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2 years ago

Please help me out I will name the brainliest!!!! Answer question 1-8!

Mathematics

1 answer:

klio [65]2 years ago

8 0

Answer:

Step-by-step explanation:

3. function

4. not a function

5. function

6. not a function

7. function

8. not a function

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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

Express ratio as a fraction in simplest form

Zanzabum

Answer:

$\frac{3}{1}$

Step-by-step explanation:

The dimensions must be the same

10 yards = 10 × 3 feet = 30 feet

ratio = $\frac{30}{10}$ = $\frac{3}{1}$

6 0

3 years ago

at a particular school 50% of students travel by bus. if this represents 600 children how many children attend the school

hichkok12 [17]

Answer:

1200 students at the school

Step-by-step explanation:

Let x be the total number of students at the school

50% ride the bus

600 students ride the bus

x*50% = 600

Changing to decimal form

.50x = 600

Divide each side by .5

.50x/.5 = 600/.5

x =1200

1200 students at the school

4 0

3 years ago

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Solve for y .<br><br><br>|y| +8=18

ANEK [815]

Answer:

y=10

Step-by-step explanation:

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3 years ago

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In a class of 30 students 60% said they walk to school

Mekhanik [1.2K]

moan and groan a lot ghjiouygbnjkh

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3 years ago