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2 years ago

Select the correct answer.

Mathematics

2 answers:

sergeinik [125]2 years ago

8 0

Answer:

C. 1:27

Step-by-step explanation:

a²/b²=1/9 => a=1 and b=3

a³/b³=1³/3³=1/27

C. 1:27

RideAnS [48]2 years ago

7 0

I agree with the other answer. Here's another way to see why the answer is 1:27

The surface areas are in ratio 1:9. This means we could have one square that has area 1 and the larger square is area 9.

The smaller square has sides of 1 and the larger square has sides of 3 (square root both area values).

Now if we had a cube that has dimensions of 1 unit, then the volume is 1*1*1 = 1 cubic unit. If we had a larger cube with dimensions of 3 units, then the volume is 3^3 = 3*3*3 = 27 cubic units. We can fit 27 smaller 1x1x1 cubes into the larger 3x3x3 cube.

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37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the

Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy$

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

$D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}$

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}$

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}$

(b) C is the boundary of the region

$D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}$

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}$

• Using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}$

4 0

2 years ago

Given a function described as equation y=3x+4, what is y when x is 1,2 and 3?

koban [17]

Answer:

x=1 y= 7

x=2 y= 10

x=3 y= 13

Step-by-step explanation:

y=3x+4

y=3(1)+4

y=3(2)+4

=-10

y=3(3)+4

=13

4 0

2 years ago

Read 2 more answers

At its lowest point the Euro tunnel is 115m below sea level. At this point, the tunnel is 50m below the sea bed. How deep is the

sweet-ann [11.9K]

Euro tunnel : - 115 (115 m below sea level of 0)

-115 = S - 50
-115 + 50 = S
- 65 = S....the sea bed is -65 m (or 65 m below sea level

8 0

2 years ago

What is the sum of the polynomials? (9x4−13x3−x−7)+(7x3−2x+1) A.) −6x^6+9x^4−3x^2−6 B.)−6x^6+9x^4−x−8 C.)9x^4−6x^3−x−8 D.)9x^4−6

irinina [24]

(9x^4-13x^3-x-7)+(7x^3-2x+1)=
9x^4-13x^3-x-7+7x^3-2x+1=
9x^4+(-13+7)x^3+(-1-2)x-7+1=
9x^4+(-6)x^3+(-3)x-6=
9x^4-6x^3-3x-6

Answer: Option D.)9x^4−6x^3−3x−6

5 0

2 years ago

Read 2 more answers

5x + 3 = 23 5. 4 = 3a – 14 6. 2y + 5 = 19 i need help with this equation

mrs_skeptik [129]

Answer:

Step-by-step explanation:

5x + 3 = 23 x=4

5. 4 = 3a – 14 a=6

6. 2y + 5 = 19 y=7

6 0

3 years ago