Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
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a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
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b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724
Answers:
f(-3) = -1
f(-1) = 2
f(3) = 5
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Explanations:
Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.
Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1
Through similar steps, you should find that f(-1) = 2 and f(3) = 5
Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.
I believe that 1 cup has 8 fluid ounces, and for 3 it is 24 fluid ounces, and for 5 it is 40 fl oz, for 7 it is 56 fl oz
For gallons the first one is 16, for 5 it is 20, for 6 it is 24, and for 7 it is 28.
For the gallon with pint measurement, the first one is 32 pt, the second one is 40, the third one is 48, and the fourth one is 56.
For quarts the first one is 2 pt, the second is 4 pt, the third one is 6 pt, and the fourth one is 8 pt.
Answer: -3
Step-by-step explanation:
Loses means negative. It is getting lesser and if you use a number line and start from zero, you move to the left side of it and get -3. I hope that helps.
Step-by-step explanation:
Claim: There's 14 Goats and 9 Chickens!!
Data:
Working with the Provided Information.
Let the Number of goats be x
let the Number of Chickens be y
x + y = 23..... (i)
Since the goat Possesses Two Pair of Legs... Which is a Total of 4 Legs... We say Let its Contribution be 4x.
The Chicken has Only a Pair Of Legs...Which is a total of 2 legs.... We say let its contribution be 2y
4x + 2y = 74 .....(ii)
BRINGING BOTH EQUATIONS TOGETHER.
x + y = 23
4x + 2y = 74
From Eqn i
x= 23 - y
Substitute into eqn ii
4(23 - y ) + 2y = 74
92 - 4y + 2y = 74
92 - 2y = 74
2y = 92 - 74
2y = 18
y= 9.
Substitute y into any of the eqns to get x
x + y = 23
x + 9=23
x = 23 - 9
x = 14
This simply proves that there are 14 Goats and 9 Chickens!!!.
HAVE A GREAT DAY!