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We know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere
if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere
if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere
examples
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area
2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area
3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area
Given:
Number of 100-meter races = 5
The time it took Isabella to complete each race, in seconds, was 12.7, 12.807, 12.78, 12.08, and 12.087.
To find:
The decimals in order from greatest to least.
Solution:
The time it took Isabella to complete each race, in seconds, was shown below:
12.7, 12.807, 12.78, 12.08, 12.087
We need to arrange this data in descending order.
In all 5 numbers the digits before decimals are same. On comparing the digits on the tenth place and hundredth place, we get
12.807 > 12.78 > 12.7 > 12.087 > 12. 08
Therefore, the required order of given data is 12.807, 12.78, 12.7, 12.087, 12. 08.
The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:[2]
<span>exponents and roots </span>
<span>multiplication and division </span>
<span>addition and subtraction </span>
<span>This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations. </span>
<span>It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 − 4 = 3 + (−4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 − 3 + 7 as the sum of 1, negative 3, and 7, and add in any order: (1 − 3) + 7 = −2 + 7 = 5 and in reverse order (7 − 3) + 1 = 4 + 1 = 5. The important thing is to keep the negative sign with the 3. </span>
<span>The root symbol, √, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called vinculum) over the radicand. Other functions use parentheses around the input to avoid ambiguity. The parentheses are sometimes omitted if the input is a monomial. Thus, sin x = sin(x), but sin x + y = sin(x) + y, because x + y is not a monomial. Calculators usually require parentheses around all function inputs. </span>
<span>Stacked exponents are applied from the top down, i.e., from right to left. </span>
<span>Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results from their removal. </span>
Answer:Cell content
Started at 20° and dropped 4° each minute -4
Cell content
Started at −20° and rose 1° each minute 1
Cell content
Started at 20° and dropped 1° each minute -1
Cell content
Started at −20° and rose 4° each minute 1
Step-by-step explanation:
