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Genrish500 [490]
3 years ago
5

The graph below shows the distance d you run, in miles, as a function of time t, in minutes, during a 5-mile run. Your friend sa

ys that the graph is not continuous because it stops at d = 5, so the graph is discrete. Do you agree? Explain.
The graph is on the right to question 33.
Mathematics
1 answer:
notka56 [123]3 years ago
4 0
The correct answer for this question is this one:

"Y<span>our friend says that the graph is not continuous because it stops at d = 5, so the graph is discrete." Your friend is wrong. The graph is still continuous because the graph shows continuity. The problem only shows the graph at certain t time. This means that the graph can be extended at any t time.</span>
You might be interested in
Roberto wants to display his 18 sports cards in an album . Some pages hold 2 cards and others hold 3 cards .
nexus9112 [7]

Answer:

Step-by-step explanation:

Assuming Roberto wants to completely fill each page that he puts cards in, this function describes the number of 2-card pages, a, and 3-card pages, b.

2a + 3b =18

Ricardo can fill up 9 2-card pages, and 6 3-card pages.

a=9, b=0

We must add 2 3-card pages at a time,so that we have an even number for the 2-card pages:

a=6, b=2

Add 2 to b once more:

a=3, b=4

One more time:

a=0, b=6:

Thus, Ricardo can display his figures in the following page combinations:

a=9, b=0

a=6, b=2

a=3, b=4

a=0, b=6

Remember that a= number of 2-card pages and b=number of 3-card pages

There are 4 different ways that Ricardo can arrange his figures in terms of what kind of pages he uses. 

3 0
3 years ago
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
What is the distance between (−5,−4) and (-6,4)?
Helga [31]

The distance formula is:  d  =  sqrt( (x2 - x1)2 + (y2 - y1)2 )

 

For this problem, let (-5, -4) be the "first" point, so  x1 = -5  and  y2 = -4

                      and let (-6, 4) be the "second" point, so  x2 = -6  and  y2 = 4.

 

Then:  d  =  sqrt( (-6 - -5)2 + (4 - -4)2 )  =  sqrt( (-1)2 + (8)2 )  =  sqrt( 1 + 64 )  =  sqrt( 65)

 

The distance formula is just the Pythagorean Theorem applied to an x-y graph.

 

You would get the same final answer if you let (-5, -4) be the second point and (-6, 4) be the first point.

6 0
3 years ago
HURRY!!!!<br> What is the equation of the line shown in this graph?
zalisa [80]

Answer:

x = - 2

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

Where c is the value of the x- coordinates the line passes through.

The line passes through (- 2, - 3) and (- 2, 2)

Both of these points have an x- coordinate of - 2, thus

x = - 2 ← equation of line

3 0
3 years ago
Find the probability that when a couple has four ​children, at least one of them is a girl. ​(Assume that boys and girls are equ
AveGali [126]

Answer:

0.9375 = 93.75% probability that at least one of the four children is a girl.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have the following sample space

In which b means boy, g means girl

b - b - b - b

b - b - b - g

b - b - g - b

b - b - g - g

b - g - b - b

b - g - b - g

b - g - g - b

b - g - g - g

g - b - b - b

g - b - b - g

g - b - g - b

g - b - g - g

g - g - b - b

g - g - b - g

g - g - g - b

g - g - g - g

Total outcomes

There are 16 total outcomes(size of the sample space)

Desired outcomes

Of these outcomes, only 1(b - b - b - b) there is not a girl.

So the number of desired outcomes is 15.

Probability:

P = \frac{15}{16} = 0.9375

0.9375 = 93.75% probability that at least one of the four children is a girl.

7 0
3 years ago
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