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daser333 [38]
2 years ago
6

Use words to describe the following sequence,then find the next 3 numbers in the sequence 49,64,81,11...

Mathematics
1 answer:
solmaris [256]2 years ago
8 0

The next three numbers in the sequence are 121, 144, and 169

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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
A boat travels 30 miles up the river in the same amount of time it takes to travel 38 miles down the same river. If the current
Ksenya-84 [330]
X miles per hour  -  <span> speed of the boat in still water
(x - 2)  -  speed up the river
(x + 2)  -  speed down the river
</span>
\frac{30}{x - 2} = \frac{38}{x + 2}
30 * (x + 2) = 38 * (x - 2)
30x + 60 = 38x - 76
- 8x = - 136
x = 17 miles per hour  -  <span>the speed of the boat in still water.</span>
5 0
2 years ago
2/3 feet is how many inches
leonid [27]

Answer:

(2/3) foot =  8 inches

3 0
2 years ago
Look at the picture please and solve, if its wrong ill report you for just picking a random answer
Sveta_85 [38]

Answer: - (27/40)

Step-by-step explanation:

-(3/8) / (5/9) is the same as -(3/8) × (9/5)

-((3×9) / (8×5))

-(27/40)

7 0
3 years ago
HELP ME PLZZ I NEED HELP WITH THIS AND MAKE SURE YOU EXPLAIN!!!!!!!!!!!!!!!!
Reil [10]

Answer:

C. 7/9 and 0.7 (with bar notation)

Step-by-step explanation:

The division keeps going with the remainder as 7 and 9 can only go into 70 with a 63 so to show the 7 keeps going you would have to use bar notation above 7.

8 0
3 years ago
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