Answer:
An airplane cruises 1 kilometer in 1/12 of a minute. What is its cruising speed?200
A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min. Find the number A(t) of pounds of salt in the tank at time t.
Answer:
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
Step-by-step explanation:
Given - A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min.
To find - Find the number A(t) of pounds of salt in the tank at time t.
Proof -
Given that,
Capacity of water = 400 gallons
rate in flow = 4 gal/min
rate out flow = 8 gal/min
Concentration in = 3 lbs/gal
Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)
Now,
Let
A(t) = Amount of salt in the tank at time t
Now,
Initially tank has 400 gallons of water, So
A(0) = 0 ................(1)
Now,
Rate of change in the amount of salt = [tex]\frac{d}{dt} A(t)[/tex]
= (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)
= (4) (3) - (8) ([tex]\frac{A(t)}{400 - 4t)}[/tex]
= 12 - [tex]\frac{2A(t)}{100 - t)}[/tex]
⇒[tex]\frac{d}{dt} A(t)[/tex] + [tex]\frac{2A(t)}{100 - t)}[/tex] = 12
Now,
Integrating Factor, I.F = [tex]e^{\int {\frac{2}{100 - t} } \, dt }[/tex]
= [tex]e^{-2ln(100 - t)}[/tex]
= (100 - t)⁻²
⇒I.F = (100 - t)⁻²
The solution becomes
A (I.F) = ∫ (I.F)(12) dt + C
⇒A (100 - t)⁻² = ∫12(100 - t)⁻² dt + C
⇒A (100 - t)⁻² = -12(100 - t)⁻¹ (-1) + C
⇒A(t) = [tex]12(100 - t)+ C(100 - t)^{2}[/tex]
Now,
We have A(0) = 0
⇒C = -12/100
∴ we get
A(t) = 12(100 - t) - [tex]\frac{12}{100}[/tex] (100 - t)²
= 12(100 - t) [ 1 - [tex]\frac{100 - t}{100}[/tex] ]
= 12(100 - t) ([tex]\frac{t}{100}[/tex])
= [tex]\frac{3t(100 - t)}{25}[/tex]
⇒A(t) = [tex]\frac{3t(100 - t)}{25}[/tex]
∴ we get
The number A(t) of pounds of salt in the tank at time t = [tex]\frac{3t(100 - t)}{25}[/tex]
Can someone help fast to find a and c
Answer: 15 10
Step-by-step explanation:
how does the digit 5 in the number 357 compare with the digit 5 in number 465
Answer:
The digit 5 in 357 is in the tens place while the digit in the number 465 is in the ones place
Step-by-step explanation:
Good luck
Divide round your answer to the nearest hundredth 5608.67÷7
Answer:
5608.67 ÷ 7 = 801.24
Which transformation could NOT be used to prove that two circles are congruent to one another?
Answer: D
Step-by-step explanation:
BRAINIEST FOR CORRECT ANSWER!! :))) ——————-
Determine the possible side lengths of the third side of a triangle with known side
lengths of 5 and 8.
A) 5 < c < 8
B) 3 < c < 13
C-5 < c <-8
D) -3 < C < -13
Steve watched television for 3/4 hour on Monday and 5/6 hour on Tuesday. How much longer did he watch television on Tuesday than on Monday?
_______ hour
According to this diagram, what is cos 28°? 62° 17 8 28° 90° 15 O A. 17 15 O B. 8 17 O c. 15 17 O D. O E. 8 15 15 OF.
Answer:
C. [tex] Cos(28) = \frac{15}{17} [/tex]
Step-by-step explanation:
Recall: SOHCAHTOA
Thus,
[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]
Reference angle = 28°
Adjacent = 15
Hypotenuse = 17
Plug in the values
[tex] Cos(28) = \frac{15}{17} [/tex]
Write a equation that can be used to find y, the number of gallons water used for showering for x minuets
Answer:
y = 6x
Step-by-step explanation:
To write an equation, find the unit rate or constant of proportionality (k).
Using a point on the line, (3, 18):
Constant of proportionality, k = y/x = 18/3
k = 6
To write an equation, substitute k = 6 into y = kx.
Thus:
y = 6x
what is the graph of the system? y < -2
Answer: The answer is -2 it's just going to stay as -2 because y has no value.
Answer: this is the graph i wish that could help :)
A store baked 1,344 bagels and placed them into bags to sell. Each bag contained 6 bagels.How many bags of bagels were made? Explain the strategy you used to solve this problem.
3. Write in fraction form: 15.43
(5 Points)
15 43/100
O 154 3/100
O 1543/100
O 15 43/10
Answer:
1543/100 is the answer
Please do not send me a link to the answers I will have u reported but please answer this in feet
Answer:
24.5
Step-by-step explanation:
HELP WILL MARK BRAINLIEST IF RIGHT!!!
Answer:
im so sorry bt I dont know this one
Step-by-step explanation:
Posted this 4 times nobody knows?
Answer:
D. f(x) = 2^x
Step-by-step explanation:
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
The base is always 2. The exponent changes and is x.
Answer: D. f(x) = 2^x
A fair spinner has 10 equal sections: 4 red, 3 blue and 3 green.
It is spun twice.
What is the probability of getting the same colour twice?
Answer:
4 divided by 10 is 40% 3 divided by 10 is 30 percent
Step-by-step explanation:
for red there would be 40 percent probability and green and blue both have 30% probability.
What is the some of the finite arithmetic series?
Answer:
455
Step-by-step explanation:
I need help look in screenshot plzz
Answer:
45
Step-by-step explanation:
3 to the power of 2=9
and 9x5 =45
please answer the following questions!
Answer:
3 cm cube: 27
6 cm cube: 216
Step-by-step explanation:
First, you would need to find the volume of the 3 cm cube: 3*3*3=27
To build this cube you would need 27 1 cm cubes
For the 6 cm side cube you would need to do 6*6*6=216
So you would need 216 1 cm cubes
Hope this helps!
PLEASE HELP I GIVE BRAINLIEST
Answer: 777654
Step-by-step explanation:
lol
x-8=17
plssssss help me
Answer:
25
Step-by-step explanation:
17+8
"Death Valley Hike"
A hiker in Death Valley begins the climb out of the valley from 150 feet below sea level. 5
minutes later, the hiker is 87.5 feet below sea level.
a) Write an equation that models this situation.
b) What is the y-intercept and what does it represent?
c) What is the x-intercept and what does it represent?
d) What is the slope and what does it represent?
e) What is the hiker's distance below sea level after 10 minutes?
Answer:
I'm pretty sure E
Step-by-step explanation:
think about it he traveled 70 feet in 5 minutes so he would still be below sea level
what property of equality is used to isolate the term with variable in the equation 2 x + 2 = 4?
A. Addition property
B. Reflexive property
C. Multiplication property
D. Transitive property
(it will help me a lot)
Answer:
I think it is addition property
I need help please ????! Anyone wanna help me
Answer:
the inverse operation for addition is subtraction
In ΔDEF, the measure of ∠F=90°, FD = 78 feet, and EF = 11 feet. Find the measure of ∠D to the nearest tenth of a degree.In ΔDEF, the measure of ∠F=90°, FD = 78 feet, and EF = 11 feet. Find the measure of ∠D to the nearest tenth of a degree.
Answer:
8 degrees
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Hi please help me.. will give brainlest
Answer:
Volume = l*w*h
Equation: 1620 = 9*9*h
1620=81h
h=20 cm
On a youth soccer team 3 out of 12 team members have played in previous years. Based on this information, if 150 kids are in the youth soccer league, then how many could be expected to have played the year before?
Solve for x
This is also an octagon if it helps!
Answer:
x = 10
Step-by-step explanation:
it has 8 sides so:
total interior angle degrees = (180° x 8 sides) - 360° = 1080°
11x + 14 + 4x + 87 +2x + 70 + 4x + 31 + x + 92 + 3x + 167 + 5x + 48 + 2x + 251 = 1080°
combine like terms:
32x + 760° = 1080°
subtract 760° from both sides of the equation:
32x = 320°
divide both sides by 32:
x = 10
what is the percent increase
from 3.49 to 3.89
What is the y-intercept of the line?
1
1/2
-2
0
Answer:its 1
Step-by-step explanation: