 2500x)4

R(x) = 960,000 - 40000x + 60000x - 2500x² + 160,000 + 10000x

R(x) = 1120000 + 30000x - 2500x²

R(x) = -2500x² + 30000x + 1120000

now for maximum revenue; R'(x) is to zero

R'(x) = d/dx( -2500x² + 30000x + 1120000 ) = 0

⇒ -5000x + 30000 + 0 = 0

⇒ -5000x + 30000 = 0

⇒ 5000x = 30000

x = 30000 / 5000

x = 6

R'(X) = -5000 < 0 ⇒ MAXIMUM

∴ Revenue is maximum at x = 6

so cost of ticket ;

price per ticket = (24 - x) = 24 - 6 = $18

so price per ticket = $18

Number of people = 40000 + 2500x

= 40000 + (2500 × 6)

= 40000 + 15,000

= 55,000

Therefore, 55,000 will attend at that price

8 0

2 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

Virty [35]

Hence it is a simply rearrangement of the equation to start with, in order to make  the subject:

This is the graph in 'slope-intercept' form. From here it is easy to see that gradient = and that y-intercept = 490.

The easiest way to draw a straight-line graph, such as this one, is to plot the y-intercept, in this case (0, 490), then plot another point either side of it at a fair distance (for example substitute  = -5 and  = 5 to procure two more sets of co-ordinates). These can be joined up with a straight line to form a section of the graph, which would otherwise extend infinitely either side - use the specified range in the question for x-values, and do not exceed it (clearly here the limit of -values is 0 ≤ x ≤ 735, since neither x nor y can be negative within the context of the question - the upper limit was found by substituting  = 0).

In function notation, the graph is:

The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.

When the profit is higher, the gradient is not changed (this is defined by the relationship between the $2 and $3 prices, not the overall profit) - instead the -intercept is higher:

Therefore we have gleaned that the new y-intercept is.

Clearly I cannot see the third straight line. However the method for finding the equation of a straight line graph is fairly simple:

1. Select two points on the line and write down their coordinates
2. The gradient of the line =
3. Find the change in  (Δ
4. Find the change in  (Δ
5. Divide the result of stage 3 by the result of stage 4
6. This is your gradient
7. Take one of your sets of coordinates, and arrange them in the form , where your  is the gradient you just calculated
8. There is only one variable left, which is  (the y-intercept). Simply solve for this
9. Now generalise the equation, in the form , by inputting your gradient and y-intercept whilst leaving the coordinates as  and

For example if the two points were (1, 9) and (4, 6):

Δ = 6 - 9 = -3
Δ = 4 - 1 = 3
=  = -1
I choose the point (4, 6)
6 = (-1 * 4) + c
6 = c - 4
c = 10
Therefore, generally,

Within the context of the question, I imagine the prices of the two lunch specials will be the same in the third month and hence the gradient will still be  - this means steps 1-6 can be omitted. Furthermore if the axes are clearly labelled, you may even be able to just read off the y-intercept and hence dispose with steps 1-8!

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3 years ago

Tess gets a snow in a cone-shaped container. The container has a diameter of 3 inches 5 inches. If the snow cone consts $0.20 pe

Papessa [141]

Answer:

Step-by-step explanation:

times 3x5 then add 18+20

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3 years ago

8. How many times would an athlete run around the field shown to cover a distance of 2km?

IgorLugansk [536]

Step-by-step explanation:

1km=1000m

so 2×101=202

then divide by 60 min

so 202÷60=3.36

3 0

2 years ago