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allsm [11]
3 years ago
6

The average price of a two-bedroom apartment in the uptown area of a prominent American city during the real estate boom from 19

94 to 2004 can be approximated by p(t) = 0.15e0.10t million dollars (0 ≤ t ≤ 10) where t is time in years (t = 0 represents 1994). What was the average price of a two-bedroom apartment in this uptown area in 2002, and how fast was it increasing? (Round your answers to two significant digits.) HINT [See Quick Example 3.]
Mathematics
1 answer:
alexgriva [62]3 years ago
4 0

Answer:

p(t) = 0.19e0.10t

=>p'(t) = 0.19e0.10t (0.10*1)

=>p'(t) = 0.019e0.10t

t = 0 represents 1994

for 2002, t=2002-1994 =8

in 2002

average price =p(8)

=>average price = 0.19e0.10*8

=>average price =0.422853... million

rate of increase =p'(8)

=>rate of increase = 0.019e0.10*8

=>rate of increase =0.0422853... million per year

p(8)=$ 0.42 million

p'(8)=$ 0.042 million per year

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Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= \pi r^2h

According to the problem,

\pi r^2 h=25

\Rightarrow h=\frac{25}{\pi r^2}

The surface area of the base of the can is = \pi r^2

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× \pi r^2)

The lateral surface area of the can is = 2\pi rh

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× 2\pi rh)

                                                 =\$2.5 \pi r h

Total cost of metal is C= 2.00 \pi r^2+2.5 \pi r h

Putting h=\frac{25}{\pi r^2}

\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}

\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}

Differentiating with respect to r

C'=4\pi r- \frac{62.5}{ r^2}

Again differentiating with respect to r

C''=4\pi + \frac{125}{ r^3}

To find the minimize cost, we set C'=0

4\pi r- \frac{62.5}{ r^2}=0

\Rightarrow 4\pi r=\frac{62.5}{ r^2}

\Rightarrow  r^3=\frac{62.5}{ 4\pi}

⇒r=1.71

Now,

\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0

When r=1.71 cm, the metal cost will be minimum.

Therefore,

h=\frac{25}{\pi\times 1.71^2}

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0
3 years ago
At the beginning of year 1 Lisa invests $500 at an annual compound interest rate of 3% she makes no deposits to or withdrawals f
Alenkinab [10]
6((500*.03)+500) this is the answer, I think.
7 0
3 years ago
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15) The diameter of a cylinder is 12 and height is 11. Find the surface area of the figure. ​
kirza4 [7]

Answer:

A=640.88

Step-by-step explanation:

if the diameter is 12, the radius , r=12/2=6

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A=2*3.14*6*11+2*3.14*(6)^2=640.88

7 0
3 years ago
If Radhika adds these two numbers and represents the sum on an abacus, and if the beads on the ten's place are 2 and the beads o
xxTIMURxx [149]

Answer:

Explained below.

Step-by-step explanation:

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8 0
3 years ago
~please help, thank you~
solong [7]
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so volume of cylinder=1/3 times height tiimes pi times radius^2
subsitute
use pi=3.14
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the naswer is the top left choice
6 0
3 years ago
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