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2 years ago

A group of three friends cycle from Llanfyllin to Vyrnwy at 12 km/h.

Mathematics

1 answer:

garik1379 [7]2 years ago

6 0

The average speed for the journey from Llanfyllin to Bala is 14 km/h

Average speed is the ratio of total distance travelled to total time taken. Also, average speed can be given as the average of the different speeds.

Let d₁ represent the distance from Llanfyllin to Vyrnwy and t represent the time taken, since the speed is 12 km/h, hence:

12 = d₁/t

d₁ = 12t

Let d₂ represent the distance from Vyrnwy to bala and t represent the time taken. Since they spent the same time, since the speed is 16 km/h, hence:

16 = d₂/t

d₂ = 16t

Average speed = total distance/total time

Average speed = (d₁ + d₂) / (t + t)

Average speed = (12t + 16t) / 2t

Average speed = 28t / 2t

Average speed = 14 km/h

Hence their average speed for the journey from Llanfyllin to Bala is 14 km/h.

Find out more at: brainly.com/question/23774048

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A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 1.5 feet, 30 feet a

Nimfa-mama [501]

Answer:

x₁ > x₂

Step-by-step explanation:

Both actions imply a parable trajectories, since both are projectile shot cases.

Let´s call x₁ maximum distance in the first case

The maximum height is just in the middle of the curve, therefore x₁ the maximum horizontal distance is equal to 60 feet.

In the second case, the parable curve is modeled by:

y = x₂*( 0.08 - 0.002x₂) or y = 0.08*x₂ - 0.002*x₂²

A second degree equation, solving for x₂ and dismissing the value x₂ = 0

we get:

y = 0 ⇒ x₂*( 0.08 - 0.002x₂) = 0 x₂ = 0

And 0,08 - 0.002*x₂ = 0

- 0.002*x₂ = - 0.08

x₂ = 0.08/0.002

x₂ = 40 f

Then x₁ > x₂

3 0

2 years ago

(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =

frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0

2 years ago

At a cafe, for every 5 sodas sold there are 9 teas sold. What is the ratio of teas sold to sodas sold? A) 5 : 9 B) 9 : 5 C) 9 :

frutty [35]

For 5 sodas sold, there are 9 teas sold

the ratio is tea: soda, or 9:5

B) 9:5 is your answer

hope this helps

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MArishka [77]

Answer:

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1 answer

Step-by-step explanation:

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2 years ago

For the equations y=3.5x and y=25x + 40.50, x represents time in hours and y represents cost in dollars . Which equation is not

CaHeK987 [17]

Answer:

y=25x+40.50 is not the equation of proportional relationship because if you were to graph the equation, the line would not go through the origin of the graph. You can tell beause of the y-intercept that is given in the equation, 40.50.

Step-by-step explanation:

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2 years ago

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