Answer:
Triangle ABC has been translated 1 unit to the left and 4 units up
Step-by-step explanation:
Choose one of the points, for example B, and follow the units to B prime and see how many units vertically and horizontally the point as been translated.
Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
__
We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
Answer:
$131.71
Step-by-step explanation:
Given:
Original price: $234.45
Markdown: 78%
---------------------------------------------------------------------------
Actual Selling Price: 131.71
Markdown: 102.74
-------------------------------------------------------------------------
The opposite angles of a quadrilateral inscribed in a circle adds up to 180°.
This means that angles A and C add up to 180°, so do angles B and D.
Therefore, (x - 10) + (x - 2) = 180°
2x - 12 = 180°
2x = 192°
x = 96°
Hence,
Angle A = 96° - 10° = 86°
Angle B = 180° - (96° + 2°) = 82°
Angle C = 96° - 2° = 94°
Angle D = 96° + 2° = 98°
