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2 years ago

Create truth table to determine whether or not the following statements are logically equivalent

Mathematics

1 answer:

otez555 [7]2 years ago

4 0

The statement is totally false.

$\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q$

because (P and ¬P) is a contradiction.

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A fisherman can row upstream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then started down

ikadub [295]

Total time = upstream time + downstream time
he rowed the same distance both ways.
upstream time = D/4
downstream time = D/6
total time = D/4 + D/6 = 3D/12 + 2D/12 = 5D/12 = 3 hours
D = 3*12/5 = 36/5 or 7.2 miles
where D is the one-way distance. The total distance he rowed is 2*D = 72/5 or 14.4 miles

6 0

3 years ago

Read 3 more answers

Identify all of the following solutions of square root of x minus 8 end root plus 8 equals x.

Anit [1.1K]

$\sqrt{x-8} +8=x \\ \sqrt{x-8} =x-8 \\ {( \sqrt{x-8} )}^{2} = {(x-8)}^{2} \\ x-8= x^{2} -16x+64 \\ x^{2} -16x-x+64+8=0 \\ x^{2} -17x+72=0$

$(x-8)(x-9)=0 \\ x-8=0 \ and \ x-9=0 \\ x=8 \ and \ x=9$

4 0

3 years ago

Read 2 more answers

Bir araç 5 saatte 80km yol almaktadır. Buna göre bu aracın hızı kaç m/dk'dır?

8090 [49]

80 km = 80000 m
5 saatte = 300 dk’dir
80000m/300 dk’dir = 266.666667 m/dk’dir
(Yazım yanlışsa kusura bakmayın türkçe bilmiyorum :) )

6 0

2 years ago

Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?

scoray [572]

Step-by-step explanation:

With this kind of problem, we're looking at an equation in the form

y - y1 = m(x - x1)

(m = slope)

so we can substitute m, y1, and x1 with the values we're given.

y - y1 = m(x - x1)

y - 1/3 = 3/4(x - 4)

Answer:

y - 1/3 = 3/4(x - 4)

6 0

3 years ago

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kari74 [83]

The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or $2^6 = 64$ miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship $x * 2^6 = k$ , for some constant k.

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

$\dfrac{x}{2^6} = \dfrac{15x}{y^6} \\ (x)(y^6)=(2^6)(15x)$

Cancelling our x's (because we don't need to solve for them), we have

$y^6 = 15(2^6) = 15(64)=960$

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

$\sqrt[6]{y^6} = \sqrt[6]{960}$

Using a calculator, we see that $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .

6 0

3 years ago