This is adding two vectors, one magnitude 300 direction east, and one magnitude 100 direction 30 degrees northeast.
For the resulting sum we can use the Law of Cosines or just add up the components. Let's try it both ways.
Components first. In the east direction we have
300 + 100 cos 30° = 300 + 100(√3/2) = 386.60 miles per hour
In the north direction we have
0 + 100 sin 30° = 100 (1/2) = 50 miles per hour
So a total speed of
sqrt{386.6^2 + 50^2} = 389.82 miles per hour
Answer: 389.82
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OK let's try the Law of Cosines. We have sides 300 and 100 and included angle 150°.
Answer: ( 0, 2 )
Step-by-step explanation:
You have to put coordinates of each graph on these equations y = -x + 2 and y = (1/2)x + 2. If putting coordinates satisfies both equations, then that coordinate will be the solution.
For example, let's put (0, 2) to equations.
y = -x + 2
2 = -0 + 2
2 = 2, true
y = (1/2)x + 2
2 = (1/2) × 0 + 2
2 = 2, true
So, ( 0, 2 ) is the solution.
Answer:
-56
Step-by-step explanation:
Formula to get determinant is::
![\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20ad-bc)
0(0)-8(7)
0 - 56
-56
Answer:
The pairs of functions that best represent the equation are f(x)=x² and g(x)=1/x
Step-by-step explanation:
For this problem, you will have to multiply each equation in the answer choices until you find the pair that has a product of x.
Let's start with the first answer choice.
(f * g)(x)
<em>f(x)=x²</em>
<em>g(x)=1/x</em>
Now, we multiply these terms together.
x² * 1/x = x²/x
Now, divide x from x². When you are dividing exponents, the exponential numbers subtract. So, since there is no exponent on x, then we assume this exponent to be 1. So, when dividing you will subtract 1 from 2.
x²/x = x
So, the answer to the problem is answer choice A. These functions multiply together to get you a final product of x.
