Answer:
Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)
Step-by-step explanation:
This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.
First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.
Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.
Well if you have a radius remember to divide by 2 . So divide your number by 2. And you should get 5x
Step 1: Replace f(x) with y: y=-8-5x
Step 2: Switch X and Y: X=-8-5y
Step 3:Solve for y: x+8=-5y ≈ y=(x+8)/-5
Step 4: Replace y with F^-1(x): f^-1(x)=(x+8)/-5 :)
The formulas for arc length and area of a sector are quite close in their appearance. The formula for arc length, however, is related to the circumference of a circle while the area of a sector is related to, well, the area! The arc length formula is
. Notice the "2*pi*r" which is the circumference formula. The area of a sector is
. Notice the "pi*r squared", which of course is the area of a circle. In our problem we are given the arc length and the radius. What we do not have that we need to then find the area of a sector of the circle is the measure of the central angle, beta. Filling in accordingly,
. Simplifying by multiplying by 360 on both sides and then dividing by 36 on both sides gives us that our angle has a measure of 60°. Now we can use that to find the area of a sector of that same circle. Again, filling accordingly,
, and
. When you multiply in the value of pi, you get that your area is 169.65 in squared.
