Answer: 55.872
Step-by-step explanation:
Point A would be zero; Point B, the end of the 1/2-hour time interval, would be 1/2 (representing 1/2 hour). Then Amy needs to subdivide the interval A to B into three equal time intervals and to determine the length of each of these subintervals.
I would begin with 1/2 and divide that by 3:
1
--
2
====
3
--
1
Inverting the fraction in the denom. and multiplying, we get
1 1 1
-- * ---- = -----
2 3 6
So Amy will spend 1/6 th of an hour, or 10 minutes, on each chore.
Note that 3 times 1/6 comes out to 1/2 (hour), which is were we started.
Answer:
a)
We know that:
a, b > 0
a < b
With this, we want to prove that a^2 < b^2
Well, we start with:
a < b
If we multiply both sides by a, we get:
a*a < b*a
a^2 < b*a
now let's go back to the initial inequality.
a < b
if we now multiply both sides by b, we get:
a*b < b*b
a*b < b^2
Then we have the two inequalities:
a^2 < b*a
a*b < b^2
a*b = b*a
Then we can rewrite this as:
a^2 < b*a < b^2
This means that:
a^2 < b^2
b) Now we know that a.b > 0, and a^2 < b^2
With this, we want to prove that a < b
So let's start with:
a^2 < b^2
only with this, we can know that a*b will be between these two numbers.
Then:
a^2 < a*b < b^2
Now just divide all the sides by a or b.
if we divide all of them by a, we get:
a^2/a < a*b/a < b^2/a
a < b < b^2/a
In the first part, we have a < b, this is what we wanted to get.
Another way can be:
a^2 < b^2
divide both sides by a^2
1 < b^2/a^2
Let's apply the square root in both sides:
√1 < √( b^2/a^2)
1 < b/a
Now we multiply both sides by a:
a < b
Answer:
4 miles per hour
Step-by-step explanation:
I took it on k-12
Answer:
1. 5 cups of yellow paint.
2. 15 cups of yellow paint to 3 cups of blue paint.
3. 1:5 is the proportional relationship.
4. 5 is the constant of proportionality, it represents the . of yellow cups of paint.
Step-by-step explanation:
sorry if 4 is wrong
