MATHEMATICS COLLEGE

A small company that manufactures snowboards uses the relation below to model its profit. In the model,represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of

Answers

Answer 1

Answer:

Answer:

a) x₁ = 14

x₂ = - 6

b) x = 4

c) P(max ) = 4000000 $

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x² - 32x - 336 = 0 or x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8 ±√(64) + 336 ]/2

x₁,₂ = [ 8 ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁ = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32

x = 32/8

x = 4 Company has to sell 4 ( 4000 snowboard)

to get a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64 + 128 + 336

P(max) = 400 or 400* 10000 = 4000000

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Janine is packing carrots. Each large box holds 20 2-pound bags of carrots. If janine has 800 bags of carrots, how many boxes can she fill?

Answers

Answer: The number of boxes she can fill is 40

Step-by-step explanation:

Given : Janine is packing carrots. Each large box holds 20 2-pound bags of carrots.

i.e. the number of 2-pound bags of carrots in each box = 20

The number of bags of carrot = 800

The number of boxes she can fill is given by :-

$(800)/(20)=40$

Therefore , the number of boxes she can fill is 40.

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Population the populations P (in thousands) of Las Vegas Nevada from 1960 through 2009 can be modeled by p = 70.751e 0.0451t, where t is the time in years,with t = 0 corresponding to 1960.(a) Find the populations in 1960,1970,1980,1990,2000,and 2009.
(b) Explain why the change in population from 1960to 1970 is not the same as the change in population from 1980 to 1990.
(c) Use the model to estimate the population in 2020.

Answers

Answer:

the answer is below

Step-by-step explanation:

The model is:

$p=70751e^(0.0451t)$ where t is the time in years.

when t=0 (year 1960) $p=70751e^(0.0451*0)=70751$

when t=10 (year 1970) $p=70751e^(0.0451*10)=111071$

when t=20 (year 1980) $p=70751e^(0.0451*20)=174368$

when t=30 (year 1990) $p=70751e^(0.0451*30)=273737$

when t=40 (year 2000) $p=70751e^(0.0451*40)=429734$

when t=49 (year 2009) $p=70751e^(0.0451*49)=644882$

The change in population from 1960to 1970 is 111071-70751 =40320

The change in population from 1980 to 1990 is 273737-174368=99369

The change from 1960to 1970 is not the same as the change from 1980 to 1990 because the model function is not linear, it is exponential. Therefore, the rate of the change is not constant.

The population in 2020 using the model can be estimated as

when t=60 (year 2020) $p=70751e^(0.0451*60)=1059091$

How did you do this question?

Answers

Answer:

R = ∞

I = (-∞, ∞)

Step-by-step explanation:

Use the ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│

lim(n→∞)│x 2n! / (2(n+1)!)│

lim(n→∞)│n! / (n+1)!││x│

lim(n→∞) (1 / (n+1))│x│

The series converges if the limit is less than 1.

The limit is always less than 1, so the radius of convergence is infinite.

So the interval of convergence is (-∞, ∞).

4.1 Number Talk: DivisionFind each quotient mentally.

645 divided by 100

645 divided by 50

48.6 divided by 30

48.6 divided by x

Answers

Answer:

645/100 = 129/20 or 6.45

645/50 = 129/10 or 12.9

48.6/30 = 1.62

48 divided by x = 48.6/x

Step-by-step explanation:

645/100

Factor the number:

= 5*129/100

Factor the number:

= 5*129/5*20

Cancel the common factor:

= 129/20

645/50

Factor the number:

5*129/50

Factor the number:

5*129 / 5*10

Cancel the common factor:

= 129/10

48.6/30

Write the problem in long division format

Multiply the quotient digit (1) by the divisor (30)

Subtract 30 from 48

Add a decimal and bring down the next number

Divide 186 by 30 to get 6

Continue...A few steps later...

Subtract 60 from 60

Solution is 1.62

48.6/x

Re-write division as a fraction:

48.6/x

Help me please!!!!!!!!!!!!!

Answers

Step-by-step explanation:

0 < X < 24

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A sample of 16 items from population 1 has a sample variance 5.8 and a sample of 21 items from population 2 has a sample variance 2.4. Test the following hypotheses at the .05 level of significance. H0: Population 1 Variance < Population 2 Variance Ha: Population 1 Variance > Population 2 Variance a. What is the p-value