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2 years ago

A _____________ variable _ on an ____________ variable.

Mathematics

1 answer:

Mkey [24]2 years ago

7 0

A dependent variable depends on an independent variable

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The product of two factors is x2+ 6x + 8. If one of the factors is (x + 4), what is the other factor?

ch4aika [34]

(x + 4) (x + 2)
=x^2 +2x + 4x + 8
=x^2 + 6x + 8
the other factor is (x + 2)

6 0

3 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

The triangles are similar.

MrMuchimi

25/5 = 5
and also
15/3 = 5
so
(3x+ 8)/5 = 4
3x + 8 = 20
3x = 12
x = 12/3
x = 4

answer is x = 4

7 0

3 years ago

Read 2 more answers

Solve each equation <br> 1. 3/4 f + 5 = -5<br> 2.-1/5 b - 2/5 = -2<br> Please show work

anzhelika [568]

Sole for f by simplifying both sides of the equation then isolating the variable so that means f=-40 over 3 for number one

for the second equation you do the same thing you did for number one and the answer will be
b=8

4 0

3 years ago

If f(x) = 3x + –, what is f(a+ 2)?

svetlana [45]

Answer:

Step-by-step explanation:

3 0

2 years ago

A _____________________ variable _________________ on an ____________________ variable.

A _____________ variable _ on an ____________ variable.