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2 years ago

PQ has endpoints P(6,-3) and Q(-2,-7). Find the coordinates of the midpoint of PQ.

Mathematics

2 answers:

tester [92]2 years ago

4 0

So the right answer is (2,-5)

please see attached picture for full solution

Hope it helps

Good luck on your assignment

Temka [501]2 years ago

3 0

Answer:

Midpoint (2 , -5)

Step-by-step explanation:

RULE: (midpoint)

Consider P(x1,y1)and Q(x2,y2) two points:

the midpoint M(x,y) of the segment PQ is defined like this:

$x = \frac{x1+x2}{2} \\\\y=\frac{y1+y2}{2}$

In our case

x1 = 6 ; y1 = -3

x2 = -2 ; y2 = -7

then

$x = \frac{6+(-2)}{2} =2\\\\y = \frac{(-3)+(-7)}{2} =-5$

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Neporo4naja [7]

Answer:

part of it is cutted out show a better picture please ill answer it

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A projectile is fired from a cliff 190 feet above the water at an inclination of 45 to the horizontal, with a muzzle velocity of

jenyasd209 [6]

Answer:

Step-by-step explanation:

I'm not sure if this problem is physics based or calculus based. So I used calculus because it just makes more sense to do so.

If the projectile is fired from 190 feet in the air, then h0 in our quadratic will be 190. Since we are being asked to find both the displacement in the x-dimension and in the y-dimension, we need a bit of physics here as well. The velocity in the y-dimension is found in

$v_{0y}=v_{0}sin\theta$ and the velocity in the x-dimension is found in

$v_{0x}=v_{0}cos\theta$

Since the sin and the cos of 45 is the same, it's made a bit simpler for us. The velocity in both the x and the y dimension is 35.35533906 feet per second.

We can use that now to write the quadratic we need to start solving these rather tedious problems.

The position function for the projectile is

$s(t)=-16t^2+35.35533906t+190$

I'm going to kind of mix things up a bit, because in order to find the distance in the horizontal dimension that the object is when it's at its max height, we need to first find out how long it takes to get to its max height. We will first take the derivative of the position function to get the velocity function of the projectile. The first derivative of the position function is

$v(t)=-32t+35.35533906$

Remember that the first derivative is the velocity function of the projectile. You should know from either physics or calculus that at its max height, the velocity of an object is 0 (because it has to stop in the air in order to turn around and come back down). Setting the velocity function equal to 0 and solving for time will give us the time that the object is at the max height.

$0=-32t+35.35533906$

I'm going to factor out the -32 to make things easier:

$0=-32(t-1.104854346)$ which gives us that at approximately 1.10485 seconds the object is at its max height.

Moving over to the horizontal distance question now. The displacement the object experiences in the horizontal dimension is found in d = rt. We know the horizontal velocity and now we know how long it takes to get to its max height, so the horizontal distance is found in

d = (35.35533906(1.10485) so

d = 39.06 feet When the object is at its max height the object is a horizontal distance of 39.06 feet from the face of the cliff. That's a.

Now to find the max height, we will use again how long it took to get to the max height and sub it in for t in the position function.

s(1.10485) = -16(1.10485)^2 + 35.35533906(1.10485) + 190 to get that the max height is

209 feet. That's b.

Now for c. We are asked when the object will hit the water. We know that when the object hits the water it is no longer in the air and has a height of 0 above the water. Sub in a 0 for s(t) in the original position function and factor to solve for t:

$0=-16t^2+$ 35.35533906t + 190 and solve for t by factoring however you find to be the easiest. Quadratic formula works great!

We find that the times are -2.51394 seconds and 4.72365 seconds. Since time will NEVER be negative, we know that the time it takes to hit the water is 4.72365 seconds.

Whew!!!

8 0

3 years ago

62 is 10 times larger than what?

NARA [144]

To find a number 10 times smaller than 62 simply move the decimal point one place to the left.

The decimal point in 62 is at the end of the number. 62. becomes 6.2 if we move the decimal one place back.

5 0

2 years ago

Read 2 more answers

State which of the following sets of ordered pairs represent a function.

zalisa [80]

Answer:

Option (D) is correct.

Step-by-step explanation:

A function can be termed as a process from a set of x values to a set of possible y-values where each x-value relates to exactly one y-value.

In other words, a relation can only be a function there is no repetition of x-values. It means a relation can not have duplicated inputs.

Given the sets

Set A: (5,2), (4, 3), (3, 4), (2,5)

Set B: (-1,-6), (0, 2), (1, 2), (3, 6)

Set C: (2, 1), (4, 2), (2, 3), (8,4)

It is clear that sets A and B represent the function because, in these sets, each x-value relates to exactly one y-value. In other words, there are no duplicated inputs.

But, set C has duplicated inputs i.e. x = 2 is repeated twice, and a function can not have a repeated input.

Therefore, we conclude that set A and set B represent a function.

Thus, option (D) is correct.

7 0

2 years ago

Which of the following equations has no solution?

daser333 [38]

Answer:

B. 3x+5−4x=−(x+8)

Explanation:

3x+5−4x=−(x+8)

Step 1: Simplify both sides of the equation.

3x+5−4x=−(x+8)

3x+5+−4x=−x+−8

(3x+−4x)+(5)=−x−8

−x+5=−x−8

Step 2: Add x to both sides.

−x+5+x=−x−8+x

5=−8

Step 3: Subtract 5 from both sides.

5−5=−8−5

0=−13

So, there is no solution

Hope this Helps!

8 0

3 years ago

Read 2 more answers