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3 years ago

What is the volume of the prism?

Mathematics

2 answers:

vazorg [7]3 years ago

7 0

Answer:

13 1/8ft³

Step-by-step explanation:

Formula for calculating the volume of a prism is base area × height

Volume = Bh where;

B is the base area

h is the height

Since the base of the prism is rectangular in shape, we will find the area of the rectangle to get the base area.

Base area = length×breadth

Base area = 2 1/2ft × 3 1/2ft

Base area = 5/2×7/2

Base area = 35/4ft²

Since height = 1 1/2ft = 3/2ft

Volume of the prism = 35/4×3/2

Volume of the prism = 105/8ft³

As a mixed number will give;

Volume of a prism = 13 1/8ft³

Arlecino [84]3 years ago

3 0

The answer would be 7 1/2 because you would add 1 1/2, 2 1/2,3 1/2 so there you go

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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

3 years ago

Please help!!! (With one or all the problems, anything is greatly appreciated if you understand probability)

professor190 [17]

Here are the answers to problem 1..

a) 11

b) 5/36

c) 25 Times because 7 has a probability of 16.667%

d) 25 Times because 10, 11, and 12 have a probability sum of 16.667% ironically...

Hope this helps. :)

6 0

3 years ago

Choose the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for

Vanyuwa [196]

The graph that represents the inequality has been shown in the attachment.

<h3>How to solve for the graph</h3>

We have these equations

y ≤ −3x + 1

y ≤ x + 3

We remove the inequality sign from both of these equations

y = −3x + 1

y = x + 3

−3x + 1 = x + 3

such that

x = -0.5

we use this value for x in any of the equations

x + 3 = -0.5 + 3

= 2.5

the point of intersection is at 2.5, -0.5

we test for the origin. 0,0

3x + 1

= 3*0 + 1

= 1

for x + 3

0+3 = 3

This is 0≤1 and 0≤3

Hence the graph should be shaded to the origin.

Read more on a graph here: brainly.com/question/14030149

#SPJ1

7 0

1 year ago

Consider 4x +12 < 28. which value of x makes the given inquality TRUE? A) 3 B) 6 C) 7 D) 10

Pepsi [2]

Answer:

Step-by-step explanation:

4(3)+12=24, which is less than 28, so the inequality would be true

7 0

2 years ago

Read 2 more answers

If 3/5 of a sum of money is 1200. what is the sum

inna [77]

Answer:

2000

Step-by-step explanation:

let the sum=x

3/5 of x=1200

x=1200×5/3=2000

5 0

2 years ago

Read 2 more answers