So if you means 33-55=-22
-22/11=x
so when dividing by a negative, just divide as usual, but just make the answer negative so
-22/11=22/11 times -1/1=2 times -1=-2
the answer is -2
Answer:
The possible values of x are 90°, 30° and 150°.
Step-by-step explanation:
Given that,
sin(2x) = cos(x) where 0° ≤ x < 180°
We know that, sin(2x) = 2 sinx cosx
2 sinx cosx = cosx
Subtract cosx on both sides
2 sinx cosx - cosx = 0
cosx (2sinx-1)=0
It means, cosx = 0 and (2sin x -1 ) = 0
cos x = cos0 and sinx = 1/2
x = 90° and x = 30°, 150°
Hence, the possible values of x are 90°, 30° and 150°.
<h3>
Answer: 6</h3>
===========================================================
Explanation:
Rule: If a set has n elements in it, then it will have 2^n subsets.
For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.
- {a,b,c} .... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } ..... the empty set
Subsets 2 through 4 are subsets with exactly 2 elements. Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol
to indicate the empty set.
For more information, check out concepts relating to the power set.
-------------------
The problem is asking what value of n will make 2^n = 64 true.
You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.
Another approach is to follow these steps.
![2^n = 64\\\\2^n = 2^6\\\\n = 6](https://tex.z-dn.net/?f=2%5En%20%3D%2064%5C%5C%5C%5C2%5En%20%3D%202%5E6%5C%5C%5C%5Cn%20%3D%206)
Which is fairly trivial.
Or you can use logarithms to solve for the exponent.
![2^n = 64\\\\\text{Log}\left(2^n\right)=\text{Log}\left(64\right)\\\\n*\text{Log}\left(2\right)=\text{Log}\left(64\right)\\\\n=\frac{\text{Log}\left(64\right)}{\text{Log}\left(2\right)}\\\\n\approx\frac{1.80617997398389} {0.30102999566399} \ \text{ ... using base 10 logs}\\\\n\approx5.99999999999983\\\\](https://tex.z-dn.net/?f=2%5En%20%3D%2064%5C%5C%5C%5C%5Ctext%7BLog%7D%5Cleft%282%5En%5Cright%29%3D%5Ctext%7BLog%7D%5Cleft%2864%5Cright%29%5C%5C%5C%5Cn%2A%5Ctext%7BLog%7D%5Cleft%282%5Cright%29%3D%5Ctext%7BLog%7D%5Cleft%2864%5Cright%29%5C%5C%5C%5Cn%3D%5Cfrac%7B%5Ctext%7BLog%7D%5Cleft%2864%5Cright%29%7D%7B%5Ctext%7BLog%7D%5Cleft%282%5Cright%29%7D%5C%5C%5C%5Cn%5Capprox%5Cfrac%7B1.80617997398389%7D%20%7B0.30102999566399%7D%20%5C%20%5Ctext%7B%20...%20using%20base%2010%20logs%7D%5C%5C%5C%5Cn%5Capprox5.99999999999983%5C%5C%5C%5C)
Due to rounding error, we don't land exactly on 6 even though we should.
Answer:
3
Step-by-step explanation:
So we have the function:
![f(x)=3x^2+2x-5](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E2%2B2x-5)
To evaluate the value of f(-2), substitute -2 for x. Thus:
![f(-2)=3(-2)^2+2(-2)-5](https://tex.z-dn.net/?f=f%28-2%29%3D3%28-2%29%5E2%2B2%28-2%29-5)
Square first:
![f(-2)=3(4)+2(-2)-5](https://tex.z-dn.net/?f=f%28-2%29%3D3%284%29%2B2%28-2%29-5)
Multiply:
![f(-2)=12-4-5](https://tex.z-dn.net/?f=f%28-2%29%3D12-4-5)
Now, subtract:
![f(-2)=8-5=3](https://tex.z-dn.net/?f=f%28-2%29%3D8-5%3D3)
So:
![f(-2)=3](https://tex.z-dn.net/?f=f%28-2%29%3D3)
And we're done!
Simplify, then see what its close to.
7/8 is close to 0 or 1, 1!