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s344n2d4d5 [400]

4 years ago

10

Determine whether the following statement is a tautology, contradiction, or neither (~PVQ) ~Q Tautology Contradiction • Neither

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1 answer:

Tom [10]4 years ago

6 0

Answer:

The statement $(\lnot P \lor Q)\rightarrow \lnot Q$ is neither a tautology nor a contradiction.

Step-by-step explanation:

A tautology is a statement that is always true.

A contradiction is a statement that is always false.

We are going to use a truth table to determine whether the statement $(\lnot P \lor Q)\rightarrow \lnot Q$ is a tautology, contradiction, or neither

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The statement $(\lnot P \lor Q)\rightarrow \lnot Q$ is compound by these simple statements:

$\lnot P$
$\lnot Q$
$(\lnot P \lor Q)$

and we are going to use these simple statements to build the truth table.

The last column contains true and false values. Therefore, the statement is neither a tautology nor a contradiction.

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Santos went on a bike ride of 90 miles. He realized that if he had gone 24 mph faster, he would have

Gnoma [55]

<h3>Answer: 6 mph</h3>

========================================

Explanation:

distance = rate*time

90 = r*t

where r is the slower speed and t is the time it takes when going that slower speed.

If r is bumped up 24 mph faster, to r+24, then Santos takes t-12 hours to get there. The second equation is

90 = (r+24)(t-12)

-------------------------------------

We can solve the first equation for r to get r = 90/t

Then plug this into the second equation and do a bit of algebra

90 = (r+24)(t-12)

90 = (90/t+24)*(t-12)

90 = 90 - 1080/t + 24t - 288

90t = 90t - 1080 + 24t^2 - 288t

0 = 90t - 1080 + 24t^2 - 288t-90t

0 = 24t^2 - 288t - 1080

24t^2 - 288t - 1080 = 0

If you apply the quadratic formula, then you should get the two solutions t = -3 and t = 15. Due to time constraints, I'll skip these steps.

We'll ignore the negative t value. It makes no sense to have a negative time.

So we focus on t = 15 as the only solution.

-------------------------------------

If t = 15, then,

r = 90/t

r = 90/15

r = 6

Santos rode his bike at <u>6 mph</u> at first. Going this speed means he takes 15 hours.

If he rode 24 mph faster, at 6+24 = 30 mph, then he would ride for 15-12 = 3 hours instead. Note that 90/30 = 3.

5 0

3 years ago

What are the common factors that Greg found?

Arada [10]

<span>The answer is: 1, 2, 7, 14 .
</span>_____________________________________________________
Explanation:
________________________________________________
FIrst, list all the factors of 42 (positive integers):
________________________________________________________
1, 42
2, 21,
3, 14,
6, 7
_________________________________________________
Then list all the factors of 28 (positive integers):
____________________________________________________
<span> 1, 28
2, 14,
4, 7
</span>_____________________________________________________
Now, list all numbers that occur for BOTH the factors of "28" AND the factors of "42"
_____________________________________________________
1, 2, 7, 14
_____________________________________________________
The answer is: 1, 2, 7, 14 .
_______________________________________________________

5 0

3 years ago

True or False (& Justify): If a ball is thrown horizontally from the top edge of a 150m building at a speed of 25 m/sec, the

kap26 [50]

Answer:

38.6 m/s

Step-by-step explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:

- A uniform motion (constant velocity) along the horizontal direction

- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction

Therefore we have to analyze the horizontal and vertical motion separately.

Along the horizontal direction, the velocity is constant during the motion, since there are no forces acting in this direction. So the horizontal velocity 3 seconds after the launch will be the same as the velocity at the launch:

$v_x = v_0 = 25 m/s$

The vertical velocity instead changes according to the suvat equation:

$v_y = u_y - gt$

where

$u_y=0$ is the initial vertical velocity

$g=9.8 m/s^2$ is the acceleration due to gravity

t is the time

Therefore, after t = 3 s,

$v_y=0-(9.8)(3)=-29.4 m/s$

So the velocity after 3 seconds is < 25, -29.4 > m/s. The magnitude of the velocity is

$v=\sqrt{v_x^2+v_y^2}=\sqrt{25^2+(-29.4)^2}=38.6 m/s$

3 0

4 years ago

A line is perpendicular to y = -1/5x+1

natta225 [31]

Answer:

$y = 5\, x + 26$ .

Step-by-step explanation:

Start by finding the slope of the line perpendicular to $y = (-1/5)\, x + 1$ .

The slope of $y = (-1/5)\, x + 1$ is $(-1/5)$ .

In a plane, if two lines are perpendicular to one another, the product of their slopes would be $(-1)$ .

Let $m$ denote the slope of the line perpendicular to $y = (-1/5)\, x + 1$ . The expression $(-1/5)\, m$ would denote the product of the slopes of these two lines.

Since these two lines are perpendicular to one another, $(-1/5)\, m = -1$ . Solve for $m$ : $m = 5$ .

The $(-5,\, 1)$ is a point on the requested line. (That is, $x_{1} = -5$ and $y_{1} = 1$ .) The slope of that line is found to be $m = 5$ . The equation of that line in the point-slope form would be:

$y - 1 = 5\, (x - (-5))$ .

Rewrite this point-slope form equation into the slope-intercept form:

$y = 5\, x + 26$ .

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3 years ago

Simplify: 5(3x-4)-6(2x+3)

never [62]

Step-by-step explanation:

I am doing the same math and I have no idea one nobody is helping me :/ there just looking at my problem and saying the wrong number :((

4 0

3 years ago

Read 2 more answers