All categories

2 years ago

What is the 185th digit in the following pattern 12345678910111213141516...?

1 answer:

4 0

1-9 = 9 digits
10-99 = 180 digits
So if we continue the pattern to 99, there are 189 digits, and the last 5 digits would be 79899. Counting backwards: 189th = 9, 188th = 9, 187th = 8, 186th = 9, 185th = 7.

The 185th digit is 7.

You might be interested in

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

1 year ago

A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

1 year ago

Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. Jam

Ad libitum [116K]

Answer:

he makes $12 less.

Step-by-step explanation:

$80X12=960 - Matts income for the year

960-816=144 -How much less James makes than Matt per year

144/12=12 - How much less James makes than Mat per month

leave 5 stars and a thanks if it was helpful.

3 0

1 year ago

Read 2 more answers

Tyler is bored in history class, so he is staring at the ceiling tiles. He notices that some tiles are perfect squares, while ot

finlep [7]

Answer:

The complete tables are shown below.

The value of x is 70.59%.

Step-by-step explanation:

Absolute frequency table:

Square Rectangle Row Total

Bright 25 10 35

Off White 23 10 33

Column Total 48 20 68

Relative frequency table

Square Rectangle Row total

Row% 71.43% 28.57% 100.00%

Bright Column% 52.08% 50.00% ____

Total% 36.76% 14.71% 51.47%

Row% 69.70% 30.30% 100.00%

Off White Column% 47.92% 50.00% ___

Total% 33.83% 14.71% 48.53%

Row% ____ ____ 100.00%

Column Column% 100.00% 100.00% 100.00%

Total% x = 70.59% 29.41% 100.00%

$\text{Value of}\ x=100.00\%-29.41\%=70.59\%$

8 0

2 years ago

Triangle R Q S is cut by line segment T U. Line segment T U goes from side Q R to side Q S. The length of Q T is 32, the length

lana [24]

Answer:

the first statement is true

Step-by-step explanation:

The side- splitter states that if the line is parallel to a side of the triangle and it intersects the other 2 sides, it divides those sides proportionally.

Thus the converse is that if the sides are proportional then the side TU is parallel to the side RS

Calculating the ratios

$\frac{QT}{TR}$ = $\frac{32}{36}$ = $\frac{8}{9}$

$\frac{QU}{US}$ = $\frac{40}{45}$ = $\frac{8}{9}$

Since the ratios are equal then TU is parallel to RS

5 0

1 year ago

Read 2 more answers