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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

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True or false a system of equations including a line and a parabola can have only 2 solutions
Sergio [31]
False, it can have none when the line does not touch the parabola, one when the line touches at one point, and 2 when the line intersects in two places.
3 0
3 years ago
A. A batch of 30 parts contains five defects. If two parts are drawn randomly one at a time without replacement, what is the pro
Zarrin [17]

Answer:

a) For this case on the first trial we have the following probability of selecting a defective part: 5/30. Because we have 5 in total defective at the begin and a total of 30 parts

For the second trial since the experiment is without replacement we have 29 parts left, and since we select 1 defective from the first trial we have in total 4 defective left, so then the probability of defective for the second trial is : 4/29

And then we can assume independence between the events and we have this probability:

(5/30)*(4/29) =0.16667*0.1379= 0.0230

b) For this case on the first trial we have the following probability of selecting a defective part: 5/30. Because we have 5 in total defective at the begin and a total of 30 parts

And since we replace the part selected is the same probability for the second trial and then the final probability assuming independence would be:

(5/30)*(5/30) =0.1667* 0.1667= 0.0278

Step-by-step explanation:

For this case we know that we have a batch of 30 parts with 5 defective.

Part a

If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective?

For this case on the first trial we have the following probability of selecting a defective part: 5/30. Because we have 5 in total defective at the begin and a total of 30 parts

For the second trial since the experiment is without replacement we have 29 parts left, and since we select 1 defective from the first trial we have in total 4 defective left, so then the probability of defective for the second trial is : 4/29

And then we can assume independence between the events and we have this probability:

(5/30)*(4/29) =0.16667*0.1379= 0.0230

Part b

If this experiment is repeated, with replacement, what is the probability that both parts are defective?

For this case on the first trial we have the following probability of selecting a defective part: 5/30. Because we have 5 in total defective at the begin and a total of 30 parts

And since we replace the part selected is the same probability for the second trial and then the final probability assuming independence would be:

(5/30)*(5/30) =0.1667* 0.1667= 0.0278

3 0
3 years ago
There is a bag of 50 marbles. Andre takes out a marble, records its color, and puts it back in the bag. In 4 trails, he gets a g
azamat

Answer:

1/4 or 25%

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Can someone help solve this
sdas [7]
The lnl is an absolute number which basically means it's positive regardless
So now its 7n-7=14
Simply add the 7 to the 14 to get it off the 7n side so you can simplify
Now it's 7n=21
Now just divide
21/7=3
3=N
That means 7 times N=21
8 0
3 years ago
I know the answer but plz explain it. 5:3 × 6:2
stira [4]
5:3 x 6:2 can also be written as a fraction
5/3 x 6/2
Multiply across
30/6
Simplify
5/1
Rewrite
5:1 is your answer, or if your teacher does not want it simplified, 30:6

Hope I helped! :)
3 0
3 years ago
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