Step-by-step explanation:
Here, the total length of fencing available = 390 yd
Let L = length of the side parallel to river
W = width of other 3 sides.
So, total fencing L + 3 W = 390 yd
or, L = 390 - 3 W
Now, Area of the field = L x W
= (390 - 3 w) (W)
or, A = -3 W² + 330 W
The maximum value of above function is at W =
So, W = 55 yards
Now, L = (390 - 3 (55) ) = 165 yards
Now, maximized area = L x W
= 55 x 165 = 9075 sq yds
II 1
III 2
Answer:
Total number of dozen muffins they both bake is
Step-by-step explanation:
Given : Arthur baked dozen muffins. Nina baked dozen muffins.
We have to find the total number of dozen muffins did they both bake.
To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and number of dozen of muffins Nina bake
That is
Mathematically written as ,
Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake
Given : Arthur baked dozen muffins
and Nina baked dozen muffins.
Total number of dozen muffins =
Simplify, we get,
Total number of dozen muffins =
Adding, we get,
Total number of dozen muffins =
Thus, Total number of dozen muffins they both bake is
1 14/24
B)
1/2
C)
19/12
D)
1 7/12
To simplify the answer and write it as a mixed number is D)1 7/12
To add the fractions 1/6, 3/4, and 2/3, we need to find a common denominator.
The common denominator for 6, 4, and 3 is 12.
Converting the fractions to have a denominator of 12:
1/6 = 2/12
3/4 = 9/12
2/3 = 8/12
Now we can add the fractions:
2/12 + 9/12 + 8/12 = 19/12
The sum of the fractions is 19/12.
To simplify the answer and write it as a mixed number, we divide the numerator (19) by the denominator (12):
19 ÷ 12 = 1 remainder 7
Therefore, the answer is 1 7/12.
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(a) A + B: The result is -4i - 6j, with a magnitude of 2√13 and a direction angle of arctan(3/2).
(b) A - B: The result is -2i + 6j, with a magnitude of 2√10 and a direction angle of arctan(-3).
The given vectors are:
B = -i - 4j
A = -3i - 2j
(a) A + B:
To add two vectors,
Simply add their corresponding components.
So, A + B = (-3i - 2j) + (-i - 4j)
Combining the i-components, we get:
-3i - i = -4i.
And combining the j-components, we get:
-2j - 4j = -6j.
Therefore, A + B = -4i - 6j.
To find the magnitude of A + B,
Use the Pythagorean theorem:
|A + B| = ,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -4 and y = -6,
So: |A + B| =
|A + B| = 2√13
To find the direction angle of A + B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case,
x = -4 and y = -6,
so: θ = arctan(-6 / -4)
θ = arctan(3/2)
Therefore, the magnitude of A + B is 2√13 and the direction angle is arctan(3/2).
(b) A - B:
To subtract two vectors,
Subtract their corresponding components.
So, A - B = (-3i - 2j) - (-i - 4j).
Combining the i-components, we get:
-3i + i = -2i.
And combining the j-components, we get:
-2j - (-4j) = 2j + 4j = 6j.
Therefore, A - B = -2i + 6j.
To find the magnitude of A - B,
Use the Pythagorean theorem:
,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -2 and y = 6,
so:
|A - B| = 2√10
To find the direction angle of A - B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case, x = -2 and y = 6,
so:
θ = arctan(6 / -2)
θ = arctan(-3)
Therefore,
The magnitude of A - B is 2√10 and the direction angle is arctan(-3).
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The complete question is:
For vectors B =−i −4j and A =−3i −2j ,
Calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.
The resulting vectors after adding and subtracting vectors A and B are A + B = -4i - 6j with a magnitude of 7.21 and A - B = -2i + 2j with a magnitude of 2.83. The direction angle for the vectors are calculated using arctan of the absolute value of the components' ratios.
For vectors B = -i - 4j and A = -3i - 2j, you first need to add and subtract these vectors component-wise to get the resulting vectors. Addition gives A + B = -i + (-3i) + -4j + (-2j) = -4i - 6j, whereas subtraction gives A - B = -3i - (-i) + -2j - (-4j) = -2i + 2j.
The magnitude of a vector is calculated by the Pythagorean theorem: (magnitude of A+B) = sqrt((-4)^2 + (-6)^2) = 7.21 and (magnitude of A-B) = sqrt((-2)^2 + 2^2) = 2.83.
The direction angle is found using arctan(|Ay / Ax|), but adjustment must be made depending on the quadrant of the resulting vector. In conclusion, (a) A + B = -4i - 6j, |A + B| = 7.21, angle = arctan(6/4), and (b) A - B = -2i + 2j, |A - B|= 2.83, angle = arctan(2/2).
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