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.
Anyone know the answer?
Answer:
5 feet = 152.4 centimeters 10 inches =25.4
Step-by-step explanation:
I learned from my classes of how to convert feet to centimeters and etc.
A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1–10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly less than the mean rating for detergent B.
Answer:
B is the better detergent
Step-by-step explanation:
If A has a lower number on the 1-10 scale, that means on average it was closer to the lower end, or the least clean end. This means that A cleans worse than B., and B is better.
The two laundry detergents B cleans better.
Although the questions seems to be tricky at the begging because of a lot of numbers, but actually it is not.
Given to us in the question that, 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B.
Thus, we can say that the sample size for both detergent A and detergent B is same. Also, the sample is distributed randomly meaning the sample is unbiased (fair).
Also, as given the mean rating for detergent A is found to be significantly less than the mean rating for detergent B. And we know that the mean is the average of a set of given numbers.
Therefore, we can conclude that if detergent A has a lower mean meaning, it has cleaned the clothes with less effectiveness as compared to detergent B.
Hence, Out of the two laundry detergents, B cleans better.
To know more visit:
https://brainly.com/question/16967035
find the value of x that makes lines u and line v parallel, help!!
Answer:
We are told they are parallelHence 10x+16+5x+14=18015x+30=180 15x=150x=1084.5 divided by 6261.45
Answer:
74.1
Step-by-step explanation:
if a number, n, divided by 8 equals 2.5, what is n?
Answer:
n is 20
Step-by-step explanation:
If n/8=2.5, then you can just do 8*2.5 to find n. 2.5*8=20
Answer:
n=20 because if you multiple 2.5 and 8 you will get 20 so if you divide 20 and 8 then you get 2.5
Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 529 square meters. Round each dimension to 4 decimal places
Answer:
[tex]x=23/\sqrt{6}[/tex],
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
Step-by-step explanation:
From the question we are told that
Surface area is 529 square meters
Generally the dimensions of the cuboid
[tex]v=x^y[/tex]
[tex]D=4xy+2x^2 =529[/tex]
[tex]V=x^29(\frac{529-6x^2}{4x})[/tex]
[tex]V' =529-6x^2/4[/tex]
[tex]v'=0[/tex]
Therefore
[tex]529=6x^2[/tex]
[tex]x=\sqrt{\frac{529}{6} }[/tex]
[tex]x=23/\sqrt{6}[/tex]
Mathematically
[tex]v''=\frac{12x}{4}[/tex]
[tex]v''=-3\frac{23}{\sqrt{6} }<0[/tex]
[tex]y= \frac{529-2*(\frac{529}{6} }{4*\frac{23}{\sqrt{6} } }[/tex]
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
Therefore
[tex]x=23/\sqrt{6}[/tex]
and
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
PLEASE HELP ME ANSWER THIS I WILL GIVE FREE THANKS
Answer:
C: Two solutions
Step-by-step explanation:
If you try to solve the problame you can find to solution's
Hope this Help's
Answer:
lol too bad laurenercsp6fpli
Step-by-step explanation:
Which of the following numbers
is a solution to this inequality?
14x > 36
3
2.
Answer:
[tex]x=\frac{18}{7}[/tex]
Step-by-step explanation:
which letters show the function rising?
A) A
B) E
C) A and E
D) A, B, and E
Answer:
c) a and e
Step-by-step explanation:
literally look at it b is just highest point, c is decreasing, d is lowest point... a is rising and e is also rising
s
is inversely proportional to
t
.
When
s
=
0.3
,
t
=
8
Work out
s
when
t
=
0.4
Answer:
s inversely proportional 1/t
s=0.3, t=8
s=k/t
0.3=k/8
k=0.3×8
k=2.4
find s when t=0.4
s=2.4/0.4
s=6.0 or 6
how many 2/3s are in 3
Answer:
7 and 1/3
Step-by-step explanation:
Which is the measure of ∠XYZ?
Answer:
you get the measure of angle XYZ by adding the measures of angles XY? and ZY?
70 +35 = 105 degrees is the measure of angle XYZ
A community garden center host a plant giveaway every spring to help community members start there gardens. Last year the give away supported 50 families by giving away 150 plants. Based on this ratio hawa many plants will they give away this year in order to support 65 families
Answer:
195 plants (verified) ✅Step-by-step explanation:
We will use a proportion to solve this.
x/y = x/y
let x = the number of families in each case
let y = the number of plants in each case
Since we don't know the second y, we will leave that as y and solve for it.
50/150 = 65/y
Cross-multiply
50y = 9750
Divide
195 = y
Now, we can check this by substituting the value of y back into the equation and seeing if both sides equal.
50 (195) = 9750
9750 = 9750 ✅
One quart of milk costs $1.05 and 1 gallon of milk costs $3.89. Which is a better buy? Explain.
HHELLPPP PLEASW HIRRY I WILL MARK BRAINLIEST
Answer: 1/36
Step-by-step explanation: 18 x 18 = 324
3 x 3 = 9
9/324 = 3/108 = 1/36
Answer:
1/36! good luck! :D
Step-by-step explanation:
who want's to do my homework? :D Also this might get deleted cause brainly is out to get me D:
Simplify the following rational expression. Use absolute value symbols when needed.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
1. [tex]\sqrt[3]{\frac{8}{216} }[/tex]
2. [tex]\sqrt[3]{\frac{1}{27} }[/tex]
3. [tex](\frac{1}{27})^{\frac{1}{3} }[/tex]
3. Since [tex](\frac{1}{3}^{3})[/tex] is [tex]\frac{1}{27}[/tex], the answer should be [tex]\frac{1}{3}[/tex].
Find the height of an equilateral triangle with side length 8.
Answer:
U need to just do
[tex] \sqrt{3 \div 4} a {}^{2} [/tex]
Answer:
4[tex]\sqrt{5}[/tex]
Step-by-step explanation:
The segment from a vertex to the side opposite is a perpendicular bisector.
The equilateral Δ is divided into 2 right triangles with legs 8 and 4
let height be h, then using Pythagoras' identity
h² = 4² + 8² = 16 + 64 = 80 ( take the square root of both sides )
h = [tex]\sqrt{80}[/tex] = 4[tex]\sqrt{5}[/tex] ← exact value
PLS HELP!!! due to inflation nominal prices are usually there were to demand increases. After the second increase the price for a certain item was twice as big as the original. By what percent was the first increase, if the second increase was 25%
Answer:
The first increase was of 60%.
Step-by-step explanation:
The initial value of the product is x.
The first increase was of y.
The second increase is of 25%, that is, 1.25.
The final price was double the original, so 2x.
This situation can be modeled by the following equation:
[tex]xy(1.25) = 2x[/tex]
We want to find y.
Simplifying by x
[tex]1.25y = 2[/tex]
[tex]y = \frac{2}{1.25}[/tex]
[tex]y = 1.6[/tex]
After the first increase, the value was 1.6 of the original value, that is a increase as a percent of (1.6 - 1)*100 = 60%.
The discount price of a hat is $24 whats the regular price if the discount is 20%
Answer:
30
Step-by-step explanation:
discounting by 20% is the same as marking to 80% of the original cost. 80% = .8
set up equation and solve
.8x=24
x=30
Find the measure of angle b (15
Answer:
Angle b is 15 measure the scale
Find the unit rate of 624 calories in 3 servings. Its 8th grade math.
Answer:
you can look up the exact quizizz your taking and find all the answers
Step-by-step explanation:
for example: look up your question on the quizizz and then type it in the search bar and add quizziz to the end of it and you should find all your answers there<3
What separates the terms in this algebraic expression?
x + 3
HELPP MEEE
Answer:
I believe its the + symbol that separates it?
G**gle confirmed it I was right!!
tell whether each question is true or false.
a.
[tex] \sqrt[3]{60} = 20 \: true \: or \: false[/tex]
b.
[tex] \sqrt[3]{64} = \sqrt{16 \:} true \: or \: false[/tex]
c.
[tex]25 = \sqrt[3]{125} \: true \: or \: false[/tex]
d.
[tex]12 = \sqrt[]{144} \: true \: or \: false[/tex]
e.
[tex] \sqrt{ \frac{4}{9} } = \sqrt[ 3]{ \frac{8}{27} } \: true \: or \: false[/tex]
Answer:
E
Step-by-step explanation:
Me sale a mi
Answer:
a is false, b. is true, c. is true, d. is true
Step-by-step explanation:
Which is the percent for 1.67
Answer:
The answer is 167%Step-by-step explanation:
Convert decimal to a percentage by multiplying the decimal by 100.167%I hope it helps you ❤❤❤plz hellp me plzzzzzzzzzz
Answer:
3n+6
Step-by-step explanation:
What is the image of (−8,−8) after a dilation by a scale factor of 1/2 centered at the origin?
Answer:
(-4,-4)
Step-by-step explanation:
Since this is centered at (0,0), we have to multiply the x and the y coordinates by the scale factor.
-8 × 1/2 = -4
The equation y = 3.5x represents the total cost y in dollars of buying x pounds of cheddar cheese at Art’s Deli. The graph below shows the total cost y in dollars of buying x pounds of cheddar cheese at Jon’s Deli. What conclusion can you draw about the cost of cheddar cheese at these delis? Cheddar cheese costs $4 more per pound at Jon’s Deli than Art’s Deli. Cheddar cheese costs $0.50 more per pound at Jon’s Deli than Art’s Deli. Cheddar cheese costs $3.50 less per pound at Art’s Deli than Jon’s Deli. You pay the same price per pound for cheddar cheese at both delis.
Step-by-step explanation:
i think its X=2.75
What are the interest cost and the total amount due on a six-month loan of $1,800 at 14.4 percent simple annual interest
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Principal (P)= $1,800
Number of periods (t)= 6 months
Monthly interest rate (r)= 0.144/12= 0.012
To calculate the interest to be paid and the total amount due, we need to use the following formula:
I= P*r*t
I= 1,800*6*0.012
I= $129.6
Total amount= $1,929.6
If X=3 and y=3, then x =?
Answer:
3
Step-by-step explanation:
You said x=3
Answer:
if the answer isn't 3 then its 1
the integers -10 and 10 are=
Answer:
Opposites of each other?
Step-by-step explanation:
I am not sure, the only thing that is not making them equal to each other is that they have opposite signs.
