Question

Help with Math..? Will give Medal.

Answer 1

Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answer 2

I know the solution to f(x) = -x2 + 6x + 6 will be -1. But I don't know what the answer is.

Answer 3

I think it's D.

Answer 4

@amistre64 Can you check my answer?

Answer 5

If it is D, then at 2 seconds it is f(x)=-x^2+6x+6=-(2^2) + 6(2) + 6=14 ft.
then at 5 seconds it is -(5^2) +(5)^6) +6 =-25 +30 + 6 = 11 ft
(14-11)ft/(5-2)sec= 3/3 ft/sec - 1 ft/sec

Answer 6

So I was right..?

Answer 7

No wait, I was wrong.

Answer 8

i believe average is the slope of the line between a stated interval

Answer 9

The slope between the two lines would be -5/3, right?

Answer 10

No wait, -3/3

Answer 11

Which would give us -1

Answer 12

slope between the 2 points ... an average speed is the slope, an average distance i want to say is displacement

Answer 13

too early to think in circles :)

Answer 14

Right, I get it. So you're saying that the distance between x = 2 and x = 5 has a slope of -1.

Answer 15

yes, so the average speed would be defined by the slope

Answer 16

So the answer is B?

Answer 17

Oh wait, he said average speed, so the answer IS D.

Answer 18

@radar Could you help with another?

Answer 19

What is the domain of the following parabola?

All real numbers

x ≥ 1

x ≤ 2

y ≥ -3

I think it's A.

Answer 20

I might, but you did see how you can check your answer .

Answer 21

Yes, I did.

Answer 22

I think it's A because the parabola goes on forever..

Answer 23

I get confused on range and domain

Answer 24

Domain = all x values
Range = all y values

I get confused on them too :l

Answer 25

You know you may be right even though big values of x will take a long time to get there, Looking a B, we see x can equal 0 so that is out. I thank C is out as we can se x can = 2 Obviously D is out as y goes to high values, thru the process of elimination I would say you are correct.

Answer 26

Oh, okay.

Answer 27

Yes, I would say of those choices A is the best answer, good luck with those thing.

Answer 28

I have one more, this is it:

The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function and the other is an exponential function. Which function is most likely increasing quadratically?

x f(x) g(x)
1 2 2
2 5 4
3 10 8
4 17 16
5 26 32

f(x) because it grows slower than g(x)

f(x) because it eventually intersects g(x)

g(x) because it grows faster than f(x)

g(x) because it will not intersect f(x)

I chose A, because I think g(x) is the exponential function and f(x) is the quadratic function. And I know that exponential functions will eventually intersect and grow more than quadratic functions. So I think it's A because f(x) is slower than g(x) because it will eventually grow less than g(x).

Answer 29

It could be A, because f(x) does grow slower than g(x).

It can't be B, because f(x) will not eventually intersect g(x), it's the other way around.

It cannot be C, because it's asking what is the quadratic function, not what is the exponential one.

It couldn't be D, because they DO intersect each other.

Answer 30

I am puzzled by this I graphed two functions one being x^2, the other being 2^x and the 2^x eventually reached higher values than the x^2, so it looks like the g(x) is a exponential function, as far as intersection is concerned that doesn't help me as both graphs would have to cooperate to intersect. I am inclined to go with your reasoning. This is new ground for me.

Answer 31

So you're saying that f(x) is the exponential one, instead of g(x)?

Answer 32

No i said I think the 2^x (expotential) was the fastest growing, thus the quadratic was the slower as you also surmised.

Answer 33

Ah, thank you so much.

Answer 34

They were all correct.

Answer 35

You're welcome, good luck with your studies. I gotta go now for breakfast.

Answer 36

Enjoy!