. 6.8 • 102
Help me c:
Answer:693.6
Step-by-step explanation:
102
6.8
8• 2 16
Suppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows into the second lake, and then water from the second lake flows further downstream. The in and out flow from each lake is 500 liters per hour. The first lake contains 100 thousand liters of water and the second lake contains 200 thousand liters of water. A truck with 500 kg of toxic substances crashes into the first lake. Assume that the water is being continually mixed perfectly by the stream.
a. Find the concentration of toxic substances as a function of time in both lakes.
b. When will the concentration in the first lake be below 0.001 kg per liter?
c. When will the concentration in the second lake be maximal?
Answer:
a. For the first lake;
c = (m·t - 0.005·m·t²)/100000
For the second tank, we have;
c = m·t/200 - m·t²/80000
b. t ≈ 1.00505 hours
c. 200 hours
Step-by-step explanation:
The flow rate of water in and out of the lakes = 500 liters/hour
The volume of water in the first lake = 100 thousand liters
The volume of water in the second lake = 200 thousand liters
The mass of toxic substances that entered into the first lake = 500 kg
The concentration of toxic substance in the first lake = m₁/(100000)
Therefore, we have;
The quantity of fresh water supplied at t hours = 500 × t
The change
The change in the mass of the toxic substance with time is given as follows
dm/dt = (m - m/100000 × 500 × t)/100000
c = (m·t - 0.005·m·t²)/100000
For the second tank, we have;
c = m/100000 × 500 × t - (m/100000 × 500 × t)/200000 × 500 × t
Using an online tool, we have;
c = m·t/200 - m·t²/80000
b. When c < 0.001 kg per liter, we have m < 0.001 × 100000, which gives m < 100
Substituting gives;
0.001 = (100·t - 0.005·100·t²)/100000, solving with an online tool, gives;
t ≈ 1.00505 hours
c. For maximum concentration, we have;
c = m·t/200 - m·t²/80000
m/200000 = m·t/200 - m·t²/80000
1/200000 = t/200 - t²/80000
dc/dt = d(t/200 - t²/80000)/dt = 0
Solving with an online tool gives t = 200 hours
What is the rate of change of y= 34x - 2
y + 4 = 14(x-12), determine the slope and the y-intercept.
Answer:
Step-by-step explanation:
y + 4 = 14(x - 12)
y + 4 = 14x - 168
y = 14x - 168 - 4
y = 14x - 172
The speed of light is 3 x 10^8 meters/second. If the sun is 1.5 X 10^11 meters from earth, how many seconds does it take the sunlight to reach the Earth? (Time = Distance/Speed).
Answer:
Time = 500 seconds or 8.333 minutes
Step-by-step explanation:
Time = Distance/Speed
Speed of light = 3 x 10^8 meters/second
Distance=1.5 X 10^11 meters
Time = 1.5 X 10^11 meters/3 x 10^8 meters/second
We solve using the scientific notation. When 8 is taken to the top it is subtracted from 11 ( the base 10 is the same -- laws of exponents)
Dividing 1.5 by 3 gives 0.5 .
Time = 1.5 X 10^(11- 8) meters/3 meters/second
Time = 0.5 X 10^3 seconds
Time = 500 seconds
Dividng seconds with 60 will give minutes
Time= 500/60 = 8.333 minutes
anyone stressed?? vent to me. and (so this will count as a question)
Laura earns $115 a month babysitting. If she saves all of the
money she earns in June and July and uses it to buy a bicycle
that cost $158, how much money will she have left?
A. $230,00
B. $43.00
C. $60.00
D. $72.00
Answer:72
Step-by-step explanation:
115+115=230
230-158=72
If you add the 115 a month that she earns from babysitting, then add both the months pay together, than subtract 158(cost of the bicycle) by the total pay, you should get 72$
Answer: D. $72
Step-by-step explanation:
If she earns $115 a month and June and July is a combination of two months then we will have to find the amount she earn toegther in June and July by multiplying 2 by $115.
2(115) = 230
She earned $230 in those months, and if the bicycle cost $158 , then we will have to subtract $158 from $230 to find her remaining amount.
$230 - $158 = $72
Hello sam hhehehe .dk ;
Answer:
hello
Step-by-step explanation:
Write the equation of line
that has slope of 4 and
goes through the point 0-3
Answer:
y=4x-3
Step-by-step explanation:
What is the solution of 3(x-1) - X = 3 + 2(x-3)?
Answer:
3(x-1) -X =3+ 2(x-3)
3x-3 -X = 3+2x-6
2x-3= 2x-3
2x-2x =-3+3
0=0
Plz help me give 13 point it’s timed helpplz
Answer:
yyyy
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Estimate the value of the irrational number (0.6289731...)^2. Up to how many decimal digits is the estimation correct?
(1.) 5
(2.) 4
(3.) 6
(4.) 7
Answer:
6
Step-by-step explanation:
i am 96% sure it is 6
i might be wrong tho so i would wait for another answer ._.
Answer:
Its 6 and give the other guy his brain he deserves it
Step-by-step explanation:
(6+2i)÷3i solve this problem
ANSWER THIS CORRECTLY AND I WILL 5 STAR U AND GIVE U POINTS AND THANK YOU
IF NOT ME AND MY CLASS WILL REPORT YOU FOR WRONG ASNWERS AND GIVE U ONE STAR
HELP ME OUT PLS :))
HAPPY THANKSGIVING ALL!
Answer:
C
Step-by-step explanation:
given:
m= -2 and (3, -1)
point-slope form: y-y1= m(x-x1)
y - (-1) = -2(x-3)
y + 1 = -2(x-3)
Answer:
C.
Step-by-step explanation:
A.) y - 1 = -2(x - 3)
y - 1 = -2x + 6
y = -2x + 6 + 1
y = -2x + 7
B.) y - 1 = -2(x + 3)
y - 1 = -2x - 6
y = -2x - 6 + 1
y = -2x - 5
C.) y + 1 = -2(x - 3)
y + 1 = -2x + 6
y = -2x + 6 - 1
y = -2x + 5
D.) y + 1 = -2(x + 3)
y + 1 = -2x - 6
y = -2x - 6 - 1
y = -2x - 7
Solve the equation. 4d + 2d – 4d + 4 = 3d
Answer:
d = 4
Step-by-step explanation:
1. Simplify both sides of this equation, to start off with.[tex]4d+2d−4d+4=3d
[tex]4d+2d−4d+4=3d[/tex]
[tex]4d+2d+−4d+4=3d[/tex]
2. Combine all the like terms you see here.(4d+2d+−4d)+(4)=
d+4=3d[/tex]
(2d+4=3d)[/tex]
3. Subtract 3d from both sides of this equation.[tex]2d+4−3d=3d−3d[/tex]
[tex] - d + 4 = 0[/tex]
4. Subtract 4 from each sides of the equation.[tex]−d+4−4=0−4[/tex]
[tex] - d = - 4 [/tex]
5. Divide both of the sides by -1.
[tex] \frac{ - d}{ - 1} = \frac{ - 4}{ - 1} [/tex]
Therefore, the answer is d = 4.
what is the equation of a line that passes through (-7, 3) and is perpendicular to -5/3x = 1/4y -8
Select all answers that apply
Y = 3/20x + 81/20
Y-3 = 3/20(x+7)
Y-3 = -20/3(x+7)
Y = -20/3x -32
3x -20y = -81
The answer can be anything thing that occurs during solving the problem or is the answer.
Answer:
The 1st, 2nd and 5th options are correct.
Step-by-step explanation:
The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.
①Rewrite the given equation into the form of y=mx+c to find the gradient.
[tex]- \frac{5}{3} x = \frac{1}{4} y - 8 \\ \frac{1}{4} y = - \frac{5}{3} x + 8 \\ y = - \frac{20}{3} x + 32[/tex]
Thus, the gradient of the given equation is [tex] - \frac{20}{3} [/tex].
② Find gradient of unknown line.
The product of the gradients of perpendicular lines is -1.
Let m be the gradient of the unknown line.
[tex]- \frac{20}{3} m = - 1 \\ m = - 1 \div ( - \frac{20}{3} ) \\ m = - 1 \times ( - \frac{3}{20} ) \\ m = \frac{3}{20} [/tex]
③Substitute the value of m into the equation.
[tex]y = \frac{3}{20} x + c[/tex]
④ Find the value of c by substituting a pair of coordinates.
When x= -7, y= 3,
[tex]3 = \frac{3}{20} ( - 7) + c \\ 3 = - \frac{21}{20} + c \\ c = 3 + \frac{21}{20} \\ c = 4 \frac{1}{20}[/tex]
Thus, the equation of the line is [tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex].
Thus, the 4th option is incorrect.
Writing c as an improper fraction,
[tex]y = \frac{3}{20}x + \frac{81}{20} [/tex]
Thus, the 1st option is correct.
-3 from both sides of the equation:
[tex]y - 3 = \frac{3}{20} x + \frac{21}{20} [/tex]
Factorise 3/20 out of the right hand side:
[tex]y - 3 = \frac{3}{20} (x + 7)[/tex]
Thus, the 2nd option is correct.
The 3rd option is incorrect as factorising -20/3 out would leave us with -0.0225 as the coefficient of x.
Let's look at the 5th option.
[tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex]
×20 on both sides:
[tex]20y = 3x + 81[/tex]
-20y on both sides:
[tex]3x - 20y + 81 = 0[/tex]
-81 on both sides:
[tex]3x - 20y = - 81[/tex]
Thus, the 5th option is also correct.
Solve for x. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
sin90 = sinx
19 17
sin x=0.8947
x=63.47°
Tom has $5.05 in quarters and dimes. How many coins are quarters if the total
number of coins is 28? Try creating a system of equations and solving this by either
substitution or elimination.
quarters
Help due by 8 am tm
Answer: The answer would be 7.03
Step-by-step explanation: cause you gotta get the 28 in there i hope im right
Answer:
15 quarters
Step-by-step explanation:
Assuming q = quarters and d = dimes...
First, set up the equations. q + d = 28 since we have 28 coins, and the latter is because a quarter is worth $0.25 and a dime is worth $0.1 - totaling $5.05.
q + d = 28
.25q + .10d = 5.05
Try to get one of the variables equal to the equation above. In this case, I tried to get the "q" variables equal to each other.
q + d = 28
4(.25q + .10d) = 4(5.05)
After this, you "subtract" the two equations from each other. Remember that d = 1d, and 1 - .4 = .6
q + d = 28
q + .4d = 20.20
Divide both sides by .6 to get d by itself.
.6d = 7.8
There are 13 dimes.
d = 13
Subtract 13 from the total coins (28) to get the amount of quarters.
28 - 13 = 15
13 dimes, 15 quarters. Hope this helped!
what the slope of (-15,9) (-10,3)
Answer:
The formula for slope:
[tex]y2-y1/x2-x1[/tex]
so[tex](3-9)/(-10--15)[/tex]
which is
this:[tex]-6/5[/tex]
so the slope is
this: [tex]-6/5[/tex]
Hope this helps :D
simplify (x^2+3)^2-(x^2-1)^2
Answer:
Simplify the expression.
8x² + 8
Answer:
8(x^2 +1)
Step-by-step explanation:
(x^2 + 3)^2 - (x^2 - 1)^2
(x^2 + 3 - (x^2-1)) • (x^2 + 3 + (x^2 - 1))
(x^2 + 3 - x^2 + 1) • (x^2 + 3 + (x^2 - 1)
(3 + 1) • (x^2 + 3 + x^2 - 1)
4(2x^2 + 1)
4 • 2(x^2 + 1)
8(x^2 +1)
Two sides of a triangle are 12 meters and 16 meters. What is the largest the third side can be?
A) 22 meters
B) 24 meters
C) 26 meters
D) 28 meters
Answer:
The largest third side would be 26 meters.
Option B is correct.
Step-by-step explanation:
We are given two sides of triangle 12 meters and 16 meters.
We need to find What is the largest the third side can be?
We know that the length of third side should be less than the sum of two sides of triangle
third side < length of first side + length of second side
third side < 12+16
third side < 28
So, the length of third side should be less than 28
We need to find the largest the length of third side can be: from options 22, 24 and 26. We would not consider 28 because length should be less than 28.
So, the largest third side would be 26 meters.
Option B is correct.
At Gary's car wash 49 cars can be washed in 4 hours. At this rate, how many cars can be washed in 8 hours?
Answer:
98
Step-by-step explanation:
49 + 49 = 98
In a class of 38 students, 15 play hockey and twice as many play basketball. Each student in the class plays either hockey or basketball. How many students play both hockey and basketball?
Answer:
7 students
Step-by-step explanation:
Venn Diagram:
15hockey and 30 basket ball.
45 in total:
45-38=7
so 7 students.
Check:
15:7:30
subtract 7 in middle
8:7:23
8+7+23=38
Correct !!!
Hope this helps plz hit the crown :D
A 3-foot rain barrel is being filled from the runoff of a roof. The barrel has already collected 2.75 feet of water. For
every additional inch of rainfall into the barrel, the level of water in the rain barrel rises by 0.75 inch.
What is the y-intercept of the linear model representing the change in height of water, in inches, based on the
rainfall, in inches?
ssssssssssssssssssssssssssssss
Which chemical equation is balanced?
Question 2 options:
CH4 + O2 → H2O + CO2
CH4 + O2 → 2H2O + CO2
6CH4 + O2 → 2H2O + 2CO2
CH4 + 2O2 →2H2O + CO2
help
Step-by-step explanation:
CH4 + 2O2 →2H2O + CO2
the answer
Answer:
The balanced chemical equation of the given reaction are;
b.CH4 + 202-> 2H20 + CO2
Step-by-step explanation:
C=C
H4=2H2
2O2=O2+2O(2O2)
I Think it helps you.
If a person who weighs 70 kilograms has a brain that weighs 1.4 kilograms, what percent of the persons body weight is brain
Answer:
the answer would be around 1.5 to two percent
Step-by-step explanation:
Can someone please help me with this problem? I don’t understand how to do it..
Answer:
y=x+2
Step-by-step explanation:
y=mx+b
m is slope
b is y intercept
it crosses the y intercept at (0,2) therefore b is 2
rise over run is 1 so slope is 1
fill in
y=1x+2
or y=x+2
you can fill in any (x,y) point into this
7a(3b - 2c + 4)
Help?
Answer:
21ab-14ac+28aStep-by-step explanation:
[tex]7a(3b - 2c + 4)\\\\\mathrm{Distribute\:parentheses}\\\\=7a\times \:3b+7a\left(-2c\right)+7a\times\:4\\\\\mathrm{Apply\:minus-plus\:rules}\\\\+\left(-a\right)=-a\\\\=7\times\:3ab-7\times\:2ac+7\times\:4a\\\\Simplify\\\\21ab-14ac+28a[/tex]
Please help!
Which shows the greatest common factor of these numbers being 14?
A.
28 = 2 x 2 x 7
63 = 3 x 3 x 7
B.
28 = 2 x 2 x 7
42 = 2 x 3 x 7
C.
42 = 2 x 3 x 7
84 = 2 x 2 x 3 x 7
D.
42 = 2 x 3 x 7
63 = 3 x 3 x 7
Answer:
B. 28 = 2 x 2 x 7
42 = 2 x 3 x 7
Step-by-step explanation:
B is the correct answer. If you look at the list in answer choice B, you will see that each number has a common factor of 2 and 7. When you multiply 2 and 7 together, you get a product of 14.
Answer:
B !
Step-by-step explanation:
what is the equation of a line in slope intercept form that passes through points (4,3) and (1,-6)
pls help quick : )
Answer:
y = 3x-9give me brainliest please
Step-by-step explanation:
To find the equation of a line that passes through two points, use point-slope form.
[tex]y-y_{1} = m(x-x_{1})[/tex] ...
where [tex](x_{1}, y_{1})[/tex] is the first point, and [tex]m[/tex] is the slope.
Start with the slope (m). To find the slope, you find the change in y over change in x, or [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{-6-3}{1-4}[/tex] = [tex]\frac{-9}{-3}[/tex] = 3
[tex]m=3[/tex]
Then, put the values into point-slope equation.
[tex]y-y_{1} = m(x-x_{1})[/tex] = [tex]y-3 = 3(x-4)[/tex] = [tex]y-3 = 3x-12[/tex] = [tex]y = 3x-9[/tex]
Jade has $100 to spend on shoes and socks.She buys a pair of shoes for $75 and and wants to spend the rest of the money on socks.Each pair of socks costs $3.50. What is the greatest number of pairs of socks that jade can buy
Answer:
21.5
Step-by-step explanation: