Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]
[tex]R_{in} =3 \ lb/min[/tex]
At a slower of 4 gal/min, the solution gets pumped out;
So,
[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]
[tex]R_{out} = \dfrac{2A}{50+t }[/tex]
The differential of the equation is:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]
For the linear differential equation, the integrating factor is determined as:
[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]
[tex]= (50+t)^2[/tex]
Multiplying [tex](50+t)^2[/tex] with the above integration factor;
[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]
[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]
[tex](50+t)^2 A = (50 +t)^3 + c[/tex]
[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]
[tex]A(30) = 76.09 \ pounds[/tex]
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
Three robots ran the same distance. The first robot ran 150 meters per minute.
The second robot ran 150 meters per minute faster than the first robot and 120
meters per minute faster than the third robot. The winner finished 2 minutes
before the robot that finished in second place. What distance (in meters) did the
robots run?
Answer:
900 meters.
Step-by-step explanation:
Trust me. Russian School Of Math answer :)
Trevor is making 2/3 of a recipe for chicken noodle soup. He adds ½ cup of chopped celery. The equation 2/3 c = 1/2 can be used to find the number of cups c of chopped celery in the original recipe. How many cups of chopped celery does the original recipe call for?
Answer:
Cups of chopped celery in original recipe = [tex]\frac{3}{4}\ cups[/tex]
Step-by-step explanation:
Given that:
Trevor is making 2/3 of a recipe
Number of cups of chopped celery used = 1/2 cup
The following equation can be used to find the original number of cups of chopped celery used in recipe.
[tex]\frac{2}{3}c=\frac{1}{2}[/tex]
Multiplying both sides by 3/2
[tex]\frac{3}{2}*\frac{2}{3}c=\frac{1}{2}*\frac{3}{2}\\\\c= \frac{3}{4}\\[/tex]
Hence,
Cups of chopped celery in original recipe = [tex]\frac{3}{4}\ cups[/tex]
Please help I’m stuck!!!!
Answer: abe
Step-by-step explanation: start at origin and is proportional
Select the correct answer.
15
If no denominator equals zero, which expression is equivalent to I
7
+
I + 62
6
OA.
OB.
221 + 132
12 - 36
221 48
12 - 36
22
12 – 36
221 + 48
12 – 36
O C.
OD.
Reset
Next
Answer:
See Explanation
Step-by-step explanation:
Your question is poorly formatted. However, I'm able to deduce that your question involves at least 2 algebraic fractions that needs to be simplified.
So, I'll make use of the following expression:
[tex]\frac{3n}{n + 3} + \frac{5}{n - 4}[/tex]
When you follow the steps I'm about to provide, you'll arrive at the right answer
Required
Determine an equivalent expression
[tex]\frac{3n}{n + 3} + \frac{5}{n - 4}[/tex]
Step 1: Take L.C.M of the denominators
[tex]LCM = (n+3)(n-4)[/tex]
Step 2: Evaluate the fractions
[tex]\frac{3n}{n + 3} + \frac{5}{n - 4}[/tex] [tex]= \frac{3n(n-4)+5(n+3)}{(n+3)(n-4)}[/tex]
Step 3: Open the brackets at the numerator
[tex]\frac{3n}{n + 3} + \frac{5}{n - 4}[/tex] [tex]= \frac{3n^2-12n+5n+15}{(n+3)(n-4)}[/tex]
Step 4: Collect and evaluate like terms
[tex]\frac{3n}{n + 3} + \frac{5}{n - 4}[/tex] [tex]= \frac{3n^2-7n+15}{(n+3)(n-4)}[/tex]
Follow the above steps, and you'll be able to solve your question.
Which Figure has a line sysmmetry F,H,J,L,R
Answer:
njnjfsdnjfe
Step-by-step explanation:
Answer:
we cant see
Step-by-step explanation:
Rise over run (-5,2) and (1,-2)
(4,10) and (-2,-5) slope
Answer/Step-by-step explanation:
6. Given, (-5, 2) and (1, -2):
[tex] \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_2} [/tex]
[tex] = \frac{-2 - 2}{1 - (-5)} [/tex]
[tex] = \frac{-4}{6} [/tex]
[tex] = \frac{-2}{3} [/tex]
9. Given, (4, 10) and (-2, -5):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_2} [/tex]
[tex] = \frac{-5 - 10}{-2 - 4} [/tex]
[tex] = \frac{-15}{-6} [/tex]
[tex] slope = \frac{5}{2} [/tex]
X= What does ×= 88, 89 or 90
Based on the table, which function represents the same relationship? The x column has 0, 1, 2, 3. The y column has 0.0625, 0.25, 1, and 4.
Answer
A g(x) = (0.25)
B g(x) = 256(0.25)
C92) = 0.0625(4)"
D g(x) = 0.5(4)"
Answer: C 92) = 0.0625(4)
Step-by-step explanation:
it iz
summer babysitting. She decided
to put this money in a bank that
earns a 5% simple interest rate.
How many years will it take to
double her initial deposit?
A) 10 years
B) 12 years
C) 15 years
D) 18 years
E) 20 years
Answer: B.12 years
Step-by-step explanation:
Simplify:1/5 + (-2/3)?
Answer:
SOOOOOO
Step-by-step explanation:
YOU MAKE IT 1/5 + -2/3
INTOOO
3/15+-10/15
THENNNN
YOU ADD THEMMM
AND UU GETTTT
-7/15
SOOO THAT UR ANSWER ITSS A THE FIRST ONE
-7/15
Help me plssssssssss
Answer:
The answers are as follows:
5. [tex]12+3 = 3+12[/tex]
7. [tex](6+4)+8 = 6+(4+8)[/tex]
9. [tex](10*5)*7 = 10*(5*7)[/tex]
Step-by-step explanation:
5. 12 and 3
Commutative property of addition states that the order of two numbers in addition doesn't matter; the result will be the same. If a and b are two numbers then the property will be:
a+b = b+a
For the given question, the commutative property will be:
[tex]12+3 = 3+12[/tex]
Associative property deals with three numbers or variables. It states that when 3 numbers are being added or multiplied their order doesn't affect the result.
It can be stated as:
(a+b)+c = a+(b+c)
7. 6,4 and 8
The associative property will be:
[tex](6+4)+8 = 6+(4+8)[/tex]
9. 10,5 and 7
[tex](10*5)*7 = 10*(5*7)[/tex]
Hence,
The answers are as follows:
5. [tex]12+3 = 3+12[/tex]
7. [tex](6+4)+8 = 6+(4+8)[/tex]
9. [tex](10*5)*7 = 10*(5*7)[/tex]
if i run 160 meters 20 times in 2 hours how fast am i going
Answer:
1700 meters / hour
Step-by-step explanation:
160x20 = 3200
3200/ 2 = 1700
Please help! Question posted above ^
Answer:
( x^2 - 6 )^2
Step-by-step explanation:
x^4 -12x^2 +36Find one factorFactor by grouping(x^2 - 6x) (x^2 - 6x)*solution* ( x^2 - 6 )^2
Victor purchased motor oil for $2 a bottle and car wax for $4 a bottle. The inequality 2x + 4y < 16 can
be used to determine the number of bottles of motor oil, x, and the number of bottles of car wax, y,
Victor purchased for less than $16, not including tax. Which of the following ordered pairs best
represents a reasonable combination of bottles of motor oil and car wax that Victor could have
purchased?
Answer:(3,2)
Step-by-step explanation:
please anwser this for me!!
Answer:
No
Step-by-step explanation:
The relation given as represented by the table of values is definitely not a function. This is because, 1 domain value (x-value), is having two range values (y-values), 2 and 5, that are assigned to it.
A function cannot have two y-values assigned to one x-values.
Could y’all pls help out brainlest correct answer only
Answer:
The third option with the decimal on top as a fraction
Answer:
C
Step-by-step explanation:
Think of the proportional relationship as algebra.
k*number of MovieTickets = Cost, where k is the constant of proportionality.
To find k, you can substitute values in the table and solve for k.
In this example:
k*5 = $28.75
k = $28.75/5
This answer is C.
The amount a tutor is compensated for one-hour individual or group
tutoring sessions is shown in the table. The relationship between
compensation and number of sessions is linear.
Sessions
1
2
3
4
5
39.50
69.00
98.50
128.00 157.50
Group ($)
Individual ($)
29.50
49.00
68.50
88.00
107.50
a. Find the rate of change and the initial value for the group sessions.
b. Find the rate of change and the initial value for individual sessions.
c. Compare and contrast the rates of change and initial value.
Answer:
Step-by-step explanation:
the slope is 29.5, so it is 29.5$ per hour for group
39.5-29.5 = 10$ for initial for group
49-29.5 = 19.5 perhour for individual
29.5-19.5 = 10$ for initial for indiivudla
same initial but different rates
What is the equation of the line that passes through the point (2, -2) and has a
slope of -1/2?
Answer:
Step-by-step explanation:
use the point-slope formula [y-y1 =m(x-x1) ] with the given info
for the point P=(x1,y1) =(2,-2) and the slople m = -1/2
plug those into the formula
y-(-2)= -1/2(x-2)
y+2= -1/2x + 1
y= -1/2x+1 - 2
y = -1/2x - 1
:) got it?
these are hard untill you get the idea of the two formulas
point-slope: y-y1 = m(x-x1) and
slope-intercept: y= mx+b
memorizing those will help a lot
I don’t know this someone help
Answer:
yes what that guy said is right
Given the equation in point slope form y-5=1/2(x+1)
Answer:
The slope of this equation is 11/2. The point is (1/2, 0)
Step-by-step explanation:
I hope this is the right answer, good luck!
I am once again asking for your help with solving this problem.
Answer:
llll, Vl, Vll
Step-by-step explanation:
SOMEONE PLEASE PLEASE HELP ME ON THIS!!
X=22
14 plus 8 gives you x
[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:
35
Step-by-step explanation:
Can someone please help me with this question?
Answer:
anime girl
Step-by-step explanation:
anime girl
What is this number in standard form?
(8 X 100) + (4 x 1) + (6 x 1/100 ) + (3 x 1/1000)
Answer:
804.063
Step-by-step explanation:
just multiply each part and add
800 +4 +.06 +.003
804.063
M +2m + 3 for m = 12
What’s thatta
Answer:
39
Step-by-step explanation:
12+2×12+3
12+24+3
36+3
39
PEMDAS
What is the value of the expression 30 X 5 + 6 X 4
will give brainliest
Answer:
174
Step-by-step explanation:
Answer:
30 × 5 + 6 × 4= 150 + 24= 174Step-by-step explanation:
I hope it helps ❤❤Scrat the squirrel has a few nuts. When he put them in groups of 5 nuts, two nuts were left, and
when he laid them out in groups of 3 nuts, there were no nuts left. How many nuts among the
options provided below could belong to Scrat?
Answer:
The options are not shown, so i will solve this in a general way.
Let's suppose that there are N nuts
If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.
If we divide the N nuts into groups of 3, there is no remainder.
This means taht N is a multiple of 3. then we can write:
N = 3*k
where k is a random integer.
Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:
N = 5*j + 2
where j is a random integer.
Now we only need to find a pair of k and j (both positive integers) such that:
3*k = 5*j + 2
We can rewrite this as:
k = (5/3)*j + (2/3)
Now we could just input different values of j, and see if k is also an integer:
j = 2
k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4
Then the pair j = 2, k = 4 is a possible solution.
N = 3*k = 3*4 = 12
N = 5*j + 2 = 5*2 + 2 = 12
From this we can conclude that N = 12, so Scrat has 12 nuts.
Now with the equation
k = (5/3)*j + (2/3)
We can find other possible combinations of j and k, that will give different values for N.
for example, if j = 5:
k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9
Then the pair j = 5, k = 9 is also a possible solution:
N = 3*k = 3*9 = 27
N = 5*j + 2 = 5*5 + 2 = 27
In this case, Scrat has 27 nuts.
PLEASE HELP ME I NEED HELP PLEASE HELP
PLEASE GIVE THE ANSWER UNDER THE QUESTION AND RATIO
Answer:
6. 225 feet in 3 minutes = 75 feet in 1 minute (slower)
360 feet in 5 minutes = 72 feet in 1 minute
7. $4 for 5 ounces = $0.80 for 1 ounce (most expensive)
$14 for 20 ounces = $0.70 for 1 ounce
8. 72 people in 6 hours = 12 people in 1 hour
117 people in 9 hours = 13 people in 1 hour (greater rate per hour)
Answer:
A = 369 feet in 5 minutes B = $4 for 5 ounces C = 117 people in 9 hours
What is the distance from –8 to 4 on a number line?
Answer:
13 away
i used my fingers
Answer:
12
Step-by-step explanation:
-8_-7_-6_-5_-4_-3_-2_-1_0_1_2_3_4
Just count he bottom lines
Find (f+g)(x) and (f-g)(x)
f(x)=2x+7 g(x)=5x-4
Answer:
for (f+g)(x): 7x + 3; x = -3/7
for (f-g)(x): -3x - 3; x = -1
Step-by-step explanation:
(f+g)(x) = (2x+7)+(5x-4)
Eliminate parentheses.
2x + 7 + 5x -4
Combine like terms.
7x + 3
If you are solving for x, move the 3 to the other side.
7x = -3.
Then divide each side by 7.
x = -3/7
(f-g)(x) = (2x+7) - (5x -4)
Distribute the negative.
(2x+7) + (-5x+4)
Eliminate parentheses.
2x + 7 - 5x - 4
Combine like terms.
-3x -3
If you are solving for x, move the -3 to the other side.
-3x = 3
Then divide each side by -3.
x = -1.