How do I do this. I know it’s supposed to be a pattern but it doesn’t make any sense.
1 answer:
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Answer:
distance: 320.624 miles
direction: 43.576°
Step-by-step explanation:
The speed and direction can be found by adding the given vectors.
... 320∠40° + 20∠130°
... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))
... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)
The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.
... = √(232.278² +221.013²)∠arctan(221.013/232.278)
... = 320.624∠43.576°
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A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.
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<em>Comment on coordinate systems</em>
Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.
Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.
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Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.
Answer:
The measures of the angles are
,
and
Step-by-step explanation:
Let
x-----> one angle
y----> the smallest angle
z----> the third angle
we know that
-----> equation A
----> equation B
-----> equation C
substitute equation B and equation C in equation A and solve for y
<em>Find the measure of x</em>
<em>Find the measure of z</em>
therefore
The measures of the angles are ,
and
Answer:
1400ft²
Step-by-step explanation:
Given
Room Dimension: 20 ft by 25 ft by 10 ft
Where Length = 20 ft
Width = 25 ft
Height = 10 ft
Required
Surface area of painted walls and ceiling
We'll assume that the room is rectangular in shape and all 4 sides are covered.
<em>This means that Mickey will paint 4 walls and 1 ceiling.</em>
The dimension of the 2 of the 4 walls is as follows;
20ft by 10ft, 25ft by 10ft,
Because opposite sides of a rectangle are equal, the dimension of the remaining 2 walls is: 20ft by 10ft, 25ft by 10ft
Calculating the area of the 4 walls;
The dimension of the ceiling is as follows:
20ft by 25ft
Calculating the area of the ceiling
So, the area Micky will cover = Area of 4 walls + Area of ceiling
Total Surface Area
Total Surface Area =
Hence, Micky will cover 1400ft²