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
What is m∠D ?
Aleksandr [31]
All triangles have angles that add up to 180, so we can take the top triangle, which has angles 14, 45, and x, and say they add up to 180, so 180-14-45=x and x = 121. For E, all angles that look like that and have opposite angles, then these opposites are equal, so both sides of E are 121. then we use the bottom triangle to solve for D with the fact that all triangles' angles add to 180 again. 180-27-121 = D, so D=32
3 0
3 years ago
Read 2 more answers
Help Please: Two boats start their journey from the same point A and travel along directions AC and AD, as shown below: What is
Roman55 [17]

Answer:

  230.9 ft

Step-by-step explanation:

The side ratios of a 30°-60°-90° triangle are 1 : √3 : 2

In ∆ABC, BC = AB/√3 ≈ 115.47 ft

In ∆ABD, BD = AB√3 ≈ 346.41 ft

Then the length CD is ...

  346.41 ft -115.47 ft = 230.94 ft

The distance CD is about 230.9 ft.

8 0
3 years ago
You plan on purchasing a car in the next year. The car that you are interested in lists for $23,000 after taxes, license, and do
oksano4ka [1.4K]

Answer:

c. 8 months.

Step-by-step explanation:

First off let's get the current total of how much we have saved.

2/3 of $23,000 = 15,333.33.

Now we need to get our total salary to calculate for our Social Security and Medicare.

Total Salary : $1312.00 x 2 = $2,624.00

Social Security : 6.2% or 0.062 x 2,624 = $162.69

Medicare : 1.45 or 0.0145 x 2,624 = $38.05

Now that we have our Social Security and Medicare, we can then solve for our taxes.

Taxes: $53 + $101.35 = 154.35 x 2 = $308.7

Now we can add our monthly expenses to the other expenses.

Monthly Expenses : $1,150.12

1,150.12 + 162.69 + 38.05 + 308.7

= $1659.56 Total Expenses.

Now that we have our total expenses we simply subtract it to our monthly salary.

2624.00-1659.56

= $964.44 Extra Money Monthly

Now we proceed to solve for how much more we need to make the total payment.

23000 - 15,333.33

= 7666.67

Now that we have out total balance, we just need to divide the balance to our extra money monthly.

7666.67 / 964.44

= 7.949 Months or 8 Months

6 0
3 years ago
Write the standard form of the equation of the line passing through the point -2, two and perpendicular to the line 5x-y=-4
PtichkaEL [24]

Answer:

..

Step-by-step explanation:

7 0
3 years ago
Bryan's monthly Netflix subscription costs $10. If he charges it
sergij07 [2.7K]

Answer:

$50

Step-by-step explanation:

If he pays $10 every month, and he pays for 5 months, it would be 10 x 5, which means he would be $50 in debt.

4 0
3 years ago
Other questions:
  • What is the APR of a payday loan for $1095 due in 15 days that charges a
    10·2 answers
  • Please help me, due soon ​
    10·2 answers
  • A local truck rental agency advertises the following offer for a medium size truck: flat fee of $30 plus $12.95 per day plus 10
    15·2 answers
  • A cube with 2 inch sides is placed on a cube with 3 inch sides. Then a cube with 1 inch sides is placed on the 2 inch cube. What
    14·1 answer
  • The radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cyliner in terms of π. 6726π
    9·2 answers
  • You buy 6 videos on sale. The videos are on sale for $8 and $10. You spend $52. How many $8 videos did you buy?
    8·2 answers
  • - 27 - 13c=9<br><br><br> would this come out to be a fraction?
    12·1 answer
  • Pls Help me with this property
    8·1 answer
  • Solve for the value of a.
    11·1 answer
  • Our school planned to plant 150 seedlings in a tree planting activity. However,
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!