The measure of central angle XYZ is StartFraction 3 pi Over 4 EndFraction radians. What is the area of the shaded sector? 32Pi u
2 answers:
Answer:
<em>96π units²</em>
Step-by-step explanation:
Find the diagram attached
Area of a sector is expressed as;
Area of a sector = θ/2π * πr²
Given
θ = 3π/4
r = 16
Substitute into the formula
area of the sector = (3π/4)/2π * π(16)²
area of the sector = 3π/8π * 256π
area of the sector = 3/8 * 256π
area of the sector = 3 * 32π
<em>area of the sector =96π units²</em>
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Answer:
3/5 has the smallest denominator
Step-by-step explanation:
Question:
There exist infinitely many common fractions a/b , where a > 0 and b > 0 and for which 3/5 < a/b< 2/3. Of these common fractions, which has the smallest denominator? Express your answer as a common fraction.
Solution
A Common fraction is a rational number written in the form: a/b. Where a and b are both integers.
The denominator and numerator in this case are greater than zero. That is, they are non zeros.
The least common denominator (LCD) of two non- zero denominators is the smallest whole number that is divisible by each of the denominators.
To find the smallest denominator between 3/5 and 2/3, we would convert the fractions to equivalent fractions with a common denominator by finding their LCM (lowest common multiple).
When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator and the smaller fraction is one with the smaller numerator.
In our solution after comparing, the smaller fraction would have the smallest denominator.
Find attached the solution.
Answer:
22% = 0.22
Step-by-step explanation:
Lat'e express all the given numbers in decimal form so we understand how they are located on the number line.
We start with 2/11 , since the number we are looking for has to be larger than this \, and smaller than 1.42:
So we understand that we are looking for a number that can be placed between the lower boundary (0.181818...) and the upper boundary (1.42) on the number line. That is: we are looking for a number greater than 0.18181818... and less than 1.42.
Now let's look at each of the given options (also writing them in decimal form to facilitate the comparison with the lower and upper boundaries we just found):
This number is grater than the upper boundary given to us (1.42), it would be placed to the right of 1.42 on the number line. Therefore we discard it for not being in the requested interval (section) of the number line.
0.153 is already in decimal form, and clearly less than (thus to be placed on the left of) the lower boundary (0.181818...) of the requested interval. Therefore we discard it for not being in the requested interval (section) of the number line.
22% in decimal form is written as: . This number is greater than the lower boundary (0.181818...) and also less than the upper boundary (1.42). Therefore it is a choice that would make the sentence true.
which is clearly greater than the upper boundary of the interval, so we discard it.