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
rosijanka [135]
2 years ago
10

The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

he x-axis is an equilateral triangle, then the volume is
(A) sqrt(3)/8(e^2-1)
(B) sqrt(3)/4(e^2-1)
(C) sqrt(3)/2(e^2-1)
PLS EXPLAIN
Mathematics
2 answers:
FinnZ [79.3K]2 years ago
7 0

Answer:

A.) sqrt(3)/8(e^2-1) <em>i</em><em>s</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>a</em><em>n</em><em>s</em><em>w</em><em>e</em><em>r</em>.

Step-by-step explanation:

<h3>#CarryOnLearning</h3>
yanalaym [24]2 years ago
3 0

Answer:

A

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of <em>y</em> = eˣ, <em>y</em> = 0, <em>x </em>= 0, and <em>x</em> = 1. Each cross-section perpendicular to the <em>x</em>-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each <em>x</em> value. So, we integrate from <em>x </em> = 0 to <em>x </em>= 1.

The area for an equilateral triangle is given by:

\displaystyle A=\frac{\sqrt{3}}{4}s^2

Where <em>s</em> is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at <em>x</em> is simply <em>y</em>, which is eˣ.

Therefore, our volume is:

\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx

Substitute:

\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx

Evaluate the integral. Simplify:

\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx

Integrate using u-substitution:

\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)

Evaluate:

\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)

Therefore, the volume of the solid is:

\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)

Our answer is A.

You might be interested in
A sail is in the form of a right triangle that is four times as high as it is wide. The sail is made from 8 square meters of mat
Sedbober [7]

Answer:

I DON'T KNOW PLEASE PLEASE TELL

4 0
2 years ago
3. I am collecting baseball cards. My goal before I turn 18 is to have 500 cards. When I tumed 10,
vladimir2022 [97]

Based on the scenario given, the equation to describe the situation will be: c + 125 + 89 = 500 and 286 cards need to be collected.

Number of cards given by grandfather = 125 cards

Number of cards that will be given by father = 89 cards

Therefore, based on the information given, the equation to describe the situation will be:

c + 125 + 89 = 500

Therefore, we can then use the equation to calculate the number of cards that need to be collected. This will be:

c + 125 + 89 = 500

c + 214 = 500

c = 500 - 214

c = 286

Therefore, the person needs to collect 286 cards.

Read related link on:

brainly.com/question/24910157

7 0
2 years ago
Change improper fraction to mixed numbers<br><br> Complete A
Elena-2011 [213]

Step-by-step explanation:

<u>Step 1:  Convert improper fraction into a mixed number</u>

\frac{7}{6}

\frac{6}{6} + \frac{1}{6}

1 + \frac{1}{6}

1\frac{1}{6}

Answer: 1\frac{1}{6}

6 0
3 years ago
Read 2 more answers
How do you do this i totaly forgot.
vagabundo [1.1K]

Step-by-step explanation:

7^2+8^2=113

Then square root 113 which is 10.63 to 2.d.p

So x=10.63

5 0
2 years ago
True or False. The area of the trapezoid is 24 sq. inches. (A = 1/2h(b1 + b2) or decompose the figure.
Amanda [17]

Answer:

false

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • The area on a wall covered by a rectangular poster is 294 square inches. The length of the poster is 1.5 times longer than the w
    7·2 answers
  • Help me pls will give lots of points and stuff pls pls pls
    6·2 answers
  • Suppose that each time Diana Taurasi takes a 3-point shot, she has a 37% probability of success, independent of all other attemp
    13·1 answer
  • In speed skating, the distance of 10,000 meters consists of 25 laps. A skater sets the
    14·1 answer
  • 2. George estimates that each bale of hay in his field weighs 62.5 pounds on
    14·2 answers
  • 12x-32/4 can you please help me iam in a rush...thanks!
    13·1 answer
  • In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the e
    11·2 answers
  • Solve the simultaneous equations<br>3x-5y=5​ and x+10y=4
    12·1 answer
  • A + b and 26 (grater then ,less then,or equal to)
    7·1 answer
  • type the correct answer in the Box. Use Roman numerals instead of words. The graphs of functions f and g are shown. Function g i
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!