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Sidana [21]
3 years ago
11

Please help out with this problem I have. Brainliest answer will be given

Mathematics
1 answer:
Viktor [21]3 years ago
6 0
C I think because the lines intercept at a common point
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Evaluate the integral. W (x2 y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 1) and base vertices at (0, 0, 0), (1, 0,
In-s [12.5K]

Answer:

\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}

Step-by-step explanation:

Given that:

\iiint_W (x^2+y^2) \ dx \ dy \ dz

where;

the top vertex = (0,0,1) and the  base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)

As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)

\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \  dz

\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz

\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0  \ dz \  ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}

\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0  \ dz \  ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz

\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz

\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0

\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}

7 0
3 years ago
50% increase followed by a 33 1/3% decrease
vredina [299]

Answer:

A 50% increase followed by a 33/1/3% decrease. = ? (1 + 0.5)*(1 - 0.3333333) = 1.5 * 0.666667 = 1. Result is same as original.

6 0
3 years ago
Read 2 more answers
Out of 30 questions, Ahmad answer 12 of them incorrectly. What percent of the questions did he answer correctly?
kati45 [8]
First, you would need to determine how many questions he got correct. 
30 - 12 = 18

Next, you would need to create an equation for this problem. Let x represent the unknown percentage. 
\frac{18}{30} = \frac{x}{100}

Now, you would cross multiply. 
30x = 1,800

The last step would be to isolate the x. To do this, you would divide both sides of the equal sign by 30. 
x = 60

Ahmad got 60% of the questions correct. 

I hope this helps!
7 0
3 years ago
Helpppppp I’ll Mark you brainliest
Debora [2.8K]

Answer:

6.32

Step-by-step explanation:

:|

3 0
3 years ago
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Whats 2+2+9+7+10+67+89+572+53+4=?
Sav [38]

Step-by-step explanation:

815..............…......…

7 0
3 years ago
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