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marishachu [46]
2 years ago
14

PLEASE ANSWER!! A prop for the theater club's play is constructed as a cone topped with a half-sphere. What is the volume of

Mathematics
1 answer:
ira [324]2 years ago
6 0

Answer:

Volume of prop = 706.5 in³

Step-by-step explanation:

Given:

Radius = 5 in

Height = 17 in

Find:

Volume of prop

Computation:

Volume of prop = Volume of cone + Volume of hemi-sphere

Volume of prop = 1/3(π)(r²)(h) + 2/3(π)(r)³

Volume of prop = 1/3(3.14)(5²)(17) + 2/3(3.14)(5)³

Volume of prop = 444.83 + 261.67

Volume of prop = 706.5 in³

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Find three positive consecutive integers such that the product of the smallest and the largest is 17 more than three times the m
trapecia [35]
There are two answers to this question
the first possible answer is 5, 6, and 7 and the second possible answer is -4, -3, and -2


Step-by-step explanation:

let the three numbers be (x-1), x, and (x+1)
the product of the smallest and largest number is 17 more than 3 times the middle number, or
(x-1)(x+1) = 3x+17, or
x^2-1 = 3+17, or
x^2-3x-18 = 0
(x-6)(x+3) = 0
So x = 6 or -3
Then just subtract one and add one to get the other integers. the three numbers are 5, 6, and 7 or -4, -3, and -2
3 0
3 years ago
Drag each tile to the correct box. Vector t, with a magnitude of 4 meters/second and a direction angle of 60°, represents a swim
astraxan [27]

Answer:

From top to bottom, the boxes shown are number 3, 5, 6, 2, 4, 1 when put in ascending order.

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet tell you the magnitude of the sum. For a problem such as this, it is even more convenient to let the calculator give you all the answers at once.

The TI-84 image shows the calculation for a list of vectors being added to 4∠60°. The magnitudes of the sums (rounded to 2 decimal places—enough accuracy to put them in order) are ...

... ║4∠60° + 3∠120°║≈6.08

... ║4∠60° + 4.5∠135°║≈6.75

... ║4∠60° + 4∠45°║≈7.93

... ║4∠60° + 6∠210°║≈3.23

... ║4∠60° + 5∠330°║≈6.40

... ║4∠60° + 7∠240°║≈ 3

_____

In the calculator working, the variable D has the value π/180. It converts degrees to radians so the calculation will work properly. The abs( ) function gives the magnitude of a complex number.

On this calculator, it is convenient to treat vectors as complex numbers. Other calculators can deal with vectors directly

_____

<em>Doing it by hand</em>

Perhaps the most straigtforward way to add vectors is to convert them to a representation in rectangular coordinates. For some magnitude M and angle A, the rectangular coordinates are (M·cos(A), M·sin(A)). For this problem, you would convert each of the vectors in the boxes to rectangular coordinates, and add the rectangular coordinates of vector t.

For example, the first vector would be ...

3∠120° ⇒(3·cos(120°), 3·sin(120°)) ≈ (-1.500, 2.598)

Adding this to 4∠60° ⇒ (4·cos(60°), 4°sin(60°)) ≈ (2.000, 3.464) gives

... 3∠120° + 4∠60° ≈ (0.5, 6.062)

The magnitude of this is given by the Pythagorean theorem:

... M = √(0.5² +6.062²) ≈ 6.08

___

<em>Using the law of cosines</em>

The law of cosines can also be used to find the magnitude of the sum. When using this method, it is often helpful to draw a diagram to help you find the angle between the vectors.

When 3∠120° is added to the end of 4∠60°, the angle between them is 120°. Then the law of cosines tells you the magnitude of the sum is ...

... M² = 4² + 3² -2·4·3·cos(120°) = 25-24·cos(120°) = 37

... M = √37 ≈ 6.08 . . . . as in the other calculations.

4 0
2 years ago
The image is located at the bottom of the screen.
Setler79 [48]

Answer:

..... surface area = 16 km^2.

7 0
3 years ago
There is multiple questions here please help me
Colt1911 [192]
1. a. Unique Solution

2. a. Unique Solution

3. b. No Solution

4. c. Infinitely Many Solutions

5. b. No Solution
4 0
3 years ago
Read 2 more answers
Find the measure of the angle indicated for 17 &amp; 18
marusya05 [52]

Answer:

17. 49

18. 62

Step-by-step explanation:

alright so all u gotta know here is that all triangles add up to 180 degrees

17. 50+83= 133

180-133= 49 degrees

18. 44+74= 118

180-118 = 62 degrees

5 0
2 years ago
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