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GrogVix [38]
2 years ago
12

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

Mathematics
1 answer:
rewona [7]2 years ago
3 0

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 ]

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Angelica's salary this year is 14% higher than it was four years ago. If she earns $46,170.00 this year, what did she earn four
Alona [7]

Answer:

D. $39,706.20

Step-by-step explanation:

In this problem, you are subtracting 14%. A way you could do this is buy finding 14% of $46,170.00, then subtracting that from itself. Or instead, you could find 86%. This works because its like your subtracting 14% from the whole 100%. so 100 - 14 = 86.

Method 1:

$46,170.00 x 0.14 = 6463.8

$46,170.00 - 6463.8 = 39706.2

Method 2:

100 - 14 = 86

$46,170.00 x 0.86 = 39706.2

either way the answer is still correct. i hope this make sense and that it helps you!

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Answer:

$1.12

Step-by-step explanation:

One way to solve this problem is through an algebraic equation. Set up the equation like this, 10-3.28=6x. This equation works because 3.28 is subtracted from 10, which represents how much was spent in total. Then, this is equal to 6x, which represents the total cost of six keys.

So, to solve first subtract 3.28 from 10, this gives you 6.72. Then, divide both sides by 6. This equals 1.12, which is the cost of each key.

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The constant of proportionality is equal to 11.

<h3>Constant of Proportionality</h3>

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In this question, the constant of proportionality is that value that doesn't change or represents the number of players while x represented the number of games they played.

The constant of proportionality can be solved mathematically as

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The constant of proportionality is the value that makes y = 11x and it is 11.

Learn more on proportionality here;

brainly.com/question/28413384

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