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
DiKsa [7]
3 years ago
12

Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 3). Cro

ss-sections perpendicular to the y-axis are equilateral triangles. V
Mathematics
1 answer:
Reil [10]3 years ago
4 0

Answer:

27/2

Step-by-step explanation:

Given

Vertices (0, 0), (3, 0), and (0, 3)

Since the base of the equilateral in the plane perpendicular to the x-axis goes from the x-axis to the line y = 3 - x.

So, the length of each side of the triangle is (3-x)

Calculating the area;

Area = ½bh

Where b = base = 3 - x

height is calculated as;

h² = (3-x)² + (½(3-x))² --- from Pythagoras

h² = 9 - 6x + x² + (3/2 - ½x)²

Let h² = 0

0 = 9 - 6x + x² + (9/4 - 6/4x + ¼x²)

0 = 9 + 9/4 - 6x - 6/4 + x² + ¼x²

0 = 45/4 - 30x/4 + 5x²/4

0. = 5x²/4 - 30x/4 + 45/4

0 = 5x² - 15x/4 - 15x/4 + 45/4

0 = 5x(x/4-¾) - 15(x/4 - ¾)

0 = (5x - 15)(x/4 - ¾)

5x = 15 or x/4 = 3/4

x = 3 or x = 3

So, h = 3

Area = ½bh

Area = ½ * (3-x) * 3

Area = ½(9-3x)

Volume= Integral of ½(9-3x) {3,0}

V = 9/2 - 3x/2 {3,0}

V = 9x/2 - 3x²/4 {3,0}

V = 9(3)/2 - 3(3)²/4

V = 27/2 - 27/4

V = 27/2

You might be interested in
This is complicated- what is 3x + (-2x)?
allochka39001 [22]
3x + (-2x) would be just subtracting 2x from 3x, so it would be 1x or x. Hope this helped<3
6 0
3 years ago
Read 2 more answers
What is the size of the sample space for flipping 7 coins? Write your answer as a single integer.
Elenna [48]
I think the answer is 6
4 0
2 years ago
Read 2 more answers
A doctor told his patient to drink 3 full cups and 1/2 of a cup of medicine over a week. If each full cup was 4 1/2 pints,how mu
fenix001 [56]
-3x4.5=13.5.    4.5x0.5=2.25

-13.50
+2.25
_____
15.75 pints
6 0
3 years ago
A commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude o
natita [175]

Answer:

x\geq 29,000  and  x\leq 41,000

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

x\geq 29,000

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

x\leq 41,000

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

x\geq 29,000  and  x\leq 41,000

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

5 0
3 years ago
Solve the equation. 6 = 2(x + 8) - 5x<br> A. 2/3 <br> B. 3 1/3 <br> C. - 2/3 <br> D. -3 1/3
Zinaida [17]
6 = 2(x+8) - 5x
⇒ 2x+ 2*8 -5x= 6
⇒ (2x -5x)+ 16= 6
⇒ -3x = 6 -16
⇒ -3x = -10
⇒ x= -10/(-3)
⇒ x= 10/3
⇒ x= 3 1/3

The correct answer is B. 3 1/3~
4 0
3 years ago
Read 2 more answers
Other questions:
  • <img src="https://tex.z-dn.net/?f=1%2F2x%5E3%20%2B%20x%20-7%20%3D%20-3%5Csqrt%7Bx%7D%20%20-1" id="TexFormula1" title="1/2x^3 + x
    10·1 answer
  • a right triangle has a base that measures 39 inches and a height that measures 80 inches what is the length of the hypotense
    13·1 answer
  • What Type of Measure do we use for length
    13·1 answer
  • What is the slope of the line y=1
    13·1 answer
  • Correct answer will get brainliest!
    11·1 answer
  • What is the value of the expression if m
    11·1 answer
  • Determine if the triangles are similar. If similar, state how and complete the similarity stated.​
    8·1 answer
  • Please help me with this question I will give brainliest.
    5·1 answer
  • Find the perimeter of the following shapes <br> 3.6 cm<br> 3 cm<br> 7.2 cm
    13·1 answer
  • I am thinking of a number (s).
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!