Question1 Determine whether the equation defines y as a line

Question#1

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. (If an answer does not exist, enter DNE.)

3x = 7y + 6

Yes

No    

y = __________

Question#2

Determine whether the equation defines y as a linear function of x.

Yes

No    

If so, write it in the form

y = mx + b.

(If an answer does not exist, enter DNE.)

y = ___________

Question#3

A manufacturer has a monthly fixed cost of $42,500 and a production cost of $6 for each unit produced. The product sells for $11/unit.

(a) What is the cost function?

C(x)

(b) What is the revenue function?

R(x)

(c) What is the profit function?

P(x)

(d) Compute the profit (loss) corresponding to production levels of 6,000 and 11,000 units.

P(6,000)

P(11,000)

Question#4

Find the point of intersection of the pair of straight lines.

(x, y) = ( )

Question#5

Find the break-even point for the firm whose cost function C and revenue function R are given.

C(x) = 14x + 9,000; R(x) = 23x

(x, y) = ( )

Question#6

An office building worth $3 million when completed in 1997 was depreciated linearly over 50 years; that is, the book value of the building decreases at a constant rate, so that at the end of 50 years the book value is zero.

What was the book value, in dollars, of the building in 2012?
$  

What will be the book value, in dollars, in 2020?
$  

What will be the book value, in dollars, in 2028?
$

Question#7

Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species and the air temperature. When the temperature is 70°F, the crickets chirp at the rate of 120 chirps/min, and when the temperature is 80°F, they chirp at the rate of 160 chirps/min.

(a) Find an equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets.
N = ____________

(b) Use this function to determine the rate at which the crickets chirp when the temperature is 98°F.
___________________ chirps/min

Question#8

A division of the Gibson Corporation manufactures bicycle pumps. Each pump sells for $10, and the variable cost of producing each unit is 40% of the selling price. The monthly fixed costs incurred by the division are $45,000. What is the break-even point for the division? (Round your answers to the nearest whole number.)

(x, y) = ( )

Question#9

The sales of digital cameras (in millions of units) in year t is given by the function

f(t) = 3.04t + 6.86      (0 t 3)

where t = 0 corresponds to the end of 2001. Over that same period, the sales of film cameras (in millions of units) is given by

g(t) = 1.65t + 16.63      (0 t 3).

(a) Show that more film cameras than digital cameras were sold in 2001.

(b) When did the sales of digital cameras first exceed those of film cameras?________________

8

x+4y= 0

Solution

Since 1 Qn per post is allowed, you may post the 2nd Qn separately to get answer to the same.

Question#1

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. (If an answer does not exist, enter DNE.)

3x = 7y + 6

Yes, it does.

No    

Rearrange the equation ,

7y = 3x-6

Divide the whole equation by 7,

y = 3/7 *x -6/7

Compare this to the equation: y = mx+b

Now, slope is m and intercept is b

So, Slope is m = 3/7 and intercept is -6/7 in the equation y = m*x+b