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3 years ago

A car moves at a speed of 30m/s to the west for 3hr. What is the displacement of the car in km?

1 answer:

5 0

(30m/s divided by 2)x 10800 ( convert 3hr to seconds by x with 60squared)
= 162000 m ( convert m to km by dividing with 1000)
= 162 km

Plz mark as brainleast if this answers helped ya.

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Match each compound inequality on the left to the graph that represents its solution on the right.

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Step-by-step explanation:

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3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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3 years ago

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3 years ago

Estimate the answer to 341÷28

Dmitriy789 [7]

To estimate this question, you can round the numbers to be compatible, to make it easier for yourself. The numbers should be able to be divided cleanly, as this is an estimate, not the actual problem solving. You could, for example, round 341 to 300, and 28 to 30, and divide them to get 10.
Hope that helped.

3 0

3 years ago

Read 2 more answers

A cylinder has a radius of 20 cm and a height of 2 cm. Find the height of another cylinder that has a radius of 4 cm and the sam

iogann1982 [59]

Answer:

The height of the another cylinder 'h' = 7

Step-by-step explanation:

Explanation:-

Step 1:-

Surface area of the cylinder = 2пrh + 2пr^2

Given radius of first cylinder is 20cm

given height of the first cylinder is 2 cm

The surface area of first cylinder is = 2пrh + 2пr^2

= 2п(20)(2)+2п(2)^2

= 4п(20+2)

The surface area of first cylinder is 88п

Step 2:

given data The surface area of first cylinder is 88п is same as second cylinder also

Find the height of the second cylinder

Given Radius of the second cylinder r = 4

Surface area of the cylinder = 2пrh + 2пr^2 = 88п

2п(4)h+2п(4)^2 =88п

on simplification we get

2п (4h+16) = 88п

after cancellation '2п' value and on simplification, we get

4h+16 = 44

4h = 44-16

4h = 28

h=7

Therefore the height of the another cylinder is 'h' =7

3 0

3 years ago

A car moves at a speed of 30m/s to the west for 3hr. What is the displacement of the car in km?​

A car moves at a speed of 30m/s to the west for 3hr. What is the displacement of the car in km?