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guajiro [1.7K]
2 years ago
12

Tom started an entertainment company. The net value of the company (in thousands of dollars) ttt months after its creation is mo

deled by v(t)=4t^2-24t-28v(t)=4t 2 −24t−28v, left parenthesis, t, right parenthesis, equals, 4, t, squared, minus, 24, t, minus, 28 Tom wants to know when his company will be at its lowest net value. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. v(t)=v(t)=v, left parenthesis, t, right parenthesis, equals 2) How many months after its creation does the company reach its lowest net value? months
Mathematics
1 answer:
Furkat [3]2 years ago
8 0

Step-by-step explanation:

Given the expression for the net value of an entertainment company after t months modeled by the equation;

v(t)=4t²-24t-28

1) To write the expression in a factored form, we need to factorize the equation given;

v(t)=4t²-24t-28

divide through by 4

v(t)=t²-6t-7

v(t)= t²-7t+t-7

v(t)= t(t-7)+1(t-7)

v(t)= (t+1)(t-7)

Hence the function in a factored or vertex form is v(t)= (t+1)(t-7)

2) To know the number of months after the company creation that the company reaches its lowest value, we will substitute v(t) = 0 into the factored form of the expression as shown;

v(t)= (t+1)(t-7)

0 = (t+1)(t-7)

(t+1)(t-7) = 0

t+1 = 0 and t-7 = 0

t = -1 and t = 7

But t cannot be negative

Hence t = 7 months

This means that the company reaches its lowest net value after 7 months

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The value 3 will be entered. It's a positive value to indicate he is not in debt of any kind. 
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2 years ago
Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0
2 years ago
A dealer paid $10,000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction pri
pickupchik [31]
<span>Given situation:
=> A deadler paid $10 000 for a boat at an auction.
=> At the dealership, a sales person sold the boat for 30% more than the auction price
=> 10 000 dollars + 30%
=> Then the salesperson received a commission of 25% of the difference between the auction price and the dealership price
=> 10 000 + 25%
Let’s find the solution
=> 10 000 x .30 = 3000
=> 10 000 + 3 000 = 13 000, he sell it for this price
=> then he received a commission
=> 13 000 – 3 000 = 10 000
=> 10 000 x .25
=> 2500 , his commission </span>



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2 years ago
The graph shows the function representing the recommended amount of mulch, in cubic yards, for circular flowerbeds based on the
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Answer: 13

Step-by-step explanation:

4 0
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A random draw is being designed for 210 participants. A single winner is to be chosen, and all the participants must have an equ
Over [174]

Answer: The correct number of balls is (b) 4.

Step-by-step explanation:  Given that a single winner is to be chosen in a random draw designed for 210 participants. Also, there is an equal probability of winning for each participant.

We are using 10 balls, numbered through 0 to 9. We are to find the number of balls which needs to be picked up, regardless of order, so that each of the 210 participants can be assigned a unique set of numbers.

Let 'r' represents the number of balls to be picked up.

Since we are choosing from 10 balls, so we must have

^{10}C_r=210.

The value of 'r' can be any one of 0, 1, 2, . . , 10.

Now,

if r = 1, then

^{10}C_1=\dfrac{10!}{1!(10-1)!}=\dfrac{10!}{1!9!}=\dfrac{10\times 9!}{1\times 9!}=10

If r = 2, then

^{10}C_2=\dfrac{10!}{2!(10-2)!}=\dfrac{10!}{2!8!}=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}=45

If r = 3, then

^{10}C_3=\dfrac{10!}{3!(10-3)!}=\dfrac{10!}{3!7!}=\dfrac{10\times 9\times 8\times 7!}{3\times 2\times 1\times 7!}=120

If r = 4, then

^{10}C_4=\dfrac{10!}{4!(10-4)!}=\dfrac{10!}{4!6!}=\dfrac{10\times 9\times 8\times\times 7\times 6!}{4\times 3\times 2\times 1\times 6!}=210.

Therefore, we need to pick 4 balls so that each participant can be assigned a unique set of numbers.

Thus, (b) is the correct option.

4 0
2 years ago
Read 2 more answers
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