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2 years ago

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Pls help ASAP I will give you 20 points!!!

1 answer:

Grace [21]2 years ago

6 0

Answer: .....

ok done. Thank to me :>

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The sum of the digits of a two-digit number is 5. When the digits are reversed, the number increases by 27. Find the original nu

gavmur [86]

Answer:

<h2>14</h2>

Step-by-step explanation:

$a-\text{tens digit}\\b-\text{unity digit}\\10a+b-\text{number}\\10b+a-\text{number with reversed digits}\\a+b-\text{sum of digits}\\\\\bold{System\ of\ equations:}\\\\\left\{\begin{array}{ccc}a+b=5\\10b+a=10a+b+27&\text{subtract}\ 10a\ \text{and}\ b\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}a+b=5\\9b-9a=27&\text{divide both sides by 9}\end{array}\right$

$\underline{+\left\{\begin{array}{ccc}a+b=5\\b-a=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2b=8\qquad\text{divide both sides by 2}\\.\qquad \boxed{b=4}\\\\\text{Put the value of\ b}\ \text{to the first equation}\\\\a+4=5\qquad\text{subtract 4 from both sides}\\\boxed{a=1}$

3 0

3 years ago

Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Flura [38]

Answer:

The inequality that you have is $5^{n}>2^{2n+1}+100,\,n>4$ . You can use mathematical induction as follows:

Step-by-step explanation:

For $n=5$ we have:

$5^{5}=3125$

$2^{(2(5)+1)}+100=2148$

Hence, we have that $5^{5}>2^{(2(5)+1)}+100.$

Now suppose that the inequality holds for $n=k$ and let's proof that the same holds for $n=k+1$ . In fact,

$5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.$

Where the last inequality holds by the induction hypothesis.Then,

$5^{k+1}>(2^{2k+1}+100)\cdot (4+1)$

$5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100$

$5^{k+1}>2^{2k+3}+100\cdot 4$

$5^{k+1}>2^{2(k+1)+1}+100$

Then, the inequality is True whenever $n>4$ .

3 0

2 years ago

Critical points of x+5/x+2>0

Scorpion4ik [409]

Answer:

{-5, -2}

Step-by-step explanation:

In a case like this please use parentheses to remove ambiguities. If I were to take your "x+5/x+2" literally, I'd have to write x plus 5/x plus 2.

I suspect that you actually meant (x + 5) / (x + 2), and will start with that.

First of all, this function is not defined at x = -5 or at x = -2. Thus, -5 and -2 are critical points.

Secondly, there may be one or more critical points beyond this. To find out, we have to differentiate (x+5)/(x+2):

(x + 2)(1) - (x + 5)(1)

f '(x) = ------------------------------

(x + 2)

Here it's clear that x cannot = -2, which would cause division by zero.

Thus, our critical values are {-5, -2}.

8 0

3 years ago

The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder

Luden [163]

The volume would be 1/3π in³.

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

7 0

3 years ago

PLEASE HELP THIS IS URGENT

julia-pushkina [17]

I think the answer is y=3

5 0

2 years ago