How to find the volume using fractions?<span>Method 1: Find the volume of 1 cube ¼ x ¼ x ¼ = 1/64 u³, then multiply this by the total number of cubes (length, width, and height) in the prism. So, if the prism has a length of 4, width of 4, and a height of 4, the total number of cubes needed would be 64. 1/64 x 64 = 1 cm³.</span>
Answer:
Step-by-step explanation:
Acres of corn harvested : time taken = 8 3/4 : 5/6
How much corn can she collect in a hour. ?
Let
x = Acres of corn harvested
Acres of corn harvested : time taken = x : 1
8 3/4 : 5/6 = x : 1
35/4 : 5/6 = x : 1
35/4 ÷ 5/6 = x/1
35/4 × 6/5 = x/1
35*6/4*5 = x/1
210/20 = x/1
210 * 1 = 20 * x
210 = 20x
x = 210/20
= 10 1/2 acres
x = Acres of corn harvested = 10 1/2 acres
The answer is 9
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Answer:
Step-by-step explanation:
The best way to solve this problem is to prove that any norm defines a metric, and then proving that the supremum norm is, in fact, a norm.
<em>Let us prove that any norm defines a metric.</em>
Assume that is a norm in a linear space . Define
and let us prove that is a metric.
The first to axioms of metric are trivial:
- for all . Moreover, and if and only if .
- .
As usual, the triangular inequality is less simple, but not so hard in this case:
and this holds for every . Recall that from the definition of norm we already have a triangular inequality: .
Now, we are in conditions to prove that the supremum norm, is a norm.
<em>The supremum norm is a norm on </em>.
The supremum norm is defined as , where is a continuous function over the set . Next, we are going to prove the three axioms.
(N1): .
(N2):
(N3):
from here we get
Answer:
Step-by-step explanation:
<u>Given</u>
- x : y = 2 : 5, y is 80% of z
<u>Rearranging the ratios:</u>
- x/y = 2/5 ⇒ x/y = 0.4 ⇒ y = x/0.4 ⇒ y = 2.5x
- y is 80% of z ⇒ y = 0.8z
<u>Comparing the values of y:</u>
- 2.5x = 0.8z
- x/z = 0.8/2.5
- x/z = 0.32
- x/z = 32/100
- x/z = 8/25
- x : z = 8 : 25