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Butoxors [25]
3 years ago
9

If 8^y=16^y+2, what is the value of y? A) -8 B) -4 C) -2 D) -1

Mathematics
1 answer:
Pie3 years ago
6 0
8=2^3;\ 16=2^4

Use:\ (a^n)^m=a^{nm}

8^y=16^{y+2}\\\\(2^3)^y=(2^4)^{y+2}\\\\2^{3y}=2^{4(y+2)}\iff3y=4(y+2)\\\\3y=4y+8\ \ \ |-4y\\\\-y=8\to y=-8

Answer: A) -8.

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There are 95 children at sports camp. 1/5 of children want to play basketball. How many children want to play basketball?
GalinKa [24]
95/5=19 so 19 children wanted to play basketball
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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

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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
3 years ago
It takes most oceans about 6 hours to go from high tide to low tide.Suppose that the water level decreases at a rate of 3 feet p
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Answer:

From the level of high tide to low tide, it's 18 feet.

Step-by-step explanation:

To find the change in water level, we multiply the rate (3 ft / hr) by the time (6 hrs), obtaining 18 ft.

The water level changes by 18 ft.

8 0
2 years ago
Hamish rides his bike at an average speed of 22 km/h. How far does he ride in:
Andrej [43]
1=55 km
2=16.5km
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5 0
3 years ago
Read 2 more answers
Please help I really need it
ratelena [41]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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