Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.
Salt flows into the tank at a rate of
(2 gal/min) (6 lb/gal) = 12 lb/min
and flows out at a rate of
(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min
so that the net rate at which salt is exchanged through the tank is
ds(t)/dt = 12 - s(t)/150 … (lb/min)
Solve for s(t). The DE is separable, so we have
ds/dt = 12 - s/150
150 ds/dt = 1800 - s
150/(1800 - s) ds = dt
Integrate both sides to get
-150 ln|1800 - s| = t + C
Solve for s :
ln|1800 - s| = -t/150 + C
1800 - s = exp(-t/150 + C )
1800 - s = C exp(-t/150)
s = 1800 - C exp(-t/150)
Now given that s(0) = 50, we solve for C :
50 = 1800 - C exp(-0/150)
50 = 1800 - C
C = 1750
Then the amount of salt in the tank at any time t ≥ 0 is
s(t) = 1800 - 1750 exp(-t/150)
To find the time it takes for the tank to hold 100 lb of salt, solve for t in
100 = 1800 - 1750 exp(-t/150)
1700 = 1750 exp(-t/150)
34/35 = exp(-t/150)
ln(34/35) = -t/150
t = -150 ln(34/35) ≈ 4.348
So it would take approximately 4.348 minutes.
By the way, we didn't have to solve for s(t), we could have instead stopped with
-150 ln|1800 - s| = t + C
Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so
-150 ln|1800 - 50| = 0 + C
C = -150 ln|1750|
==> t = 150 ln(1750) - 150 ln|1800 - s|
Then s(t) = 100 lb when
t = 150 ln(1750) - 150 ln(1700)
t = 150 ln(1750/1700)
t = 150 ln(35/34)
t ≈ 4.348
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
Explain the
The fifth term of a non-linear sequence is 324. The term-to-term rule is ‘multiply by 3?
Work out the second term of the sequence.
Explain the method you used to solve this problem.
Answer:
a2=12 (the second term of the sequence is 12)
Step-by-step explanation:
a5=324
If the term to term rule is multiply by any number, we deal with geometrical sequence
The formula you should use is an= a1*r^(n-1) where n is the number of the term which we know. In our case we know
a5, so use 5 instead of n
Then you have a5=a1*r^4 where r is the number 3 (because each next term is greater than previous in 3 times)
a5=324
324= a1*3^4
324=a1*81
a1=4 (We find the first term of sequence, because having it you can easily search for every term )
Return to the formula an= a1*r^n-1
Now search for the second term using 2 instead of n in the formula
a2= a1*r^1
a2=a1*r, a1=4, r=3
a2=4*3=12
Plz solve it
Factorize: no w
Answer:
here we can go for two solution
A consumer report counted 72 low-quality, 112 medium-quality, and 711 high-quality computers based on a random sample. The report went on to say that all computers, regardless of quality, are packaged identically and sold at the same price.
Use the observed frequencies to create a probability model for the quality of the next computer purchased.
Input your answers as fractions or as decimals rounded to the nearest hundredth.
Quality Estimated Probability (in %)
___________________________________
-Low- :
-Med- :
-High- :
Answer:
Low = 72/895
Medium = 112/895
High = 711/895
Step-by-step explanation:
Low = number of low quality products over the total number of products
72 / 72 + 112 + 711
Medium = number of medium quality products over the total number of products
112 / 72 + 112 + 711
High = number of high quality products over the total number of products
711 / 72 + 112 + 711
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Low
72/895
Medium
112/895
High
711/895
Step-by-step explanation:
please help! i can’t write the equation on here so look at the picture.
Answer:
So if x= 1 , y= -20 , z = -5 , we just have to replace those values on the equation
[tex]\frac{\sqrt{yz}}{(z-x)^{2} + y } =[/tex] [tex]\frac{\sqrt{(-20) * (-5)}}{(-5-1)^{2} + (-20) } =[/tex] [tex]\frac{\sqrt{100}}{(-6)^{2} -20 }[/tex] [tex]= \frac{10}{16} =\frac{5}{8}[/tex]
Answer:
√100 / {-5-1}^² +(-20)10/(-6)^² -2010/36-2010/165/8Two lines, C and D. are represented by the equations given below.
Line C: y = x + 10
Line D: y = 3x + 2
Which of the following shows the solution to the system of equations and explains why?
(5, 17), because one of the lines passes through this point
(5. 17), because the point lies between the two axes
(4, 14), because the point does not lie
on any axis
(4, 14), because both lines pass through this point
find the length of UC
Answer:
18
Step-by-step explanation:
One way to solve this would be to just solve for random lengths, left to right, until we come to find UC.
We know JK = JH + HM + MK = 82 and JH = 22, so
82 = 22 + HM + MK
subtract 22 from both sides to isolate the unknowns
60 = HM + MK = HK
96 = HK + KU - HU
We know HK = 60
96 = 60 + KU
subtract 60 from both sides to isolate the unknown
We know KU = 36
105 = KN = KU + UC + CN
We know KU = 36 and CN = 51
105 = 36 + 51 + UC
105 = 87 + UC
subtract 87 from both sides to isolate the unknown
18 = UC
UC is what we're looking for, so the problem is solved
Sin³xcosx+sinxcos³x=sinxcosx
Answer:
Step-by-step explanation:
[tex]sin^3xcosx+sinxcos^3x\\=sinx cosx(sin^2x+cos^2x)\\=sinx ~cosx(1)\\=sin~x~cos~x[/tex]
Find the slope of the line that passes through the points (-12,10) and (-18,14).
Answer:
-2/3
Step-by-step explanation:
To find the slope we use the formula
m= ( y2-y1)/(x2-x1)
= ( 14-10)/(-18- -12)
= (14-10)/(-18+12)
= 4/-6
= -2/3
39.) Fiona bought a brand new Harley Davidson motorcycle. Since the weather was nice, she decided to go out for a ride with some of her friends. Before leaving town, she stopped to fill up her motorcycle with gas so that she had a full tank. If Fiona's motorcycle has a 4 gallon gas tank, and she only had to add 2 4/7 gallons, how much gas was in the tank before she filled up?
Answer:
1 3/7 gallonsStep-by-step explanation:
Let the amount of gas in the tank before filling was x.
We have:
x + 2 4/7 = 4x = 4 - 2 4/7x = 2 - 4/7x = 1 3/7 gallonslet the amount of gas be x
[tex]\\ \sf\longmapsto x+2\dfrac{4}{7}=4[/tex]
[tex]\\ \sf\longmapsto x+\dfrac{18}{7}=4[/tex]
[tex]\\ \sf\longmapsto x=4-\dfrac{18}{7}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{28-18}{7}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{10}{7}[/tex]
[tex]\\ \sf\longmapsto x=1\dfrac{3}{7}[/tex]
evaluate the function f ( -2) = − 3 ^2
Answer:
f ( -2) = − 3 ^245fsaf
Step-by-step explanation:
f ( -2) = − 3 ^2wqs
f(-2)= -3^2
f(-2) = -3 × (-3)
f(-2) = 9
Must click thanks and mark brainliest
Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is AAA and scale factor is \dfrac{1}{4} 4 1 start fraction, 1, divided by, 4, end fraction.
The coordinates of the resulting image will be at (1, 1), (3, 4) and (1, 2)
DilationAssuming the coordinate of the triangle ABC is A(4, 4), (12, 16) and (-4, -8).
If the coordinate is dilated by a factor of 1/4, the resulting coordinates will be at:
A' = (4/4, 4/4) = (1, 1)B' = (12/4, 16/4) = (3, 4)C' = (-4/4, -8/-4) = (1, 2)Hence the coordinates of the resulting image will be at (1, 1), (3, 4) and (1, 2)
Learn more on dilation here: https://brainly.com/question/10253650
If I have 180$ and a pack of dvds cost 18 how much can I buy
Answer:
10 packs of dvds
Step-by-step explanation:
$180 / $18 = 10 packs
You can buy a maximum of 10 dvd packs
Answer:
you can buy 10 dvds that is thr answer
Both please please :)…….,,,,,
Answer:
Step-by-step explanation:
One - 44
88% of 50 is 44
Two - 55296 60,000-4%-4%=55296
Consider the reflection of parallelogram PQRS across the line of reflection wy
Answer:
Consider the reflection of the parallelogram PQRS across the line of reflection wy if RR = 14 Then RZ= If SX=5 then = 5
Step-by-step explanation:
What is the range of the given data set? OA) 30 OB) 32 OC) 37 OD) 40
Answer:
Range = maximum number - minimum number
maximum number = 99minimum number = 62Range = 99 - 62 = 37
Answer:
37
Step-by-step explanation:
The range is the difference between the highest number and the smallest number.
Looking at the stem and leaf plot we can identify the largest and smallest number
Largest number: 99
Smallest number: 62
If range = largest number - smallest number then range = 99 - 62 = 37
In TUV, u = 17 cm, ZT=11° and ZU=103º. Find the length of t, to the nearest
centimeter
2/3 of a number is 20 less than the original number.find the number
4w - 8 = 32 the value of 4w is 40 how do you know this is true
Please help I will give you Brainlyest
Answer:
4w = 40
Step-by-step explanation:
Using the addition property of equality to add 8 on both sides gives us the answer to what 4w equals.
[tex]4w - 8 + 8 = 32 + 8\\4w=40[/tex]
Please solve this for 20 points and brainiest
Answer:
3y² + y - 10
Step-by-step explanation:
Assuming we're finding the area:
[tex](3y-5)(y+2)\\3y^2+6y-5y-10\\3y^2+y-10[/tex]
Answer:
3y² + y - 10
Step-by-step explanation:
(3y -5) (y + 2)
3y² + 6y - 5y - 10
3y² + y - 10
If m ZABD = 78°, what are mZABC and mZDBC?
(5x+3)
(5x-5)
Hi, I'm happy to help!
First, we need to solve for x. We know that ABD is 78 degrees. (5x+3), and (5x-5) combined are also 78 degrees. So, we combine the like terms of these to get a new expression.
(5x+3) +(5x-5)
10x-2=78
From here, we want to single out the x, by editing both sides in the same way.
10x-2=78
+2 +2
10x=80
÷10 ÷10
x=8
Now that we know what x is, we can plug it in to the previous expressions to get the angles of ABC and DBC.
(5x-5)
((5·8)-5)
(40-5)
35
Now, we know that ABC is 35 degrees.
(5x+3)
((5·8)+3)
(40+3)
43
Now, we also know that DBC is 43 degrees.
To verify our answer we can add ABC and DBC together to check if it totals to ABD.
35+43=78
Now, we know that the answer: ABC is 35 degrees and DBC is 43 degrees is correct.
I hope this was helpful, keep learning! :D
There is a loss of Rs 5 when a watch is sold at the discount of 10%. IF the watch is sold at the discount of 5%, there is profit of Rs 22.50. Find the marked price of the watch.
The area of a square=121m² what is the value of S?
Answer:
11 m
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
121 = s^2
Take the square root of each side
sqrt(121) = sqrt(s^2)
11 = s
Please help its due in 30 minutes will mark braniliest
Answer:
Step-by-step explanation:
It's a ray. A ray has 1 fixed point. The other end of the ray goes on forever, just as this diagram shows.
1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.
Step-by-step explanation:
We have
1-cot²a + cot⁴a = sin²a(1+cot⁶a)
First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.
We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have
1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a
Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.
sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a
= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a
We can then factor cos²a out of the numerator
sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a
= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a
Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so
sin²a = (1-cos²a)
sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1
sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a
= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a
= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a
factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1
sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a
= sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a
= sin²a + cos⁶a/sin⁴a
= sin²a(1+cos⁶a/sin⁶a)
= sin²a(1+cot⁶a)
Which of the following is equivalent to -12 + 3)?
12 + 31
– 12– 3
o 12 – 3
0 12 + 3

Answer:
[tex]12 - 3[/tex]
Step-by-step explanation:
[tex]( - 12 + 3) \\ = 12 - 3 \\ =- 9[/tex]
Hope it is helpful....A rectangular rug has the perimeter of 36 feet. The length of the rug is twice the width. What is the length
Answer:
12 ft
Step-by-step explanation:
l = 2w
P = 2(l+w)
36 = 2(2w+w)
36 = 2(3w)
36 = 6w
Divide each side by 6
36/6 = 6w/6
6 =w
l = 2w
l = 2(6)
l = 12
simplify : 3p+2p+8-3=15
Answer:
3p+2p+8-3=15
5p+5=15
5p=15-5
5p=10
p=10/5
p=2
have a great dayy.
Answer:
p = 2
Step-by-step explanation:
One is given the following equation:
3p + 2p + 8 - 3 = 15
Combine like terms. In essence, if two number have the same variable, then one can perform operations between their coefficients. If two number have no variables, then these two terms are also like terms. After combing like terms, simplify the expression.
3p + 2p + 8 - 3 = 15
5p + 8 - 3 = 15
5p + 5 = 15
Inverse operations,
5p + 5 = 15
5p = 10
p = 2
What is 0.04% of 30? Round to the nearest hundredth
Answer:
0.012
Step-by-step explanation:
Have a good day.
Answer:
.01
Step-by-step explanation:
Change the percent to decimal form
.04% = .0004
.0004 *30
.012
Round to the nearest hundredth
.01
Simplify [2(5 – 4) + 6(7 – 3)] ÷ 2
I'LL MARK BRAINLY PLEASE HELP ME I'M STRUGGLING
Answer:
13
Step-by-step explanation:
[2×1+6×4]÷2
[2+24]÷2
26÷2
13
