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Marta_Voda [28]
3 years ago
12

Find the area of a circle of radius 4 cm.​

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
4 0

Answer:

Step-by-step explanation:

Area of a circle=πr²

A=π*4²

A=16π

A=50.27 ( rounded to nearest 100th)

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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
Write each number without exponent 6.453 x 10^-3
Solnce55 [7]

Answer:

.006453

Step-by-step explanation:

6.453 x 10^-3

Move the decimal 3 places to the left since the exponent is negative

006.453

.006453

7 0
2 years ago
Ryan rode his bike of a mile. James rode his bike of a mile. Who rode farther? Exactly how much farther? Use the rectangles belo
34kurt

Answer:

Stewhapt

rectangles-by-step explanation:

5 0
3 years ago
An average person in the United States throws away 4.5 × 10² g of trash per day. In 2013, there were about 3.2×106 people in the
natka813 [3]
One person throws away 4.5 x 10² g/day.
In 2013, there were 3.2 x 10⁶ people, so they threw away
(4.5 x 10² g/day)*(3.2 x 10⁶) = 1.44 x 10⁹ g/day.

Assume that there were 365 days in 2013.
The total trash thrown away was
(1.44 x 10⁹ g/day)*(365 days) = 5.26 x 10¹¹ g

Answer:  5.3 x 10¹¹ g
4 0
3 years ago
Read 2 more answers
If someone makes $650 a week, how much will they make in a<br> year?
Arlecino [84]

Answer:

they will make $33,800 in a year.

Step-by-step explanation:

there are 52 weeks in a year, so $650×5= $33,800

5 0
2 years ago
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