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Triss [41]
2 years ago
7

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off

ered to a buyer, the number of sets sold will increase by 210 per week. (a) Find the function representing the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price. p(x)
Mathematics
1 answer:
GuDViN [60]2 years ago
6 0

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

(B) How large a rebate should the company offer the buyer in order to maximize its revenue?

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

x is quantity sold.

Thus,

R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

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NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she
Goshia [24]

Answer:

The distance from hot air balloon to the ground  AC=50.1457 ft.

Step-by-step explanation:

Labelled diagram of given scenario is shown below.

Given that,

An angle of elevation of Hot air balloon by Angie is 40°.

When she  stepped back 200 ft then angle of elevation was 10°.

Height of Angie is  5.5 ft.

To find: How far off the ground is a hot air balloon.

So, from figure

Height of Angie (BC) = 5.5ft

  In triangle ΔABD,

         ⇒                    tan {40\si {\degree}} = \frac{AB}{BD}

         ⇒                      AB = tan (40) \times BD          ....................(1)

Now, In triangle ΔABE

         ⇒                  tan (10)= \frac{AB}{200+BD}

         ⇒                 AB = tan(10)\times (200+BD)

Here, substituting the value AB from Equation (1) we get,

                        tan(10)\times (200+BD)= tan(40)\times BD

                      tan(10)\times 200+tan(10)\times BD= tan(40)\times BD

        ⇒         BD\times (tan(40)-tan(10))=tan(10)\times 20        

        ⇒                   BD\times 0.6628 = 35.2654

        ⇒                       BD = \frac{35.2654}{0.6628} =53.2067 ft        

Now, finding the value of AB from equation (1)

                                 AB= tan(40)\times 53.2067=0.8391\times 53.2067

                                 AB=44.6457 ft              

Therefore Length of AC= AB+BC = (44.6457 + 5.5) ft

                                  AC=50.1457 ft.

Hence,

The distance from hot air balloon to the ground  AC=50.1457 ft.                

6 0
2 years ago
US
SOVA2 [1]
<h3>Solution:</h3>

{7}^{3} \\   = 7 \times 7 \times 7  \\  = 7^{1 + 1}  \times 7 \\  =  {7}^{2}  \times 7 \\  = 49 \times 7

<h3>Answer:</h3>

49

<h3>Hope it helps...</h3>

ray4918 here to help

6 0
2 years ago
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