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sergij07 [2.7K]
3 years ago
7

Use the truth table method to decide whether the following · forms are tautologies, contradictions, or contingencies. *a. p >

(9= p) b. (o'q) · (~p"~9) *C. ~(p » (O' q) d. (p=~9) "(~p=~9) *e. ((p = q) · (q = p)) = (p'q) f. (p = q) = (p=~9) | *g. (p:/qY )) = ((p:g) v(p:)) h. ((pvn) = q) •~(~q~) *i. ((p'q) '~ 1) = (pv (p '~ )) j. ((pvq) • ~ 1) = (pv (q:~;)) *k. [p. (q'~)] = [((p.5) · (qv~ r)) °((p :~s) · (q"~)))
Mathematics
1 answer:
mixas84 [53]3 years ago
8 0
Contradictions beepboopbopopp
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Simplify: 6x^-2<br><br> a) 1/6x^2<br> b) 6/x^2<br> c) x^2/6<br> d) 1/36x^2
Salsk061 [2.6K]

Answer:

The correct answer choice is <u>option B. 6/x^2</u>

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Solve the compound inequality |3x-9|≤15 and |2x-3|≥5. Give answer in interval notation.
laila [671]

Answer:

The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is  (-∞,2] ∪ [8,∞)

Step-by-step explanation:

When solving absolute value inequalities, there are two cases to consider.

Case 1: The expression within the absolute value symbols is positive.

Case 2: The expression within the absolute value symbols is negative.

The solution is the intersection of the solutions of these two cases.

In other words, for any real numbers a and b,

  • if |a|> b then a>b or a<-b
  • if |a|< b then a<b or a>-b

So, being |3x-9|≤15

Solving: 3x-9 ≤ 15

3x ≤15 + 9

3x ≤24

x ≤24÷3

x≤8

or 3x-9 ≥ -15

3x ≥-15 +9

3x ≥-6

x ≥ (-6)÷3

x ≥ -2

The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]

So, being |2x-3|≥5

Solving: 2x-3 ≥ 5

2x ≥ 5 + 3

2x ≥8

x ≥8÷2

x≥8

or 2x-3 ≤ -5

2x ≤-5 +3

2x ≤-2

x ≤ (-2)÷2

x ≤ -2

Expressing the solution as an interval: (-∞,2] ∪ [8,∞)

6 0
3 years ago
Emma borrowed $300 to repair her car. the finance (interest) charge on the loan was $20, and the term on the loan was 14 days. w
Murrr4er [49]
Given:
loan amount = 300
finance charge = 20
term = 14 days.

To solve for APR.
<span>1. Divide the finance charge by the loan amount.
20/300 = 0.0667

2. Multiply the result by 365. 
0.0667 x 365 = 24.35

3. Divide the result by the term of the loan.
24.35/14 = 1.74 (APR in decimal format)
<span>
4. Multiply the result by 100.
1.74 x 100 = 174% APR</span></span>
7 0
3 years ago
What are geologists able to tell archaeologists about fossils?
Shalnov [3]

Answer:

C. . how old they are

Step-by-step explanation:

Geologist are people that deal with the internal structure of the earth.

They study Rocks, and it's deposit accumulated millions of years back.

They can also give account of what happened in the past and the types of organisms that existed in the past.

Fossils are traces of event, remains of dead animals and decomposed object.

So geologist can give account of how many years a particular fossil has lived in that particular environment.

3 0
3 years ago
T what point does the curve have maximum curvature? Y = 7ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
Nookie1986 [14]

Formula for curvature for a well behaved curve y=f(x) is


K(x)= \frac{|{y}''|}{[1+{y}'^2]^\frac{3}{2}}


The given curve is y=7e^{x}


{y}''=7e^{x}\\ {y}'=7e^{x}


k(x)=\frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}


{k(x)}'=\frac{7(e^x)(1+49e^{2x})(49e^{2x}-\frac{1}{2})}{[1+49e^{2x}]^{3}}

For Maxima or Minima

{k(x)}'=0

7(e^x)(1+49e^{2x})(98e^{2x}-1)=0

→e^{x}=0∨ 1+49e^{2x}=0∨98e^{2x}-1=0

e^{x}=0  ,  ∧ 1+49e^{2x}=0   [not possible ∵there exists no value of x satisfying these equation]

→98e^{2x}-1=0

Solving this we get

x= -\frac{1}{2}\ln{98}

As you will evaluate {k(x})}''<0 at x=-\frac{1}{2}\ln98

So this is the point of Maxima. we get y=7×1/√98=1/√2

(x,y)=[-\frac{1}{2}\ln98,1/√2]

k(x)=\lim_{x\to\infty } \frac{7e^{x}}{[{1+(7e^{x})^2}]^\frac{3}{2}}

k(x)=\frac{7}{\infty}

k(x)=0







5 0
3 years ago
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