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Lena [83]
3 years ago
14

Question 13 If the nth term of a sequence is 6n + 4 what is the 9th term?

Mathematics
1 answer:
GarryVolchara [31]3 years ago
4 0

Answer:

Step-by-step explanation:

hello :

the 9th term when : n=9

6(9) + 4 =58

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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
3 years ago
Which of the following numbers is proportional to 84/108?
lara [203]

Proportional numbers are numbers with the same equivalent ratio

98/126 is proportional to 84/108

The number is given as:

Number = \frac{84}{108}

Reduce fraction to the lowest term

Number = \frac{7}{9}

Reduce 86/110 to the lowest term

Number = \frac{86}{110}

Divide by 2/2

Number = \frac{43}{55}

43/55 is not equivalent to 7/9

Reduce 98/126 to the lowest term

Number = \frac{98}{126}

Divide by 14/14

Number = \frac{7}{9}

7/9 is equivalent to 7/9.

Hence, 98/126 is proportional to 84/108

Read more about proportional numbers at:

brainly.com/question/1781657

8 0
2 years ago
Complete the square and write in function form f(x)=x^2+5x+3
Over [174]
F(x) = x^2 +5x + 3

     = (x + 2.5)^2 - 6.25 + 3

     = (x + 2.5)^2 - 3.25

That is vertex form. I am not sure what you mean by function form
6 0
3 years ago
Point A is the midpoint of side XZ and point B is the
Ludmilka [50]

Answer:

4 units

Step-by-step explanation:

just took a quiz and got it right

6 0
3 years ago
Read 2 more answers
Find the sum of all the factors of 32 that are multiples of 4
pshichka [43]
Well all the factors of 32 are 1 and 32, 2 and 16, 4 and 8.
6 0
3 years ago
Read 2 more answers
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