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2 years ago

vector w has magnitude 25.0 and direction angle 41.7 degrees. Calculate the horizontal and vertical components of w

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

5 0

Consider the attached picture. It represents a vector, centered in the origin with angle 41.7 degrees, and a circumference with radius 25, centered in the origin.

As you can see, the horizontal and vertical components of the vector correspond to the lengths of segments OD and OC, respectively.

You might recognize this scenario from you trigonometry class: if the circle had radius 1, we would have

$OD=\cos(41.7),\quad OC=\sin(41.7)$

Since the circle has radius 25, we have to scale those coordinates:

$OD=25\cos(41.7),\quad OC=25\sin(41.7)$

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2 years ago

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LESSON 1 SESSION 1

denpristay [2]

Answer:

Between which two tens does it fall? Between 25 and 26 tens

Between which two hundreds does it fall? Between 2 and 3 hundreds

Explanation:

The place-value chart is:

Hundreds Tens Ones

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a) Between which two tens does it fall?

Using the place values you can write 253 = 25 × 10 + 3, i.e. 25 tens and 3 ones.

From that you can write:

250 < 253 < 260

250 = 25 × 10 = 25 tens

260 = 26 × 10 = 26 tens

Then, you conclude that 253 is between 25 and 26 tens.

b) Between which two hundreds does it fall?

Using the same reasoning:

253 = 2 × 100 + 5 × 10 + 3 = 253

200 < 253 < 300

200 = 2 hundreds

300 = 3 hundreds

Conclusion: 253 is between 2 hundreds and 3 hundreds.

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2 years ago

There are 8 sophomores on the academic team. At the last competition, they each took the math test. Their scores were 82%,

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Answer:

79%

Step-by-step explanation:

median is the middle no.

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78+80, divide 2= 79%

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Answer:

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Step-by-step explanation:

The key is transforming values from this distribution to a z-score range and finding the corresponding value using a z-score table.

We are looking for a value x which attains a critical z-score that corresponds to the (100-45)%=55-th percentile:

$z_{0.55} = \frac{x-\mu}{\sigma}=\frac{x-140}{18}\implies x = 18\cdot z_{0.55}+140$

The critical z value (from z-score table, online) is: -0.12, so:

$x = 18\cdot z_{0.55}+140=18\cdot(-0.12)+140\approx137.84$

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