Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Multiplying x by any positive number smaller than 1 will result in some smaller value.
For example, if the scale factor is k = 0.5, then we can think of this as the fraction k = 1/2. Multiplying by 1/2 will make any number smaller, namely, exactly half as much.
- 1/2 times 100 = 50
- 1/2 times 78 = 39
- 1/2 times 600 = 300
We are taking a fractional part of the original number, so its expected the result is smaller. It's like having a whole cake and we only take slices of that cake to end up with the new value. There's no way having one or more slice be larger than the original whole amount.
Because things are getting smaller, we call this type of dilation to be a reduction or we can call it shrinking. This is in contrast to an enlargement when k > 1.
-----------------------------------------
More info (optional section)
Claim: For some positive number k such that k < 1, we have xk < x when x is positive.
The proof of this claim is fairly straight forward.
We multiply both sides of k < 1 by x to get
k < 1
x*k < x*1
xk < x
The inequality sign does not flip because we're multiplying both sides by a positive number x.
So because xk < x, this shows that the original value x gets smaller to xk when we apply the positive scale factor k such that k < 1. This is the same as saying 0 < k < 1. Furthermore, xk < x is the same as 0 < xk < x.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
