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Arte-miy333 [17]
2 years ago
7

Evaluate the triple integral ∭Tx2dV, where T is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).

Mathematics
1 answer:
bixtya [17]2 years ago
8 0

Answer:

the integral I=81

Step-by-step explanation:

for the integral I

I=\int\limits^{}_{}\int\limits^{}_{}\int\limits^{}_{T} {x^{2} } \, dxdydz

where T is the solid tetrahedron , then

I=\int\limits^{3}_{0}\int\limits^{3}_{0}\int\limits^{3}_{0} {x^{2} } \, dxdydz = \int\limits^{3}_{0}dz\int\limits^{3}_{0}dy\int\limits^{3}_{0} {x^{2} } \, dx = (3-0)*(3-0)*1/3*(3^{3}-0^{3}) = 3^{4} = 81

the integral is equal to 81

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If Jimmy increases a number by 10%, and then decreases this new value by 10%, what percent of the original number will the final
ludmilkaskok [199]
If he increases the number by 10%, he will have 110% of the number. 
Then he reduces it by 10% of the new number, which s 11%. 
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The answer is 99%.
Hope this helps!
8 0
2 years ago
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar
sdas [7]

Complete question:

Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50. Let SSS represent the number of stacks of pancakes that Benjamin buys. 1) Which inequality describes this scenario?

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Cost of chocolate milk = $3.25

Cost of pancakes = $5.50 (stack of 4)

Number of stacks of pancakes purchased = S

Maximum amount spent ≤ $30

Cost of chocolate + (Cost of pancake stack * number of stacks) ≤ $30

3.25 + 5.50S ≤ 30

5.50S ≤ 30 - 3.25

5.50S ≤ 26.75

S ≤ 26.75 / 5.50

S ≤ 4.86

Hence maximum number of pancake stacks he can purchase without exceeding budget = 4

Hence total number of pancakes = number of stacks * number in a stack

= 4 * 4

= 16

6 0
2 years ago
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Answer:

The inglation rate can be calculated as:

R = ((year2 - year1)/year1 )*100%

A)

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B)

Year 1 = $95.00

Year 2 = $97.50

R = (($97.50 - $95.00 )/$95.00 )*100% = 2.6%

C)

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R = (($102.00 - $100.00 )/$100.00 )*100% = 2%

D)

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Year 2 = $89.25

R = (($89.25 - $88.00 )/$88.00 )*100% = 1.4%

E)

Year 1 = $115.50

Year 2 = $117.50

R = (($117.50 - $115.50 )/$115.50 )*100% = 1.7%

Then the order from least to greatest is:

D, E, A, C, B

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