Find the distance between the two points.

As shown, a section of a roller coaster track (figure 3) follows the form of y=(2/3)x1.5. locate the centroid x? of the track be

LiRa [457]

F(x)=(2/3)x^1.5

The centroid position along the x-axis can be obtained by
integrating the function * x to get the moment about the y-axis,
then divide by the area of the graph,
all between x=0 to x=3.5m.

Expressed mathematically,
x_bar=(∫f(x)*x dx )/(∫ f(x) dx limits are between x=0 and x=3.5m
=15.278 m^3 / 6.1113 m^2
=2.500 m

3 0

3 years ago

mike drove to a frineds house at the rage of 40 mph. he returned hoke by the dsne route at 45 mph the driving time for the round

wolverine [178]

Let the distance be x miles

Time = Distance / speed

Time taken by Mike to go to his friend's house = x / 40 hours

Time taken by him to return = x / 45 hours

Total time = x / 40 + x / 45 = 4 hours

= 9x + 8x = 1440 miles

17x = 1440

= x = 1440 ÷ 7

= x = 84.706

Time taken to return home = 84.706 /45= 1.882 hours .

Therefore , Mike took 1.882 hours to reach home .

8 0

3 years ago

A projectile is launched from the ground at an angle of theta above the horizontal with an initial speed of v in ft/s. The rang

VARVARA [1.3K]

Answer:

$\theta=24.4^\circ$

Step-by-step explanation:

The formula you wrote has the fraction the other way around. You can find that the range of a projectile is in reality approximated by the equation $x=\frac{v^2}{g} sin(2\theta)=\frac{v^2}{32ft/s^2} sin(2\theta)$ , where we will use ft for distances.

From the given equation we have then $\frac{x32ft/s^2}{v^2} =sin(2\theta)$ , which means $\theta=\frac{Arcsin(\frac{x32ft/s^2}{v^2})}{2}$ since the arcsin is the inverse function of the sin.

Since we have x = 170 ft and v = 85 ft/s, we can substitute these values from the equation written, and we will have $\theta=\frac{Arcsin(\frac{(170ft)(32ft/s^2)}{(85ft/s)^2})}{2}$ , and from now on we have just to use a calculator, obtaining $\theta=\frac{Arcsin(0.75294117647)}{2}=\frac{48.84579804^\circ}{2}=24.4^\circ$

3 0

3 years ago

there are five bells which ring at interval of 4,5,12 and 15 minutes respectively at what minute those bells ring at the same ti

Rus_ich [418]

<h3>Answer: 60 minutes</h3>

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

Explanation:

Let's find the LCM of 4 and 5, which are the first two items of the list.

multiples of 4 are: 4,8,12,16,20,24,...
multiples of 5 are: 5,10,15,20,25,...

The smallest item in each list is 20, so the LCM of 4 and 5 is 20.

We can replace the "4,5" in the list "4,5,12,15" with "20". So our new list would be "20,12,15".

We then repeat the process of finding the LCM of the first two items

multiples of 20 are: 20,40,60,80,...
multiples of 12 are: 12,24,36,48,60,72,...

LCM of 20 and 12 is 60.

The list "20,12,15" condenses to "60,15".

Repeat this process of finding the LCM once more and you'll find the overall LCM is 60.

Therefore, the LCM of the entire set {4,5,12,15} is 60. This is the smallest multiple shared by all four values. Interestingly enough, the outer values pair up to multiply to 60, and so do the inner values.

4*15 = 60

5*12 = 60

The bells ring together every 60 minutes

In other words, all of the bells ring together at the same time every hour (perhaps at the top of every hour; eg at 7:00 pm and at 8:00 pm, etc).

8 0

2 years ago

What is the percentage difference between 26 and 14?

topjm [15]

Answer:

0.12%

Step-by-step explanation:

Percent means out of hundred

therefore 26 in percentage is written as

$\frac{26}{100} = 0.26$

=0.26%

and 14 in percentage is written as

$\frac{14}{100}$

=0.14%

percentage difference between 26 and 14 , therefore

=0.26% - 0.14%

=0.12%

6 0

3 years ago