Answer:
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.
In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector
→
A
in a plane is described by a pair of its vector coordinates. The x-coordinate of vector
→
A
is called its x-component and the y-coordinate of vector
→
A
is called its y-component. The vector x-component is a vector denoted by
→
A
x. The vector y-component is a vector denoted by
→
A
y. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:
Step-by-step explanation:
X = 15
X + 90 = 7x
X = 7x - 90
X - 7x = -90
-6x = 90
Divide both sides by -6
X = 15
Answer:
16.2
Step-by-step explanation:
A trick to remember for right triangles is SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Here, we have the side adjacent to the angle and the hypotenuse. So we should use cosine.
cos 22° = 15 / x
x = 15 / cos 22°
x ≈ 16.2
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Answer:
24 units ²
Step-by-step explanation:
In this problem, we are given the circumference of a triangle (after finding the perimeter) and want to find the area of a circle with that circumference. Since the area of a circle is a function based on its radius, we can use the circumference to find the radius to find the area.
First, we can figure out the perimeter of the triangle, which is equal to the sum of its sides. The perimeter is 6+4+7.21 = 17.21 units.
Next, the circumference of a circle is equal to π * diameter = π * 2 * radius. Using 3.14 for π and r for radius, we get
3.14 * 2 * r = 17.21
6.28 * r = 17.21
divide both sides by 6.28 to isolate r
r ≈ 2.74
Furthermore, to find the area from the radius, we can use
area = πr². Plugging 2.74 in for r, we get
2.74² * 3.14 = area
≈23.6, rounding up to 24 units ²
