Answer:
Step-by-step explanation:
To find which one is prime, let's try to factor them all. We can use the factoring by grouping method.
and
and
So this one is not prime, since you can still factor it.
and
and
So this one is not prime, since you can still factor it.
and
and
So this one is not prime, since you can still factor it.
and
and -x+2 cannot be further factored.
Therefore, is a prime.
We have that
tan x=5
we know that
tan x =sin x/ cos x
sin x/ cos x=5------> squaring-----> sin² x/cos² x=25
remember that
sin² x+cos² x=1-----> cos² x=1-sin² x
substitute
sin² x/[1-sin² x]=25
sin² x=25-25*sin² x
26*sin² x=25
sin² x=25/26
sin x=5/√26
cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26
cos x=1/√26
the answers are
sin x=5/√26
cos x=1/√26
A = pi * r^2
D = 2.5 so r = 1.25
A = 3.14 * 1.25^2
A = 4.9 ft^2
Answer:
C. 2.8 miles per minute
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
... Tan = Opposite/Adjacent
In the relevant triangle, the side opposite the angle at the observer is the altitude of the airplane, 2 miles. The side adjacent is the horizontal distance to the airplane. At the first observation, that distance (d1) is ...
... tan(40°) = (2 mi)/d1
At the second observation, the horizontal distance to the airplane (d2) is ...
... tan(50°) = (2 mi)/d2
Solving for d1 and d2 and finding the difference (∆d), we have ...
... d1 = (2 mi)/tan(40°)
... d2 = (2 mi)/tan(50°)
... ∆d = d1 -d2 = (2 mi)(1/tan(40°) -1/tan(50°) ≈ 2·(1.1918 -0.8391) mi
... ∆d ≈ 2°0.3526 mi ≈ 0.7053 mi
This distance was flown by the plane in 15 seconds, so it will travel 4 times this distance in 60 seconds (1 minute).
... ∆d/∆t = (0.7053 mi)/(1/4 min) = 4·0.7053 mi/min ≈ 2.8 mi/min
