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Thepotemich [5.8K]
2 years ago
6

What is the volume of the triangular prism? A) 15 cm3 B) 18 cm3 C) 21 cm3 D) 24 cm3

Mathematics
1 answer:
algol [13]2 years ago
7 0

Answer:

See Explanation Below

Step-by-step explanation:

The image of the trianglular prism is missing.

However, I'll answer your question using the attachment below.

The volume of a triangular prism is calculated as follows.

V = ½lbh

Where l = length of the prism

b = base of the prism

h = height of the prism

V = volume of the prism.

From the attachment,

Length, l = 6 cm

Base, b = 3 cm

And Height, h = 4 cm

By substituting each of these values in the formula given above

V = ½lbh becomes

V = ½ * 6 * 3 * 4

V = 3 * 3 * 4

V = 36 cm³

If you follow these steps you'll get the volume of the trianglular prism as it is in your question.

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Match each symbol to the appropriate definition. 1. 2. || 3. _I_ (an upside down letter T) a. is parallel to b. is perpendicular
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2. (15 points) Find the volume of the solid generated by revolving the region bounded by the curves x=
dangina [55]

Step-by-step explanation:

First, graph the region.  The first equation is x = 3y² − 2, which has a vertex at (-2,0).  The second equation is x = y², which has a vertex at (0, 0).  The two curves meet at the point (1, 1).  The region should look kind of like a shark fin.

(a) Rotate the region about y = -1.  Make vertical cuts and divide the volume into a stack of hollow disks (washers).

Between x=-2 and x=0, the outside radius of each washer is y₁ + 1, and the inside radius is 1.  Between x=0 and x=1, the outside radius of each washer is y₁ + 1, and the inside radius is y₂ + 1.

The thickness of each washer is dx.

Solve for y in each equation:

y₁ = √(⅓(x + 2))

y₂ = √x

The volume is therefore:

∫₋₂⁰ {π[√(⅓(x+2)) + 1]² − π 1²} dx + ∫₀¹ {π[√(⅓(x+2)) + 1]² − π[√x + 1]²} dx

∫₋₂⁰ π[⅓(x+2) + 2√(⅓(x+2))] dx + ∫₀¹ π[⅓(x+2) + 2√(⅓(x+2)) − x − 2√x] dx

∫₋₂¹ π[⅓(x+2) + 2√(⅓(x+2))] dx − ∫₀¹ π(x + 2√x) dx

π[⅙(x+2)² + 4 (⅓(x+2))^(3/2)] |₋₂¹ − π[½x² + 4/3 x^(3/2)] |₀¹

π(3/2 + 4) − π(½ + 4/3)

11π/3

(b) This time, instead of slicing vertically, we'll divide the volume into concentric shells.  The radius of each shell y + 1.  The width of each shell is x₂ − x₁.

The thickness of each shell is dy.

The volume is therefore:

∫₀¹ 2π (y + 1) (x₂ − x₁) dy

∫₀¹ 2π (y + 1) (y² − (3y² − 2)) dy

∫₀¹ 2π (y + 1) (2 − 2y²) dy

4π ∫₀¹ (y + 1) (1 − y²) dy

4π ∫₀¹ (y − y³ + 1 − y²) dy

4π (½y² − ¼y⁴ + y − ⅓y³) |₀¹

4π (½ − ¼ + 1 − ⅓)

11π/3

As you can see, when given x = f(y) and a rotation axis of y = -1, it's easier to use shell method.

(c) Since we're given x = f(y), and the rotation axis is x = -4, we should use washer method.

Make horizontal slices and divide the volume into a stack of washers.  The inside radius is 4 + x₁, and the outside radius is 4 + x₂.

The thickness of each washer is dy.

The volume is therefore:

∫₀¹ π [(4 + x₂)² − (4 + x₁)²] dy

∫₀¹ π [(4 + y²)² − (3y² + 2)²] dy

∫₀¹ π [(y⁴ + 8y² + 16) − (9y⁴ + 12y² + 4)] dy

∫₀¹ π (-8y⁴ − 4y² + 12) dy

-4π ∫₀¹ (2y⁴ + y² − 3) dy

-4π (⅖y⁵ + ⅓y³ − 3y) |₀¹

-4π (⅖ + ⅓ − 3)

136π/15

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Given that ( x + 5 ) is a factor of the function f ( x ) = x^3 + x^2 − 17x + 15 , find the zeros, and write f ( x ) in factored
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Answer:

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Also, <u><em>(x+5) </em></u>is the factor of given function.

⇒(x+5) divides the function f(x).

∴ <em>(x³+x²-17 x+15) ÷ (x+5) = (x²-4 x+3) </em>  ......(1)

Now, we will factorize x²-4 x+3 to get other zeros of the function f(X).

<em>x²-4 x+3 ⇔ x²-3 x-x+3</em>

⇔ <em>x(x-3)-1(x-3) ⇔ (x-1)(x-3)</em>     ....(2)

hence, <em>x²-4 x+3 ⇔ (x -1)(x-3)</em>

From, equation (1),(2) the factors of<u><em> f(x) = x³+x²-17 x+15 are  (x -1)(x-3)(x-5)</em></u>

7 0
3 years ago
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natta225 [31]

Answer:

10,000

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