Answer:
Step-by-step explanation:
<u>Area Of A Cube </u>
Suppose a cube with side length s, the area of one side is
Since the cube has 6 sides, the total area is
But if we have the area, we can solve the above formula for s to get
We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths
The difference between them is
The side of the cube with area 1,200 square inches is longer then the side of the cube with area 768 square inches
Answer:
Which cost category in the table shows an example of direct variation? WEED-HAND
The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario? Y=63x
What would be the cost for office expenses for 24 months? $1512.00
Step-by-step explanation:
Answer:
the probability that the exceeded 65 = 0.3707
The average score of the 36 golfers exceeded 65
= 36 X 0.3707 = 13.3452
Step-by-step explanation:
<u>Step 1</u>:-
The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3.
mean (μ) = 64
standard deviation (σ) =3
by using normal distribution
given (μ) = 64 and (σ) =3
i) when x =65
P( X≥ 65) = P(z≥0.33)
= 0.5 - A(z₁)
= 0.5 - 0.1293 (see normal table)
= 0.3707
The average score of the 36 golfers exceeded 65
= 36 X 0.3707 = 13.3452
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.
