Make 11/3 into a mixed number
2 answers:
You might be interested in
Using the determinant method, the cross product is
so the answer is B.
Or you can apply the properties of the cross product. By distributivity, we have
(3i + 8j - 6k) x (-4i - 2j - 3k)
= -12(i x i) - 32(j x i) + 24(k x i) - 6(i x j) - 16(j x j) + 12(k x j) - 9(i x k) - 24(j x k) + 18(k x k)
Now recall that
- (i x i) = (j x j) = (k x k) = 0 (the zero vector)
- (i x j) = k
- (j x k) = i
- (k x i) = j
- (a x b) = -(b x a) for any two vectors a and b
Putting these rules together, we get
(3i + 8j - 6k) x (-4i - 2j - 3k)
= -32(-k) + 24j - 6k + 12(-i) - 9(-j) - 24i
= (-12 - 24)i + (24 + 9)j + (32 - 6)k
= -36i + 33j + 26k
The area of the shaded region in the given image is: 1,111.84 ft²
<h3>How to Find the Area of a Shaded Region?</h3>To find the area of the shaded region in the image given, find the areas of the unshaded region, then subtract it from the total area of the whole figure.
Area of the total figure = area of two semicircles + area of the rectangle.
Dimensions of the rectangle is given as, 18ft x 22ft.
Area of the rectangle = 18ft × 22ft = 396 ft²
The diameter of each of the semicircle = 7 + 7 + 18 = 32 ft
The radius of each of the semicircle = 1/2(32) = 16 ft
Area of the two semicircles = 2(1/2 × πr²) = 2(1/2 × 3.14 × 16²)
Area of the two semicircles = 803.84 ft²
Area of the rectangle = 32 × 22 = 704 ft²
The total area = 704 + 803.84
The total area = 1,507.84 ft²
The area of the shaded region = 1,507.84 - 396
The area of the shaded region = 1,111.84 ft²
Learn more about area of shaded region on:
#SPJ1
