Answer:
3.3 cm
Step-by-step explanation:
From the above question, we can draw out a proportion
= Small pentagon = Large pentagon
= x/7 = 7/15
Cross Multiply
x × 15 = 7 × 7
15x = 49
x = 49/15
x = 3.2666666667 cm
Approximately= 3.3 cm
Answer:
f(7) = - 25
Step-by-step explanation:
To evaluate f(7) substitute x = 7 into f(x), that is
f(7) = - 5(7) + 10 = - 35 + 10 = - 25
The answer fam is.........12(x + 3)
The answer is A. 0.5.
When you go out 1 on the X-axis you go up 0.5 on the Y-axis, thus the ratio is 0.5.
This is not easy to see, but if you go out 10 on the X-axis, it is easy to see that the Y-axis is at 5. Again giving the ratio 5/10=0.5
In order to do this, you must first find the "cross product" of these vectors. To do that, we can use several methods. To simplify this first, I suggest you compute:
‹1, -1, 1› × ‹0, 1, 1›
You are interested in vectors orthogonal to the originals, which don't change when you scale them. Using 0,-1,1 is much easier than 6s and 7s.
So what methods are there to compute this? You can review them here (or presumably in your class notes or textbook):
http://en.wikipedia.org/wiki/Cross_produ...
In addition to these methods, sometimes I like to set up:
‹1, -1, 1› • ‹a, b, c› = 0
‹0, 1, 1› • ‹a, b, c› = 0
That is the dot product, and having these dot products equal zero guarantees orthogonality. You can convert that to:
a - b + c = 0
b + c = 0
This is two equations, three unknowns, so you can solve it with one free parameter:
b = -c
a = c - b = -2c
The computation, regardless of method, yields:
‹1, -1, 1› × ‹0, 1, 1› = ‹-2, -1, 1›
The above method, solving equations, works because you'd just plug in c=1 to obtain this solution. However, it is not a unit vector. There will always be two unit vectors (if you find one, then its negative will be the other of course). To find the unit vector, we need to find the magnitude of our vector:
|| ‹-2, -1, 1› || = √( (-2)² + (-1)² + (1)² ) = √( 4 + 1 + 1 ) = √6
Then we divide that vector by its magnitude to yield one solution:
‹ -2/√6 , -1/√6 , 1/√6 ›
And take the negative for the other:
‹ 2/√6 , 1/√6 , -1/√6 ›
