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3 years ago

Please help square root math

Mathematics

1 answer:

pantera1 [17]3 years ago

7 0

Answer:

2<∛13<3 1<∛6<2

Step-by-step explanation:

Lets find the integers a and b ∛13 lies between.

a<∛13<b

a³<13<b³

=> a=2 so 2³=8 and b=3 so 3³=27 8<13<27

Similarly a<∛6<b

a³<6<b³

a=1 and b=2

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3 years ago

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3 years ago

Solve the following inequality for dd. Write your answer in simplest form. −7d−3>2d-10

LUCKY_DIMON [66]

Answer:

d < 7/9

Step-by-step explanation:

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3 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

A stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s

Papessa [141]

Answer:

23.7m

Step-by-step explanation:

Given parameters:

Time taken = 2.2s

Acceleration due to gravity = 10m/s

Unknown:

Depth of the well = ?

Solution:

To solve this problem, we simply apply one of the motion equations;

S = ut + $\frac{1}{2}$ gt²

where S = depth of the well

u = initial velocity

t = time taken

g = acceleration due to gravity

Input the parameters and solve for S;

Note initial velocity = 0;

S = $\frac{1}{2}$ x 9.8 x 2.2²

S = 23.7m

3 0

3 years ago