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2 years ago

Departure: Berlin 4:18 p.m. Arrival: Hong Kong 11:18 p.m. (7-hour time zone to the east) Travel Time:?

Mathematics

1 answer:

SIZIF [17.4K]2 years ago

7 0

Answer:

7 hours

Step-by-step explanation:

4:18+7:00=11:18

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A nitric acid solution flows at a constant rate of 6 L/min into a large tank that initially held 200 L of a 0.5% nitric acid sol

viktelen [127]

Answer:

0.88 s

Step-by-step explanation:

Let x(t) be the volume of nitric acid measured in liters after t minute. Therefore the rate of change in the volume of nitric acid (dx / dt) is:

dx / dt = rate of input of nitric acid - rate of output of nitric acid

rate of input of nitric acid = 6 L/min * 20% nitric acid / 100% solution = 1.2 L/min

rate of output of nitric acid = 8 L/min * x L / 200 L = 0.04x L/min

$\frac{dx}{dt}=1.2-0.04x\\\\\frac{dx}{dt}+0.04x=1.2 \\\\The\ integrating\ factor(IF)=e^{\int\limits {0.04} \, dt }=e^{0.04t}\\\\multiply\ through\ by \ IF:\\\\e^{0.04t} \frac{dx}{t}+e^{0.04dt}(0.04x)=e^{0.04t}(1.2)\\\\integrating:xe^{0.04t}=1.2\int\limits e^{0.04t}dt\\\\xe^{0.04t}=30e^{0.04t}+C\\\\x(t)=30+Ce^{-0.04t}\\\\At\ t=0,x=1\\\\x(0)=30+Ce^{-0.04*0}\\\\1=30+C\\\\C=-29\\\\x(t)=30-29e^{-0.04t}\\\\At \ 10\%,x=10%\ of\ 200L=2\\\\2=30-29e^{-0.04t}\\\\29e^{-0.04t}=28\\\\$

$29e^{-0.04t}=28\\\\e^{-0.04t}=0.9655\\\\t=0.88\ s$

The percentage of nitric acid in the tank reach 10% at 0.88 s

3 0

2 years ago

A teacher needs 256 lengths of string cut to 40cm each. If balls of string are 30M long, how many balls are needed?

Otrada [13]

First you need to work out how much string is needed -
256 pieces needed x 40cm each:
256 x 40 = 10240cm

Then, convert to metres (100cm = 1m)
10240 / 100 = 102.4m

Then, you work out how many balls are needed:
30 can fit into 102.4 3 times with .41m to spare. So, you need three balls of string, PLUS another one to cover the 41cm

So to conclude: 4 balls of string are needed.

4 0

2 years ago

PLEASE HELP 30 POINTS Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building mater

jarptica [38.1K]

Logarithmic functions and exponential functions are inverse and opposite of one another

The logarithmic function is $y = \log_2(x)$ , and the length at 8 pascals is 3 units

<h3>How to determine the logarithmic function</h3>

The exponential function is given as:

$f(x) = 2^x$

Express f(x) as y

$y = 2^x$

Swap the positions of x and y

$x = 2^y$

Take the logarithm of both sides

$\log(x) = \log(2^y)$

Apply the rule of logarithm

$\log(x) = y\log(2)$

Divide both sides by log(2)

$y = \frac{\log(x)}{\log(2)}$

Apply the change of base rule of logarithm

$y = \log_2(x)$

When the strength is 8 pascals, we have:

$y = \log_2(8)$

Express 8 as 2^3

$y = \log_2(2^3)$

So, we have:

$y =3 \log_2(2)$

Evaluate log 2 base 2

$y =3$

Hence, the logarithmic function is $y = \log_2(x)$ , and the length at 8 pascals is 3 units

Read more about logarithmic and exponential functions at:

brainly.com/question/11464095

7 0

1 year ago

!!!!!!!!!!! NEEEEeD HELp ASAP

marin [14]

Answer:

A = π(P)

I can't give a numeral answer because neither P nor A is defined.

4 0

3 years ago

Read 2 more answers

Least to greatest !?

Bad White [126]

The lengths are $\frac{5}{6} \frac{5}{12} and \frac{1}{3}$
finding the LCM we get
$\frac{10,5,4}{12}$
arranging them
$\frac{1}{3} \frac{5}{12} and \frac{5}{6}$

6 0

2 years ago