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pochemuha
3 years ago
11

Find the total volume of the composite figure below. Round to the nearest thousandth.

Mathematics
1 answer:
cestrela7 [59]3 years ago
3 0

Answer:

The volume of the composite figure is approximately 3567.198 cubic feet.

Step-by-step explanation:

The composite figure consists in the combination of a right cone and a cuboid. The volume of the composite (V), in cubic feet, figure can be determined by this expression:

V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h + w\cdot H \cdot l (1)

Where:

r - Radius of the circle of the right cone, in feet.

h - Height of the cone, in feet.

w - Width of the cuboid, in feet.

H - Height of the cuboid, in feet.

l - Length of the cuboid, in feet.

If we know that r = 10\,ft, h = 10\,ft, w = 20\,ft, H = 7\,ft and l = 18\,ft, then the volume of the composite figure is:

V = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)

V = \left(\frac{1000\pi}{3} + 2520\right)\,ft^{3}

V \approx 3567.198\,ft^{3}

The volume of the composite figure is approximately 3567.198 cubic feet.

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Bess [88]

Answer:

  (4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

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  Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4<em>i</em> -8<em>j</em>.

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<em>Additional comment</em>

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4 0
2 years ago
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

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1 year ago
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Answer:

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So 3.2 x 7 = 22.4

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6 0
2 years ago
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What is the area of a trapezoid if the base is 5, 17, 7 and height is 4
posledela
The area of the trapezoid would be 48
5 0
3 years ago
Example 2
PIT_PIT [208]

Answer: (a) 314.2cm², (b) 157.1cm², (c) 78.55cm² (e) 6.77

Step-by-step explanation: (a)  Area of the circle with radius of 10 cm = πr²

                                                                          = 3.142 × 10 × 10

                                                                          = 3.142 × 100

                                                                          = 314.2cm²

The formula                                                       = πr²

(b)  Area of the half of a circle known as semicircle

                                                                         = πr²/2

                                                                         = 3.142 ×10 × 10/2

                                                                         = 3.142 × 50

                                                                         = 157.1cm²

The formula                                                      = πr²/2

(c)  A quarter of a circle is called quadrant

                                                            = πr²/4

                                                            = 3.142 × 10 × 10/4

                                                            = 314.2/4

                                                            = 78.55cm²

The formula is written thus = πr²/4, which implies that the circle is divided into 4 unit

(d) The conjecture about how to determine the area of the sector is

Formula of a sector = ∅/360(πr²)

<u>Information</u>

The arc  cant be 60°, therefore information incomplete.

(e) Area of the sector with the angle AOB of 60° = 24.

To find the radius of the angle, make v the subject of the formula from the formula.

Sector area = πr²∅/360°

equate formula to 24.

Therefore πr²∅/360° = 24

Multiply through by360° to make it a linear expression

It now becomes πr²∅ =24× 360°

                                                     r² = 24  x 360/π × ∅°

                                                     r² = 24 × 360° /3.142 × 60°

                                                     r² = 3,640/188.52

                                                     r² = 45.8

To find r , we take the square root of both side by applying laws of indicies

                                    Therefore r = √45 .8

                                                      r = 6.77

(f)   General formula = ∅°/360° × (πr²)

angle substended at centre by the arc = x°

assuming the radius of the circle = ycm, Therefore,  area of the sector = { ∅°/360° × πy² }

                                                     

                                                   

8 0
3 years ago
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