The composition of two rotations about the same point (Z) is the sum of the rotations. This can be proved using the matrix versions of the rotations.
This means
where
R=rotation operator
z=centre of rotation
t1,t2 are angles of rotation
In this particular case, the composition is commutative, i.e. order does not matter because addition of the angles is also commutative.
Thus substituting values, t1=170, t2=100
So the result of the composition is a rotation of 270 degrees about Z from the original position, which is also equal to a rotation of -90 degrees.
<h2>6</h2>
Step-by-step explanation:
<h3>= 3 × 2 t</h3><h3>= 3 × 2 ( 1 ) <----> ( t = 1 )</h3><h3>= 3 × 2</h3><h3>= 6</h3>
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Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
9)To find the LCD you need to find a number that all of the denominator numbers can divide into, for this problem it would be 12. 12/6+12/4+12/3=1
2+3+4=1
9=1
No solution
10) In order to solve this problem you need to cross multiply
2(3x+5)=7(10
6x+10=70
6x=60
x=10
Have a great day!:)