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2 years ago

The difference of three times a number and five is four. Find the number

Mathematics

1 answer:

givi [52]2 years ago

4 0

The difference of three times a number and five is four. Then the number is 3

<u>Solution:</u>

Given that,

Difference of three times a number and five is four

We have to find the number

Let us frame a equation using the given information and solve the sum

Let the number be "n"

Difference of three times a number and five = 4

Three times n - 5 = 4

3n - 5 = 4

3n = 9

On dividing 9 by 3 we get 3

n = 3

Thus the required number is 3

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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)

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

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

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

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

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

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

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

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3 years ago

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Answer:

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3 years ago

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marishachu [46]

Answer:

Step-by-step explanation:

5 - 3(-2) + 1-3

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2 years ago

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For each question (a–e) below, choose one of the answers (i–viii); explain your choice.

Natasha2012 [34]

Answer:

Step-by-step explanation:

given that a deck of cards is shuffled.

we know in a deck there are 52 cards, 13 cards of each variety spade, clubs hearts and dice. Red are 26 and black are 26. kings, will be 4.

(a) the top card is the king of spades and the bottom card is the queen of spades?

(iii) 1/52 × 1/52

Top has 1/52 and bottom has 1/52 and these are independent.

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(viii) None of the above

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(vii) 2/52 × 1/51

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3 years ago

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nydimaria [60]

Answer with Step-by-step explanation:

We are given that

$f(x)=\mid x-9\mid$

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LHD

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= $-\lim_{x\rightarrow 9-}(x-9)=-1$

RHD

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3 years ago