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3 years ago

Which explanation justifies how the area of a sector of a circle is derived?

Mathematics

2 answers:

vovikov84 [41]3 years ago

7 0

Answer is calculate the area of the circle.............................

11Alexandr11 [23.1K]3 years ago

3 0

The answer is option B

hope it helps!!

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DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

2 years ago

Based on 10,500 responses from 34,000 questionnaires sent to all its members, a major medical association estimated that the an

SIZIF [17.4K]

Answer:

d) Convenience

Step-by-step explanation:

According to my research on different types of sampling techniques, I can say that based on the information provided within the question the sampling technique used in this method is called a Convenience technique. This technique collects data from all the participants that were conveniently available to participate, and does not have any criteria that needs to be met. In this situation they used the data from all the participants that responded to the questionnaires, in other words the participants that were conveniently available,

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

5 0

3 years ago

PLEASE HELP ASAP!!!!!!!

umka2103 [35]

Answer:

dum there is part A prat B and C

Step-by-step explanation:

5 0

2 years ago

Ce Powered by MathXL - Inv. 2 - Thinking With Mathematical ... Copy 4

MAVERICK [17]

Answer:

y=640-3x

Step-by-step explanation:

The total amount of ounces in the bucket is 640, and it decreases by 3 each minute. For example, if you plug in 3 for x into that equation (which would represent 3 minutes), you would lose 9 ounces of water, which makes sense in the terms of the equation.

7 0

2 years ago

HELP you purchase a car using a $22,000 loan with a 6% simple interest rate for 5 years

Hunter-Best [27]

Answer: (a) $6,600

(b) $28,600

<u>Step-by-step explanation:</u>

Interest (I) = Principal (P) x rate (r) x time (t)

I = 22,000(0.06)(5)

= 6,600

Accrued (A) = Principal (P) + Interest (I)

A = 22,000 + 6,600

= 28,600

7 0

3 years ago