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
nydimaria [60]
3 years ago
7

A region is bounded by y=e−3x, the x-axis, the y-axis and the line x = 3. If the region is the base of a solid such that each cr

oss section perpendicular to the x-axis is an equilateral triangle, set up the integral that would find the volume of that solid.
Mathematics
1 answer:
grigory [225]3 years ago
8 0

Answer:

0.333\pi units³

Step-by-step explanation:

Think process:

The equation is given as y = e^{-3x}

Let, y = f (x)

Therefore, f (x) = e^{-3x}

We know that the limits are y-axis and x= 3

Y-axis: x= 0

then limits are given as x= 0 and x = 3

Integrating  gives:

\int\limits^3_0 {e^{-3x} } \, dx = \frac{-1}{3}e^{-3x} + C

calculating from x= 0 to x = 3, we know volume is given by \pi \int\limits^a_b {f(x)} \, dx

= \pi[ \frac{-1}{3} e^{-9}  - (\frac{-1}{3} e^{0})]

= \pi[0.000041136 + 1/3]

= 0.333\pi units³

You might be interested in
How do I find the y intercept in a fraction
Furkat [3]

ANSWER:

Both functions have the same slope

The linear equation does not have a y-intercept

The table and the grahp express an equivalent function

STEP-BY-STEP EXPLANATION:

In order to compare, we must calculate the slope of the table, knowing that the equation in its slope and intercept form is the following:

\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}

The formula to calculate the slope is the following:

m=\frac{y_2-y_1}{x_2-x_1}

The points are (-6, -9/2) and (4,3), replacing:

m=\frac{3-(-\frac{9}{2})}{4-(-6)}=\frac{3+\frac{9}{2}}{4+6}=\frac{\frac{15}{2}}{10}=\frac{15}{20}=\frac{3}{4}

The slope is 3/4

Now, for b

x = 4

y = 3

m = 3/4

replacing:

\begin{gathered} 3=\frac{3}{4}\cdot4+b \\ b=3-3 \\ b=0 \end{gathered}

The equation is:

y=\frac{3}{4}x

Therefore, the true statements are:

• Both functions have the same slope

,

• The linear equation does not have a y-intercept

,

• The table and the grahp express an equivalent function

8 0
1 year ago
Sandy receives a $50000 salary for working as an engineer. If Sandy spends 60% of her
MrMuchimi

Answer:

Step-by-step explanation:

1. 50,000 x .60

2. 50,000 x .60 = 30,000

She spends 30,000 dollars on expenses per year.

6 0
3 years ago
Read 2 more answers
Dennis has 80 nickels and dimes that equal up to $6.60 how many of each coin did he have
Tasya [4]

Answer:

im really confused soryy that i cant help

4 0
3 years ago
Please help me! I am stuck on: How many students does Ms. Keller have in her 6th grade class? How do you know?
mixer [17]
Well there is no background info, it would be impossible to guess
7 0
3 years ago
Read 2 more answers
Find the value of x when the triangle has 9 and 3
DENIUS [597]

Answer:

H²=h²+b²

H²=9²+3²

H²=81+9

H²=90

H=

\sqrt{90}

5 0
3 years ago
Other questions:
  • What is the product.... <br><br> (1.017)•(0.072)=
    10·2 answers
  • Is it 1 solution, no solution or infinite solution? <br> -28 = -7(3x + 4) + 21
    5·1 answer
  • Please explain what the answer is step by step.
    13·2 answers
  • 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the
    8·1 answer
  • The value of 8 in the number 874,500 is how many times greater than the value of 8 in the number 8,745? 10 100 1,000 10,000
    13·1 answer
  • If MO bisects angle PMN, the measure of angle PMN equal 74 and the measure of angle OMN equals 2x + 7, find the value of x
    7·1 answer
  • 2/7-3/8+2/5 Simplify​
    12·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%5E2%3D16" id="TexFormula1" title="\sqrt{x} ^2=16" alt="\sqrt{x} ^2=16" align
    13·1 answer
  • Who want 100 points?
    11·2 answers
  • G. a car travels at 60m/s for 50minutes <br> south west.calculate how far it will travel
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!