Solving a system of linear equations, we conclude that the measure of side Z is 2√13
<h3>How to find the measure of side Z?</h3>
Remember the Pythagorean theorem. It says that the square of the hypotenuse is equal to the sum of the squares of the legs.
In the image, we can identify 3 right triangles, and with the Pythagorean theorem, we can write a system of 3 equations.
x^2 = y^2 + 4^2
z^2 = y^2 + 9^2
(4 + 9)^2 = z^2 + x^2
We want to solve that for z.
Now, the second equation can be rewritten to:
y^2 = z^2 - 9^2
Now let's replace the first equation into the third one, so we get:
(4 + 9)^2 = z^2 + (y^2 + 4^2)
Now we can replace y^2 by z^2 - 9^2
(4 + 9)^2 = z^2 + ((z^2 - 9^2) + 4^2)
Now we can solve this:
(13)^2 = z^2 + z^2 - 9^2 + 4^2
(13)^2 + 9^2 - 4^2 = 2*z^2
104/2 = z^2
52 = z^2
√52 = z
√(4*13) = z
√4*√13 = z
2√13 = z
We conclude that the measure of side Z is 2√13
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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 ws: (0, -1/2, √3/2).
The complete question is:
Resolve the following vectors into components:
a. The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.
(b) 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.
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.4 in or 2/5 in per month (.4 and 2/5 means the same one is in decimal and the other one is in fractions.
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Each length of the rope will be 0.8 feet long
