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3 years ago

If a sequence contains only whole numbers, which of these sequences could include the term 27?

Mathematics

2 answers:

Dima020 [189]3 years ago

6 0

Answer:

Its 2, 3, 4

Step-by-step explanation:

erik [133]3 years ago

3 0

Depending on the first term, the sequences
$a_n=2a_{n-1}+1
\\
\\a_n=3a_{n-1}
\\
\\a_n=a_{n-1}+6$
would work.

If the sequence began at 6,
$a_n=2a_{n-1}+1=6, 13, 27, ...$

If the sequence began at 1,
$a_n=3a_{n-1}=1, 3, 9, 27, ...$

If the sequence began at 3,
$a_n=a_{n-1}+6=3, 9, 15, 21, 27, ...$

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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

I've tried solving this but I'm stuck -8=2/x

USPshnik [31]

Answer:

-0.25

Step-by-step explanation:

-8= 2/x

multiply both sides by x -> -8x =2

divide both sides by -8 -> x=2/-8

Ans= -1/4 = -0.25

5 0

3 years ago

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What is 1/10 of 1000 what is 1% out of 100

Ulleksa [173]

To get 1/10 -> 1000/10 =100
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3 0

3 years ago

A ceiling light has a cross-section in the shape of a parabola. The parabola is 24 cm wide and 9 cm deep. The lightbulb is locat

Sedbober [7]

Answer:

4 cm

Step-by-step explanation:

The equation of a parabola with its vertex at the origin can be written as ...

y = 1/(4p)x^2

The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.

9 = 1/(4p)(12^2)

9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p

Then p = 4, and the bulb is 4 cm from the vertex.

4 0

3 years ago

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spayn [35]

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3 years ago

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