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3 years ago

Find the value of the following expression: (2^8 • 5^–5 • 19^0)^–2 • (5^-2/2^3)^4 • 2^28

Mathematics

1 answer:

Maru [420]3 years ago

3 0

The value of the expression is 25

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3 years ago

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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

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3 years ago

Find the with of a triangle as a 15 cm high in a hypogynous of a 19 cm

Inessa05 [86]

Answer:

This other side of the triangle is equal to about 11.7 cm

Step-by-step explanation:

In order to find out the third side of the triangle we will just use the Pythagoras Theorem.

$c^{2} =a^{2} + b^{2}$

Since we know the hypotenuse and we know one of the legs, in order to find the second leg we just substitute the values and solve the equation and so we get...

$c^{2} =a^{2} + b^{2}\\19^{2} = 15^{2} + b^{2}\\361 = 225 + b^{2} \\$

$b^{2} = 361 - 225\\b^{2} = 136\\b = \sqrt{136} \\$

And so b ≈ 11.66190

8 0

3 years ago