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lozanna [386]
3 years ago
10

Evaluate the limit. lim x ? 5 (x-5)^2/x-5

Mathematics
1 answer:
slega [8]3 years ago
7 0
As x approaches 5
hmm, we can divide the (x-5) from top and bottom to get x-5
if we input 5 for x we get
5-5=0
it approaches 0 as x approaches 5
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117. Sami opens an account and deposits $100 into it at the end of each month. The account earns 2% per year compounded monthly.
Sergio [31]

Answer:

The explicit function is:

S_{n} =Pz^{n-1} +C(\frac{z^{n-1}-1}{z-1} )

where

z=(1+\frac{0.02}{12})

and we calculate S12:

S_{12} = $1211.06

Step-by-step explanation:

Expanding a few steps of the compound interest:

S_{1}=100\\S_{2}=S_{1}(1+\frac{0.02}{12})+100\\S_{3}=S_{2}(1+\frac{0.02}{12})+100\\...\\S_{n}=S_{n-1}(1+\frac{0.02}{12})+100

We can write:

(1+\frac{0.02}{12})=z

100=C for deposits

Then, expanding the previous equations would yield:

S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C

This is a geometric series form, which can be simplified to:

S_{n}=C(\frac{z^{n}-1}{z-1} )

plugin in the values for the 12 month gives:

S_{12}=100(\frac{(1+\frac{0.02}{12})^{12} -1}{\frac{0.02}{12}})=1211.0613

6 0
3 years ago
Guys please I need to solve this help me. <br> 100(1+3.13%)7
vitfil [10]

Answer:

107.20

Step-by-step explanation:

7 0
3 years ago
In a coastal town, the humidity, measured in grams of water per kilogram of air, increases by 43% for every 1 degree celsius inc
larisa86 [58]

Answer:

In order to increase humidity by 49.17 grams per kilogram, the increase in temperature will be 18 degree Celsius approx.

Step-by-step explanation:

Initial humidity = 5.75 g/kg

Final humidity= 49.17 g/kg

Percentage increase in humidity= (49.17-5.75)/5.75 *100= 755.13

Increase in temperature= 755.13/43 = 17.56

Increase in temperature = 18 degree Celsius approx.

4 0
3 years ago
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Two points A and B whose heights differ by 10 metres are shown 1.2 cm apart horizontally on a map whose scale is 1: 10 000. a) W
PSYCHO15rus [73]

Answer:

120 meters

Step-by-step explanation:

1.2  x 10 000 = 12000 cm   = 120 meters  

6 0
3 years ago
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What is 1.8×10 + 8.4×10
Vsevolod [243]
1.8*10+8.4*10 is the equation

Basically, you are multiplying 1.8 and 8.4 by itself ten times but here is a tip:

When multiplying by ten, move the decimal once to the right

So 1.8*10=18. and 8.4*10=84.

That leaves 18+84 which is 102

Answer: 102
8 0
3 years ago
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