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2 years ago

Sum of two digits is 8. When the digits are reversed, the number increased by 36. Find the number.

Mathematics

1 answer:

GarryVolchara [31]2 years ago

6 0

Answer:

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

Solve for x:

X=8-y

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

so if y=6, then x=8-y=8-6=2

so our number is 26. 62 is 36 greater than 26.

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sattari [20]

I hope this helps you

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4 years ago

Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = $\int_a^b \delta\left|r^{\prime}(t)\right| d t$

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

$\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}$

Further simplifying;

$\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}$

Now, use integration to find the mass of the wire;

$\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}$

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

brainly.com/question/27846146

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

5 0

2 years ago

PLEASE HELP ASAP!!!!!!

Marina CMI [18]

Answer: -6.8

Step-by-step explanation:

First you have to find the mean of all the #’s so to do that you will have to add all the #’s up including the negatives and you would get -34, after you do that you will have to divide by 5 and get -6.8

8 0

3 years ago

A casino wants to offer a new game with (potentially) spectacular prizes:The player flips a fair coin until they flip heads.The

MissTica

Answer:

The casino should charge for this game at least $1 to break even.

Step-by-step explanation:

We can define the prize function as

$M(n)=2^{ n+1}$

where M is the prize money and n is the number of tails in continous flips.

The probability of n consecutive tails can be calculated as $p^n=0.5^n$ . The probaility of getting a head after the n consecutive tails is $p=0.5$ , so the probability of having n consecutive tails and a head is $p^{n+1}=0.5^{n+1}$