Answer:
Tip = $10.52
Tax = $4.21
Total bill = $67.33
Step-by-step explanation:
We are given the following in the question:
Pre-tax bill = $52.60
Tip to waiter = 20% of the pre-tax amount
Tip to waiter =
Thus, $10.52 was given to waiter.
Tax on bill = 8% of the pre-tax amount
Tax =
Thus, tax on bill was $4.21.
Total bill =
Pre-tax amount + Tax + Tip
Thus, the total bill is $67.33
Let's apply the Law of Cosines here. We want the measure of the angle opposite the side with length 16.
Call that angle C.
Then 16^2 = 36^2 + 28^2 - 2(36)(28)cos C.
Solving for C: cos C = 16^2 - 36^2 - 28^2
------------------------- = 0.904, and C = 0.44 rad
-2(28)(36) or C = 25.21 degrees
So each of the 2 equal angles shown has the measure 25.21 degrees.
Unfortunately, I don't know the direction we should go from this point on.
Answer:
22.8 m/s at 17.4°
Step-by-step explanation:
You want to find the resultant of ...
3 cis 0° +20 cis 20° = (3, 0) +(18.794, 6.840) = (21.794, 6.840)
The magnitude is the root of the sum of the squares of the velocities in the horizontal and vertical directions:
s = √(21.794² +6.840²) ≈ 22.8
The direction is found from the fact that the tangent of the angle is the ratio of vertical to horizontal coordinates:
angle = arctan(6.840/21.794) ≈ 17.4°
The resultant velocity is 22.8∠17.4° meters per second.
Answer:
<h2>
f⁻¹(x) = ∛(x+1)</h2>
Step-by-step explanation:
Given the encoded message defined by the function f(x) = x³-1, the inverse function that the decoder would need when the message is received can be expressed as thus:
let the inverse of the function be represented as y such that y = x³-1.
Making x the subject of the formula from the equation above;
x³ = y+1
Taking the cube root of both sides:
∛x³ = ∛(y+1)
x = ∛(y+1)
replacing y with x:
y = ∛(x+1)
f⁻¹(x) = ∛(x+1)
The encoded message is the inverse function ∛(x+1)