Answer:
-1
Step-by-step explanation:
i^0 =1
i ^1 = i
i^2 =-1
i^3 = -i
It cycles through by 4
so i^4 is back to 1
Take the power , divide by 4 and look to the chart for the remainder
If the remainder is 0 then i to that power is 1
1 i
2 -1
3 -i
i^22
Take 22/4 = 5 remainder 2
The remainder is 2 so i^22 = -1
Answer:
4) 16√3 in²
5) 63 cm²
Step-by-step explanation:
The formula to use in these cases is ...
A = (1/2)ab·sin(θ)
where a, b are the side lengths and θ is the angle between them.
It helps to know the trig functions of the "special" angles used here.
sin(120°) = sin(60°) = (√3)/2
cos(60°) = 1/2
sin(135°) = cos(45°) = (√2)/2
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4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...
x = (8 in)cos(60°) = (8 in)(1/2) = 4 in
So, the bottom edge of the triangle is 12 in - 4 in = 8 in.
The area is ...
A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²
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5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...
x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm
Then the base of the triangle is ...
16√2 cm -9√2 cm = 7√2 cm
The area is then ...
A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²
Answer:
y = - 3x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
9x + 3y = - 9 ( subtract 9x from both sides )
3y = - 9x - 9 ( divide terms by 3 )
y = - 3x - 3 ← in slope- intercept form