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2 years ago

Sean took 4 hours to travel from Town A to Town B at an

Mathematics

1 answer:

anzhelika [568]2 years ago

8 0

Answer:

Tina's average speed for the whole journey = 56 kmph

Step-by-step explanation:

Time taken by Sean to travel from Town A to Town B = 4 hours.

Average speed of Sean = 70 km/h

We have equation of motion, s = ut + 0.5 at²

Time, t = 4 hours.

Initial speed, u = 70 km/hr

Acceleration, a = 0 m/s²

Substituting

s = ut + 0.5 at²

s = 70 x 4 + 0.5 x 0 x 4²

s = 280 km

Distance from Town A to Town B = 280 km

Tina took 1 hour more than Sean.

Time taken by Tina to travel from Town A to Town B = 4 +1 = 5 hours

We have equation of motion, s = ut + 0.5 at²

Time, t = 5 hours.

Displacement, s = 280 km

Acceleration, a = 0 m/s²

Substituting

s = ut + 0.5 at²

280 = u x 5 + 0.5 x 0 x 5²

u = 56 km/hr

Tina's average speed for the whole journey = 56 kmph

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A cylinder is filled up with water to 3 4 its total capacity. The solid sphere is dropped completely into the cylinder. How high

Olenka [21]

Answer:

30.3 cm

Step-by-step explanation:

Suppose the height is h after the sphere is full submerged.

4/3 $\pi$ R³ = $\pi$ r²(h-30) The volume of the sphere is equal to the volume

4/3 $\pi x$ (10/2)³= $\pi$ × (14/2)²(h-30) of the water surface rising

4/3 × 125 = 49 × (h-30)

h - 30 = 49 × 3/4 × 125

h - 30 = 0.3

h = 30 + 0.3

h = 30.3 cm

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1 year ago

Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the in

Sonja [21]

Answer with step-by-step explanation:

We are given that the recurrence relation

$f_n=5f_{n-4}+3f_{n-5}$

for n=5,6,7,..

Initial condition

$f_0=0,f_1=1,f_2=1,f_3=2,f_4=3$

We have to show that Fibonacci numbers satisfies the recurrence relation.

The recurrence relation of Fibonacci numbers

$f_n=f_{n-1}+f_{n-2}$ , $f_0=0,f_1=1$

Apply this

$f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}$

$f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}$

$f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}$

Substitute n=2

$f_2=f_1+f_0=1+0=1$

$f_3=f_2+f_1=1+1=2$

$f_4=f_3+f_2=2+1=3$

Hence, the Fibonacci numbers satisfied the given recurrence relation .

Now, we have to show that $f_{5n}$ is divisible by 5 for n=1,2,3,..

Now replace n by 5n

$f_{5n}=5f_{5n-4}+3f_{5n-5}$

Apply induction

Substitute n=1

$f_5=5f_1+3f_0=5+0=5$

It is true for n=1

Suppose it is true for n=k

$f_{5k}=5f_{5k-4}+3f_{5k-5}$ is divisible 5

Let $f_{5k}=5q$

Now, we shall prove that for n=k+1 is true

$f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)$

$f_{5k+5}=5(f_{5k+1}+3q)$

It is multiple of 5 .Therefore, it is divisible by 5.

It is true for n=k+1

Hence, the $f_{5n}$ is divisible by 5 for n=1,2,3,..

8 0

1 year ago

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and rene

mrs_skeptik [129]

Question Completion:

How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)

Answer:

1. The percentages are concentrated from 20% to 60%.

2. These data are strongly skewed left.

3. There are no gaps in the data.

Step-by-step explanation:

1. Data

Percentage loss of wetlands per state

46 37 36 42 81 20 73 59 35 50

87 52 24 27 38 56 39 74 56 31

27 91 46 9 54 52 30 33 28 35

35 23 90 72 85 42 59 50 49

48 38 60 46 87 50 89 49 67

2. Re-arrangement of

Percentage loss of wetlands per state (in ascending order)

9 20 23 24 27 27 28 30

31 33 35 35 35 36 37 38

38 39 42 42 46 46 46 48

49 49 50 50 50 52 52 54

56 56 59 59 60 67 72 73

74 81 85 87 87 89 90 91

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1 year ago

Three students solve a challenge math problem. Every day, the number of students who solve the problem doubles. There are 384 st

attashe74 [19]

OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.

So we have 3 kids and it doubles

Day 1 : 6

Day 2 : 12

Day 3 : 24

Day 4 : 48

Day 5 : 96

Day 6 : 192

Day 7: 384

So it should take 7 days or a week to solve all the problems.

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1 year ago

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djyliett [7]

I think the first one is
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And the second one is
x<2

6 0

1 year ago

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