Answer:
50.2 in^2
Step-by-step explanation:
Using the Formula
A=πr2
d=2r
Solving for A
A= 1/4 π d^2 = 1/4*π*8^2 = 50.26548
=50.2in^2
Answer:
n = 12
Step-by-step explanation:
4/6 = 8/n
4n = 48
n = 12
Answer:
11,400 ft^2
with no allowances for doors or windows
Step-by-step explanation:
ceiling: (35)(40) = 1400
walls: 2(35 x 16) + 2(40 x 16) = 2400
2400 = 1400 = 3800 ft^2
3800 ft^2 x 3 = 11,400 ft^2
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:
a. 18 cm
Step-by-step explanation:
We are given that a circle has an area of 324π cm2. We are required to determine its radius. The formula for the area of a circle with radius r units is;
We plug in the area given and solve for r;
The radius of the circle is 18 cm
