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zalisa [80]
3 years ago
13

Which conjunction or disjunction is equivalent to the given absolute value inequality?

Mathematics
1 answer:
kobusy [5.1K]3 years ago
8 0

conjuction because its an "and" statement.

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Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 36.
rewona [7]

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed  as:

y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}

Thus, the area of the surface is as follows:

\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA

= \iint_D \sqrt{x^2 +y^2 +1 } \ dA

= \int^{2 \pi}_{0} \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr \ d \theta

=2 \pi \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr

= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0

= 2 \pi \times \dfrac{1}{3}  \Bigg [ (37)^{3/2} - 1 \Bigg]

= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]

3 0
2 years ago
on monday, roger drove to work in 20 minutes. on tuesday, he averaged 15 miles per hour more, and it took him 6 minutes less to
ch4aika [34]
Let the distance to his office be x, then
On monday, speed = x/20 miles per minutes = 3x miles per hour
On tuesday, speed = (3x + 15) miles per hour
Time = distance / speed
(20 - 6)/60 hours = x/(3x + 15) hours
7/30 = x/(3x + 15)
7(3x + 15) = 30x
21x + 105 = 30x
30x - 21x = 105
9x = 105
x = 105/9 = 11.7 miles

Therfore he travels an average of 11.7 miles to work.
7 0
3 years ago
What is the alternator-to-engine drive ratio if the
quester [9]

Answer:

720

Step-by-step explanation:

hope it helps

4 0
3 years ago
Read 2 more answers
Need help on this anything will help as this point tbh?!?!
Assoli18 [71]

Answer:

Radius = 1 in

then the volume of bubble = 4/3 π r^3

= (4/3 × 22/7 × 1) in^3 = 88/21 in^3

Hope it helps

5 0
2 years ago
Positive integers are whole numbers that are greater than zero true or false
cestrela7 [59]
False they don't have to be whole numbers. As long as they're greater than 0
4 0
3 years ago
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