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Anna [14]
3 years ago
11

Using the predicate symbols shown and appropriate quantifiers, write eachEnglish language statement as a predicate wff. (The dom

ain is the whole world).
S(x): x is aspy novel
L(x): x is long
M(x): x is a mystery
B(x, y): x is better than y
a. All spy novels are long
b. Not every mystery is a spy novel
c. Only mysteries are long.
d. Spy novels are better than mysteries.
e. Only spy novels are better than my
Mathematics
1 answer:
miss Akunina [59]3 years ago
8 0

Answer:

a. All spy novels are long. S (L)

b. Not every mystery is a spy novel S (x,M)

c. Only mysteries are long M ( L)

d. Spy novels are better than mysteries S B(x, y)

e. Only spy novels are better than mystery S B(x)

Step-by-step explanation:

Spy novels and mystery novels both are long. There is a domain function representing mystery novels is better than spy novels. The spy novel can be long and and better than mystery novels. The symbol representation for spy novel and mystery novel is given in the domain function.

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Let M be the foot of perpendicular from P(x,y) on the directrix.
then SP=PM
\sqrt{(x-(-2.5))^2+(y-0)^2} =| \frac{x-2.5}{( \sqrt{1})^2 } |
squaring both sides(x+2.5)^2+y^2=(x-2.5)^2 , x^2+6.25+5x+y^2=x^2+6.25-5x

y^2=x^2+6.25-5x-x^2-6.25-5x=-10x
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find the equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(
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The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2

<h3><u>Solution:</u></h3>

Given, two points are A(-5, 5) and B(3, -3)

We have to find the perpendicular bisector of segment AB.

Now, we know that perpendicular bisector passes through the midpoint of segment.

<em><u>The formula for midpoint is:</u></em>

\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here x_1 = -5 ; y_1 = 5 ; x_2 = 3 ; y_2 = -3

\text { So, midpoint of } A B=\left(\frac{-5+3}{2}, \frac{5+(-3)}{2}\right)=\left(\frac{-2}{2}, \frac{2}{2}\right)=(-1,1)

<em><u>Finding slope of AB:</u></em>

\text { Slope of } A B=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

\text { Slope } m=\frac{-3-5}{3-(-5)}=\frac{-8}{8}=-1

We know that product of slopes of perpendicular lines = -1  

So, slope of AB \times slope of perpendicular bisector = -1  

- 1 \times slope of perpendicular bisector = -1  

Slope of perpendicular bisector = 1

We know its slope is 1 and it goes through the midpoint (-1, 1)

<em><u>The slope intercept form is given as:</u></em>

y = mx + c

where "m" is the slope of the line and "c" is the y-intercept

Plug in "m" = 1

y = x + c   ---- eqn 1

We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1

1 = -1 + c

c = 2

Now substitute c = 2 in eqn 1

y = x + 2

Thus y = x + 2 is the required equation in slope intercept form

7 0
4 years ago
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