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xeze [42]
2 years ago
9

Find the domain and range of: {(-2,0), (-1,1), (0,2),(1,3)}

Mathematics
1 answer:
Harman [31]2 years ago
6 0

Answer: domain: {-2, -1, 0, 1}

range: {0, 1, 2, 3}

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Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
hichkok12 [17]

Answer:

\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}

Step-by-step explanation:

Given that:

The surface area (S.A) z = x^2 +y^2

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA

where :

D = cylinder x^2 +y^2 =1

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, \dfrac{\partial z}{\partial x} = 2x and \dfrac{\partial z}{\partial y} = 2y

Therefore;

S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA

= \iint_D \sqrt{1+4(x^2+y^2)} \ dA

= \int^{2 \pi}_{0} \int^{1}_{0}  \sqrt{1+4r^2} \ r \ dr \d \theta

= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0

= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]

\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}

6 0
3 years ago
One week 72 people got a speeding ticket in the next week only 36 people got speeding ticket what is the percent of change inspe
kotykmax [81]
Final - initial/ initial is the formula 
6 0
3 years ago
A man gets an invoice for ​$460 with terms 4/10, ​1/15, n/30. How much would he pay 6 days after the invoice​ date?
7nadin3 [17]

Answer:

$441.60

Step-by-step explanation:

Invoice amount: $460

Term 4/10= 4% discount if paid early within the first 10 days of the invoice date

Amount due: $441.60

Discount amount: $18.40

Invoice amount: $460

Term: 1/15= 1% discount if paid early within the first 15 days of the invoice date

Amount due: $455.40

Discount amount: $4.60

Invoice amount: $460

Term: n/30= no discount if paid on or after the 30 days from the invoice date

Amount due: $460

Discount amount: $0

3 0
2 years ago
Please help I need it now please and thank you
Bingel [31]

Answer:

It would be the first one or second one

Step-by-step explanation:

the answer is up ahead

5 0
3 years ago
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The perimeter of a square closet is 12 m. What is the cost of carpeting it at $7.00 per square meter
snow_lady [41]
Area= 12m * 12m = 144m^2 *7.00$ = 1008$.
Final answer: 1008$
5 0
3 years ago
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