Answer:
1, 2, and 4
Step-by-step explanation:
The value of cos 67.4° is 5/13.
According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-
sin(90 - x) = cos x
Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos 67.4° only. Thus we can write the given equation as follows-
sin22.6° = sin(90 - 67.4°)
= cos 67.4°
Thus, sin 22.6° = cos 67.4°
Hence, cos 67.4° = 5/13
Thus, the value of cos 67.4° comes out to be 5/13.
Learn more about trigonometric identities here-
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The function that represents the difference between the moving companies' rates is:
h(x) = -2x + 200.
<h3>How to find the difference of two functions?</h3>
The difference of two functions is found subtracting the like terms from the functions.
In this problem, the functions for the rates are given as follows:
Hence the difference is given by:
h(x) = 3x + 400 - (5x + 200) = 3x - 5x + 400 - 200 = -2x + 200.
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Answer: 8 hours.
Step-by-step explanation:
We have the relation:
Time = distance/velocity
Distance = 50 miles
Velocity in horse = 9mph
Velocity walking = 3 1/2 mph = 3.5 mph
Then, if T is the total time, X is the distance that he travels in horse and Y is the distance that he travels by foot, we have:
X + Y = 50 miles:
T/2 = X/9mph
T/2 = Y/3.5mph
Then we have:
X/9mph = Y/3.5mph
X = Y*(9/3.5)
And by the first relation:
X = 50 mi - Y
then we have:
50mi - Y = Y*(9/3.5)
50mi = Y + Y*(9/3.5) = Y*(1 + 9/3.5) = Y*3.57
Y = 50mi/3.57 = 14mi
Then we have:
T/2 = 14mi/3.5mph
T = 2*(14/3.5) hours = 8 hours
