1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Llana [10]
3 years ago
8

Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis.

Mathematics
1 answer:
aivan3 [116]3 years ago
3 0

Answer:

0.089

Step-by-step explanation:

f(x) = -ln(x) and g(x) = x²

Start by graphing the region.  The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right.  The region is the triangular area between the curves and above the x-axis.

If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section.  The thickness of this square is dy.  So the volume of the square is:

dV = A dy

dV = s² dy

dV = (x₂ − x₁)² dy

dV = (e⁻ʸ − √y)² dy

The total volume is the sum of all the squares from y=0 to y=0.426.

V = ∫ dV

V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy

Evaluate with a calculator:

V ≈ 0.089

You might be interested in
How do you write this in standard form? (6-7i)/(1-2i)
xenn [34]
\frac { \left( 6-7i \right)  }{ \left( 1-2i \right)  } \cdot 1\\ \\ =\frac { \left( 6-7i \right)  }{ \left( 1-2i \right)  } \cdot \frac { \left( 1+2i \right)  }{ \left( 1+2i \right)  } \\ \\ =\frac { 6+12i-7i-14{ i }^{ 2 } }{ 1+2i-2i-4{ i }^{ 2 } }

\\ \\ =\frac { 6+5i-14\left( -1 \right)  }{ 1-4\left( -1 \right)  } \\ \\ =\frac { 6+5i+14 }{ 1+4 } \\ \\ =\frac { 20+5i }{ 5 } \\ \\ =\frac { 20 }{ 5 } +\frac { 5i }{ 5 } \\ \\ =4+i
8 0
3 years ago
Jans account balance is $2800. She pays $750 for rent. Jan wants to go on vacation but she wants to keep a balance of at least $
joja [24]

Answer:

Step-by-step explanation:

$2800 - $750 = $2050

$2050 - $500 = $1550

$750 rent

$500 vacation savings

$1500 spending money

7 0
3 years ago
Read 2 more answers
Solve for x <br><br><br><br><br><br>.problem down below ​
AleksAgata [21]
A: no solution!

first, simplify each side of the equation.

3x + 5 - 10x simplifies to -7x + 5.
8 - 7x - 12 simplifies to -7x - 4.

then, add +7x on both sides of the equation to get the variable alone. if you add 7x to each side, you get left with 0.

so, that leaves 5 = -4 which is not true. so, that means there is no solution.
5 0
3 years ago
Last night Erin completed 5/6 of the homework assignment. Tom completed 1/3 of the same assignment. How much more of the assignm
Lynna [10]

Answer:

50 more

Step-by-step explanation:

5/6=0.83= 83%

1/3=0.33= 33%

83%-33%= 50

3 0
3 years ago
(30 POINTS AND BRAINLIEST FOR BEST)
Afina-wow [57]

Answer:

Everyone would pay 116.66, but one of them would have to pay one cent extra!

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Katlyn bought a new dress for 34.65 if it was on sale for 23% off what was the original price
    14·2 answers
  • What is the product in simplest form? −5/12⋅8/13
    10·1 answer
  • Which expression is equivalent to (jk)l?
    12·1 answer
  • Circle O is shown. Line segments B D and A C intersect at point O. The length of B O is 5. Angle C O D is StartFraction 4 pi Ove
    12·1 answer
  • What is the square root of 30,300
    8·2 answers
  • Smallest to largest.
    14·1 answer
  • 6 times a number x minus 3 is less than 15 <br> what’s the inequalitys
    10·1 answer
  • -3x^2+12x-8 in vertex form using the completing the square method! ASAP PLEASE WILL MARK U WHATEVER YOU WANT! WORK NEEDED
    9·2 answers
  • What is the answer to -x(-x^3)(-x^3)
    14·2 answers
  • Write down the solution to these simultaneous equations. y=2x + 1 and y= 0.5x - 2
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!