Answer:
angle B = 33.42
Step-by-step explanation:
take angle B as reference angle
using tan rule
tan B = opposite/adjacent
tan B = 6/9
tan B = 0.66
B = 
B = 33.424
B = 33.42
Answer:
1. 5x+10y=35 x= 5 y= 1
2. 2x+12y=30 x= 3 y= 2
Step-by-step explanation:
1. 5x+10y
10+5=15; 15-10=5; x=5
10/5=2; 2/2=1; y=1
5(5)=25
10(1)= 10
25+10= 35
YAY!
2. 2x+12y
12/2=6; 6/2=3; x=3
12/6=2; y=2
2(3)=6
12(2)=24
24+6= 30
YAY!
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:
4 bottles
Step-by-step explanation:
Let o represent the number orange juice bottles Megan bought. Then the total number of juice bottles is ...
o + 12 = 4o
12 = 3o . . . . . . . subtract o
12/3 = o = 4 . . . . divide by the coefficient of o
Megan bought 4 bottles of orange juice.
Answer:
10th of June is their mother's birthday
kimberly remembers that her mother's birthday is after 6th but before 11th of june.
- after 6 is 7, before 11 is 10.
her sister sarah remembers that her mothers birthday is before 16th and after 9th of june.
- before 16 is 15, after 9 is 10.
10 are common on both cases
