If a number is divisible by 4, then it is divisible by 2

Answers

Answer 1

Answer: Yes because 2 is a factor of 4 so if a number is divisible by 4 it’s also divisible by the factors of 4.

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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 swimmer’s motion. Arrange the vectors in ascending order of the magnitudes of their vector sums with the vector t.

Answers

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

_____

Doing it by hand

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

___

Using the law of cosines

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.

Answer:

Going from top to bottom answer is

Z, X, U, Y, V, W

Step-by-step explanation:

I know this is right because I got a 5/5 of the test and I painstakingly solved each problem and my goodness it took a while.

A beluga whale is 5 yards and 3 inches long, and a gray whale is 15 yards and 5 inches long. What is the difference in length between the two whales?

Answers

Answer:

Difference in length between two whales is 362 inches or 10 yards and 2 inches.

Step-by-step explanation:

Lets convert the values to inches:

1 yard = 36 inches

Length of a beluga whale in inches:

5 yards = $5*36$ inches = $180$ inches

Therefore total length of a beluga whale = 180 inches + 3 inches

=183 inches

Length of a gray whale in inches:

15 yards = $15*36$ inches = $540$ inches

Therefore total length of a beluga whale = 540 inches + 5 inches

=545 inches

Difference in length between two whales = 545 inches - 183 inches

= 362 inches

To represent this in yards and inches we can divide the value by 36.

$(362)/(36) =10.06$ yards

=10 yards and 2 inches

Difference in length between two whales is 10 yards and 2 inches.

What is the answer?

Answers

Answer:

C. 2.75P

Step-by-step explanation:

The original value was P.

It increased by 275%. That means it increased by 275% of P.

275% of P = 2.75P

The increase in value is 2.75P.

Now we add the increase to the original value of P to find today's value.

2.75P + P = 3.75P

Answer: C. 2.75P

Write 5⁴ in expanded form. Then share the value of this exponent.

Answers

Answer: 626

Step-by-step explanation:

5x5x5x5 = 625

How does decreasing only the mass change an objects density

Answers

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Materials: Tall clear drinking glass or vase At least four of the following liquids: Fresh water Salt water Vegetable oil Rubbing alcohol Dish soap Honey Corn syrup Milk Maple syrup At least three different small items of your choice, such as: Ping pong ball Small screw, bolt, or nut Popcorn kernel Peanut Blueberry Grape Cherry tomato Instructions: Select four liquids and predict how you think they compare in density by ranking them from most dense to least dense in the data table below. Measure out ¼ cup volume of each liquid, and pour them one at a time into the clear glass or vase. Record your observations in the lab worksheet. Gently add the first small item to the liquids, and record your observation of where it settles. Repeat with the other small items. Clean up all lab materials (the liquids can be poured down the sink), and complete the lab worksheet. Data Table: Prediction: Rank the four liquids from lowest density (top) to highest density (bottom) Observation: Rank how the four liquids really compare, from lowest density (top) to highest density (bottom) Observations: What objects did you place in the liquid, and where did each settle? Object Layer where it settled Observations and Conclusions: Define density, and describe how this activity helps you compare the density of four different liquids without making mass measurements. How did the observations compare to your predictions? Did any of the results surprise you? How would the density of water change if you measured out ½ cup instead of ¼ cup? Explain your answer in complete sentences.

Answers

The less dense liquids and objects will be found at higher levels in the vase.
The density of the water would not change. Density for a substance is constant, regardless of the amount of that substance.

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