Answer:
as below
Step-by-step explanation:
to find the height of the pole recall the relationship of sin cos and tan to the triangle with this helpful mnemonic SOH CAH TOA
Sin = Opp / Hyp
Cos = Adj / Hyp
Tan = Opp / Adj
we will need to solve two triangles and subtract them.
one is the 15° one of the slope of the road and the other is the 57° one that is the angle of the sun. sooooo,
lets solve the 15° one first. We are told that the adj side is 75'
since we know the angle and the adj side and we want to find the Opp side let's use Tan b/c it has all of those in it :)
Tan(15) = Opp / 75
75*Tan(15) = Opp ( I'll put my calculator to work for this )
20.096 = Opp
that's the height of the road to the bottom of the flag pole along that flag pole axis into the ground
next lets solve the 57° triangle in the exact same way
Tan(57) =Opp / 75
75*Tan(57) = Opp
115.4898 = Opp
the tall triangle is the one that goes all the way into the ground, the small one is the one that is under the ground
so subtract the small one from the big one to find the height of the flag pole above the ground
115.4898-20.096 = 95.3938
so the flag pole is about 95.4 feet tall
:o that's pretty tall :
The answer is -8
====================================================
Explanation:
There are two ways to get this answer
Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8
-----------------------
The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4
g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8
Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8
Regardless of which method you use, the answer is -8
Answer:
Step-by-step explanation:
3 coins make for 8 possible outcomes {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
4 Possible outcomes conatin 2 or more heads.
Probability (At least 2 Heads) = Favourable outcomes/Total possible outcomes
= 4/8 = 1/2 = 0.5 (50%)
Answer:
Triangle 1: x = 80 degrees, acute
Triangle 2: x = 10 degrees, right
Step-by-step explanation:
Triangle 1:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:
Solve for x:
So, x = 80 degrees
Because all the angles are less than 90 degrees, this is an acute triangle.
Triangle 2:
By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation (with the right angle given):
Solve for x:
So, x = 10 degrees
Because there is an angle measuring 90 degrees, this is a right triangle.
