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3 years ago

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

1 answer:

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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The tangent of an angle is not which of the following?

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A salesperson earns a flat monthly salary, plus a percentage of the items sold. Which of the following functions could model the

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Which of the following is an equation of the line through (3, -1) and (−2, 14)?

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3 years ago

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Solve. Check your answer. -3/z + 7/4z = 5/z-25

Anastaziya [24]

[~Answer~] (3.):

Hello there! I'm Avery, and I'm here to help you! I mostly believe the answer Could be: (the answer is in the screenshot. I couldn't write it, so I typed it.)

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Answer Explanation~]:

1:

Combine multiplied terms into a single fraction

Find common denominator

Combine fractions with common denominator

Multiply the numbers

Re-order terms so constants are on the left

Combine exponents

Rearrange terms

Find common denominator

Combine fractions with common denominator

10:

Re-order terms so constants are on the left

11:

Rearrange terms

12:

Multiply all terms by the same value to eliminate fraction denominators

13:

Cancel multiplied terms that are in the denominator

14:

Distribute

15:

Move terms to the left side

16:

Distribute

17:

Subtract the numbers

18:

Rearrange terms

19:

Use the quadratic formula

20:

Simplify

21:

Separate the equations

22:

Solve

Answer: z = $\frac{-50 + 2\sqrt{681} }{7}$

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Last Messages~]:

Okay, I really hope my answer is correct.

I am truly sorry if it's wrong :(

Have a great morning, afternoon, or night. <333

[-!AveryIsSomeHowAlive!-}

7 0

1 year ago

onsider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutti

Sholpan [36]

Answer:

V (max) = 2 ft³

and x side of the base is x = 0,5 feet

Step-by-step explanation: See annex ( two different cubes)

We have a square piece of cardboard of 3 inches wide

Let x be lenght of side to cut in each corner

Then the base of the (future cube) is 3 - 2x, and the area is

( 3 - 2x )²

And the height is x Then volume of the cube as a function of x is:

V(x) = ( 3 - 2x )² *x or V(x) = ( 9 + 4x² - 12x )*x

V(x) = 4x³ - 12x² + 9x

Taking derivatives on both sides of the equation

V´(x) = 12x² - 24x + 9

V´(x) = 0 12x² - 24x + 9 = 0 simplifying 4x² - 8x + 3 = 0

Second degree equation solving for x

x₁,₂ = [ 24 ± √( 576) - 432 /24

x₁,₂ = [24 ±√144 ]/24

x₁,₂ = ( 24 ± 12) /24 x₁ = 1.5 feet x₂ = 0,5 feet

Of these two values we have to dismiss x₁ because if x = 1.5 we don´t have a cube ( 0 height )

Then we take x = 0,5 feet

And

V (max) = (2)²*0,5 = 4*0,5

V (max) = 2 ft³

5 0

3 years ago