The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).
<h3>Vector</h3>
a. Vector (v)
Vector (v)=v (cos Ф, sin Ф)
V=1 while the counterclockwise angle that is measured from positive x=Ф=π/4
Hence:
Vector=3(cos π/4, sinπ/4)
Vector=(3/√2, 3√2)
b. Vector w:
Vector w=1(0, cos 2π/3, sin2π/3)
Vector w=(0, -1/2, √3/2)
Therefore the vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).
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Answer: Alberto run 27 meters.
Time taken By Alberto=3 seconds
Step-by-step explanation:
Let d be the distance Alberto ran to catch Omar.
Then, distance ran by Omar=x-6
Also, 
Since, both started running at the same time.
Time taken By Alberto=
Time taken By Omar=
Now, at the point they meet time taken by both is equal.
Hence, Alberto run 27 meters.
Time taken By Alberto=
=3 seconds
The cups of onion needed to make 56 cups of salsa is 12 cups
<h3>Ratio and proportion</h3>
Fractions are written as a ratio of two integers. Given the following ratio of green pepper, onion, and tomato as 1:3:10
Total ratio = 1+3+10
Total ratio = 14
Given that there are 56 cups of salsa, the cups of onion needed is expressed as:
Cups of onions needed =3/14 * 56
Cups of onions needed = 3 * 4
Cups of onions needed = 12 cups
Hence the cups of onion needed to make 56 cups of salsa is 12 cups
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Answer:
Reserve rate = 3%
Step-by-step explanation:
Reserve Ratio = Reserve Maintained with Central Bank / Deposit Liabilities × 100
Reserve maintained = $6,000
Deposit liabilities = $200,000
Reserve Rate = Reserve Maintained with Central Bank / Deposit Liabilities × 1000
=$6,000 / $200,000 × 100
=0.03 × 100
r=0.03 × 100
=3%
Therefore,
Reserve Rate =3%
