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Kazeer [188]
3 years ago
15

Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity

Mathematics
1 answer:
elena55 [62]3 years ago
3 0
So, from our equation
u = e^x
du/dx = e^x du = e^xdxthe integral would be: 

du/(u^2 + 3)

Using the boundaries 1 to infinity
As, e^0 = 1.the solution for this integral will be

(1/(3^0.5)) * arctan(u/(3^0.5))Plugging the boundaries

(1/(3^0.5)) * (90 - 30) = 60/(3^0.5)
=0.6046
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Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest
lidiya [134]
Perimeter: P=62 feet
P=2(b+h)
62=2(b+h)
Dividing both sides of the equation by 2:
62/2=2(b+h)/2
31=b+h
b+h=31   (1)

Area: A=bh   (2)

Isolating h in equation (1)
(1) b+h=31→b+h-b=31-b→h=31-b   (3)

Replacing h by 31-b in equation (2)
(2) A=bh
A=b(31-b)
A=31b-b^2

To maximize the area:
A'=0

A'=(A)'=(31b-b^2)'=(31b)'-(b^2)'=31-2b^(2-1)→A'=31-2b

A'=0→31-2b=0
Solving for b:
31-2b+2b=0+2b
31=2b
Dividing both sides by 2:
31/2=2b/2
31/2=b
b=31/2=15.5

Replacing b by 31/2 in equation (3)
h=31-b
h=31-31/2
h=(2*31-31)/2
h=(62-31)/2
h=31/2

The dimensions are 31/2 ft x 31/2 ft = 15.5 ft x 15.5 ft
The area with these dimensions is: A=(15.5 ft)(15.5 ft)→A=240.25 ft^2

These dimensions are not in the options

1) The first option has an area of: A=(18 ft)(13 ft)→A=234 ft^2
2) The second option has an area of: A=(19 ft)(12 ft)→A=228 ft^2
3) The third option has an area of: A=(17 ft)(14 ft)→A=238 ft^2

The third option has the largest area.

Answer: Third option  
 
4 0
3 years ago
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The crafting club sold art calendars for a recent fundraiser. The table below lists the number of calendars sold by each member
solniwko [45]

Answer:

there is no table below, you have to add a picture

Step-by-step explanation:

3 0
3 years ago
The value of x-y is negative, and x and y are both positive. What can you conclude about the values of x
Stolb23 [73]
Well for two positive numbers subtracted to equal a negative number, the first number must have a value that is less than the second number. (Ex. 3-4= -1) In this case, you can conclude that x is less than y! (x<y)
3 0
3 years ago
Choose the product. -5p 3(4p 2 + 3p - 1) -20p 5 - 15p 4 + 5p 3 -20p 6 - 15p 4 - 5p 3 -20p 5 + 3p - 1 20p 5 + 15p 4 - 5p 3
Likurg_2 [28]
<span>-5p^3(4p^2 + 3p - 1) = -20p^5 - 15p^4 + 5p^3

answer is

A. first one
  </span>-20p^5 - 15p^4 + 5p^3
5 0
3 years ago
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Simplify<br> (3/2x+5) + (5/x-5)
tia_tia [17]

Answer:

(3x + 10) / (2x + 5)(x - 5).

Step-by-step explanation:

(3/2x+5) + (5/x-5)

= [3(x - 5) + 5(2x + 5) ] /  [ (2x + 5)(x - 5)]

= 3x - 15 + 10x + 25 /  (2x + 5)(x - 5)

= 13x + 10 / (2x + 5)(x - 5).

6 0
3 years ago
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