Refer to the attachment for complete calculation.
3²× 11^-9
Find the area of a parallelogram with base 15 yards and height 21 2/3
1 answer:
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Answer: nickels = 13, dimes = 7, quarters = 14
<u>Step-by-step explanation:</u>
First, set up the equations for each coin:
Next, the sum of the coins is $4.85 so substitute and solve for the variable:
Nickels + Dimes + Quarters = Sum
(0.30 + 0.05d) + 0.10d + 0.50d = 4.85
0.30 + 0.65d = 4.85
0.65d = 4.55
d = 7
Lastly, plug the d-value into the quantity equation for the nickels and quarters to find their quantity.
nickels: 6 + d = 6 + (7) = 13
quarters: 2d = 2(7) = 14
Answer:
Step-by-step explanation:
As long as the two equations represent the same straight line on the coordinate plane (they overlap), there will be infinite many intersections and infinite number of solutions.
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
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<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.
