Answer:
a. dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. y = 20000/(200 + t)
Step-by-step explanation:
a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.
Let y be the mass of salt.
The net flow into the tank dy/dt = mass flow in - mass flow out
Since only water flows into the tank, the mass flow in = 0 g/min
Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by 2t. So, the volume of the tank in time, t is V = 200 + 2t.
So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).
Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out = y/(200 + 2t) × 2 = 2y/(200 + 2t)
The net flow into the tank dy/dt = mass flow in - mass flow out
dy/dt = 0 - 2y/(200 + 2t)
dy/dt = - 2y/(200 + 2t)
Since the initial mass of salt in the tank is 100 g, y(0) = 100 g
So, the initial value problem IVP is
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.
Solving the IVP, we have
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
Separating the variables, we have
dy/y = - 2dt/(200 + 2t)
Integrating both sides, we have
∫dy/y = - ∫2dt/(200 + 2t)
㏑y = - ㏑(200 + t) + ㏑C
㏑y + ㏑(200 + t) = ㏑C
㏑[y(200 + t)] = ㏑C
y(200 + t)] = C
y = C/(200 + t) since y(0) = 100, we have
100 = C/(200 + 0)
100 = C/200
C = 100 × 200
C = 20000
So, y = C/(200 + t)
y = 20000/(200 + t)
find the missing length indicated
============================================================
Explanation:
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
--------------------------------
Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
240.
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
What is Pythagorean Theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Learn more about the Pythagorean theorem at
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Find the largest factor of 2520 that is not divisible by 6.
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
What are the odds against picking a red marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
There’s a pic of the question, answer fasterrrrr pleaseeeee
Answer:
Sorry this is NWEA so I want you to try and figure it out on your own, hint: use subtraction.
Step-by-step explanation:
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a heart.
The probability is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
3/4
Step-by-step explanation:
There are 13 hearts in a 52 deck.
52-13=39
39/52=3/4
The probability that you are not dealt a heart from the deck of cards is 3/4.
What is the probability that you are not dealth with a heart?Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)
1 - 13/52 = 39/52 = 3/4
To learn more about probability, please check: https://brainly.com/question/13234031
Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?
A)
DF = 39 cm; DE = 15 cm
B)
DF = 48 cm; DE = 52 cm
C)
DF = 65 cm; DE = 25 cm
D)
DF = 52 cm; DE = 48 cm
Answer:
D)
DF = 52
AB = 48
Step-by-step explanation:
Use the two lengths of sides already given.
Divide to find the scale factor:
20 / 5 = 4
Scale factor: 4
Now multiply to find the unknown sides:
13 × 4 = 52
12 × 4 = 48
DF = 52
AB = 48
Hope this helped.
Which expression is equivalent to 6x3 + 3y2 – 5x3 + 2y2?
Answer:
The answer is c because6X^3 minus 5X^3 is just X^3 and 3Y^2 plus 2Y^2 is 5Y^2.
Find the length represented by x for each pair of similar triangles.
18cm, 9cm, and x
30cm, 15cm, and 25cm
Answer:
15 cm
Step-by-step explanation:
Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.
We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.
Hope this helped,
~cloud
1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.
Let x be the first number in the sequence, so the first three numbers are
{x, 0.5x, 0.5²x}
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
is arithmetic, so there is some constant c such that
0.5x - 10 = x/4 + 10 + c ==> x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c ==> x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are
{160, 80, 40}
Let two events A and B be independent. Knowing P(A)=0.8 and P(A+B)=0.93. Calculate the probability P(B).
Answer:
Hello,
P(B)=0.65
Step-by-step explanation:
If P(A+B) means P(A∪B)=0.93 then you may read below.
Let's say x=P(B)
A and B being independent, P(A∩B)=P(A)*P(B)=0.8*x
Since P(A∪B)=P(A)+P(x)-P(A∩B) ,
0.93=0.8+x-0.8*x
0.2*x=0.13
x=0.65
1101001÷11 i am really confused
Answer:
100091
Step-by-step explanation:
find the sum of the given infinite geometric series. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW
Answer:
320/3
Step-by-step explanation:
First find the common ratio
20/80 = 1/4
The sum of an infinite geometric series
sum = a1/ (1-r) where a1 is the first term and r is the common ratio
=80/ ( 1-1/4)
= 80/(3/4)
= 80 *4/3
= 320/3
5, 3 = 28
7,6 = 55
4,5 = 21
3,8 = ?
Answer:
3,8 =
Step-by-step explanation:
3 X 3 + 8 = 9 + 8 = 17
Square the first number and add the second number to it.
Help very confusing to me???!
Answer:
Heyy mate... here's ur ans ;)
they asked us to apply pythagarus theorem becoz that theorem proves
that it is rectangle so lets get started
( p - perpendicular / b - base / h - hypotenuse )
a) =>
B = 8.1 m
P = 6.3 m
H = 10.15m
Now applying thm => H^2=p^2+b^2
(8.1)^2 + (6.3)^2 = (10.15)^2
65.61 + 39.69 = 103.02
so now LHS = 105.3 and RHS = 103.02 hence
LHS not equal to RHS
so is not rectangle
b) =>
B = 14.4
P = 5.2
H = 15.31
Now applying thm => H^2=p^2+b^2
(5.2)^2 + (14.4)^2 = (15.31)^2
27.04 + 207.36 = 234.39
LHS = 234.4 and RHS = 234.39
just taking approximation rhs is 234.4
hence
LHS = RHS
so it is a rectangle
please mark it brainliest <3
Ron has 22 coins with a total value of $ 1.85. The coins are nickels (5 cents) and dimes (10 cents). How many of each coin does he have?
Please help asap and thank you in advance!!
Answer:
18 dimes and 1 nickle
Step-by-step explanation:
This is because 18 time 10 is 180 and one of 5 add it and this is $1.85
Remeber a dollar is 100 cents
Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]
Answer:
y=3x
Step-by-step explanation:
-6/-2=3, -3/-1=3, 3/1=3. 6/2=3
Work out the values of a, b and k ? 30 points
Answer:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
Step-by-step explanation:
Note that the graph passes through the points: (0, 4), (1, 25), and (1.5, k).
The standard exponential function has the form:
[tex]\displaystyle y = ab^x[/tex]
The point (0, 4) tells us that y = 4 when x = 0. Therefore:
[tex](4) = a(b)^0[/tex]
Since anything raised to zero is one:
[tex]a=4[/tex]
Hence, our function is now:
[tex]y = 4(b)^x[/tex]
The point (1, 25) tells us that y = 25 when x = 1. By substituting:
[tex](25) = 4(b)^{(1)}[/tex]
Solve for b:
[tex]\displaystyle b = \frac{25}{4}[/tex]
Thus, our completed function is:
[tex]\displaystyle y = 4\left(\frac{25}{4}\right)^x[/tex]
To find k, simply substitute 1.5 for x. This yields:
[tex]\displaystyle y = k = 4\left(\frac{25}{4}\right)^{(1.5)}[/tex]
And evaluate. Hence:
[tex]\displaystyle \begin{aligned} k &= 4\left(\frac{25}{4}\right)^{3/2} \\ \\ &= 4\left(\left(\frac{25}{4}\right)^{1/2}\right)^3 \\ \\ &= 4\left(\frac{5}{2}\right)^3 \\ \\ &= 4\left(\frac{125}{8}\right) \\ \\ &= \frac{125}{2}\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle a=4, b= \frac{25}{4}, \text{ and } k = \frac{125}{2}[/tex]
"What mathematical ideas are you curious to know more about as a result of takingthis class? Give one example of a question about the material that you'd like to explorefurther, and describe why this is an interesting question to you."
One mathematical idea I've always been curious about is "integration and derivation".
Integration is about assimilating different variables. Derivation is a mathematical process whereby a result is gotten from some initial assumptions.
Integration is used everyday in different aspects of our lives. For example, if a person is travelling from let's say point A to point B, the speed used by the person might vary but through integration, one can easily get the accurate speed.
Through the division of equations into smaller bits, once can use integration to get the answer that one seeks. Architect can use integration in building the right structures at the exact places where the structures fits.
Likewise derivatives can be used by businesses in assessing whether a profit or loss will be made for a particular transaction or sale of product.
You can read more on:
https://brainly.com/question/14295614
Derive the equation of the parabola with a focus at (2,4) and a directrix of y=8
Answer:
The equation of the parabola with a focus at (2,4) and a directrix of y=8 is,
48-8y=(x-2)²
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X 5 the number of months between successive payments. The cdf of X is as follows:
0 x<1
0.30 1< x <3
F(x)= 0.40 3< x <4
0.45 4< x <6
0.60 6< x <12
1 12< x
Required:
a. What is the pmf of x?
b. Using just the cdf, compute P(3< x <6)and P(4< x)
Answer:
(a)
[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]
(b)
[tex]P(3 \le x \le 6) = 0.30[/tex]
[tex]P(4 \le x)=0.60[/tex]
Step-by-step explanation:
Given
[tex]F(x) = \left[\begin{array}{ccc}0& x<1 &\\0.30&1 \le x<3 &\\0.40&3 \le x < 4& &0.45 &4 \le x<6 &\\0.60 & 6 \le x < 12 & & 1 & 12 \le x\end{array}\right[/tex]
Solving (a): The pmf
This means that we list out the probability of each value of x.
To do this, we simply subtract the current probability value from the next.
So, we have:
[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]
The calculation is as follows:
[tex]0.30 - 0 = 0.30[/tex]
[tex]0.40 - 0.30 = 0.10[/tex]
[tex]0.45 - 0.40 = 0.05[/tex]
[tex]0.60 - 0.45 = 0.15[/tex]
[tex]1 - 0.60 = 0.40[/tex]
The x values are gotten by considering where the equality sign is in each range.
[tex]1 \le x < 3[/tex] means [tex]x = 1[/tex]
[tex]3 \le x < 4[/tex] means [tex]x = 3[/tex]
[tex]4 \le x < 6[/tex] means [tex]x=4[/tex]
[tex]6 \le x < 12[/tex] means [tex]x = 6[/tex]
[tex]12 \le x[/tex] means [tex]x = 12[/tex]
Solving (b):
[tex](i)\ P(3 \le x \le 6)[/tex]
This is calculated as:
[tex]P(3 \le x \le 6) = F(6) - F(3-)[/tex]
From the given function
[tex]F(6)= 0.60[/tex]
[tex]F(3-) = F(1) = 0.30[/tex]
So:
[tex]P(3 \le x \le 6) = 0.60 - 0.30[/tex]
[tex]P(3 \le x \le 6) = 0.30[/tex]
[tex](ii)\ P(4 \le x)[/tex]
This is calculated as:
[tex]P(4 \le x)=1 - F(4-)[/tex]
[tex]P(4 \le x)=1 - F(3)[/tex]
[tex]P(4 \le x)=1 - 0.40[/tex]
[tex]P(4 \le x)=0.60[/tex]
HELLO! CAN ANYBODY PLEASE GIVE THE ANSWERS TO THESEEEE! WOULD REALLY MEAN A LOT
Explain how the given graph is deceptive.
Complete the statements based on the bar graph.
By not starting the horizontal axis at 0, the
bar appears to be about one-fourth the height of the Pecan bar. The
bar appears to be about one-half the height of the Pecan bar. The
bar appears to be less than one-half the height of the Pecan bar. This misleads the viewer to
the number of each type of nut used
Ans:
Pine Nut
Walnut
Almond
Understimate
Answer:
In the picture below.
Step-by-step explanation:
From the commenter and answer above, confirmed on edge 2022.
Find the missing length. The triangles are similar.
Answer:
Missing length = 12
Step-by-step explanation:
Let x represent the missing length.
Since the triangles are similar, ∆KLM ~ ∆KRS, therefore, the ratio of their corresponding side lengths would be the same. This implies that:
KL/KR = KM/KS
KL = 65
KR = 65 - 52
KR = 13
KM = 60
KS = x
Plug in the values
65/13 = 60/x
Cross multiply
65*x = 60*13
65x = 780
Divide both sides by 65
65x/65 = 780/65
x = 12
A bookkeeper needs to post the cost of the desk and the chair into his records. The cost of the desk is fives times the cost if the chair. The total cost of the desk and the chair is $720, what is the cost of the chair?
Answer:
120
Step-by-step explanation:
720÷6
why?
becoz 6= 1+5
1 is the cosy of the chair
5 is the cost of the desk
An article is marked to sell at a gain of 10%. If it be sold for Rs. 7.50 less there would be loss of 5%, find the cost price.
Answer:
750,. is answer
I hope it helps
Find the sum of ∑4/k=1 (-4k)
Answer:
Hello,
Answer C: -40
Step-by-step explanation:
[tex]\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\[/tex]
In a class of 70 pupils, 36 like tasty time , 34 like ice-
cream, 6 like both tasty time }
draw a Venn diagram to show the data.
find how
many
like neither tasty time nor ice-cream
Step-by-step explanation:
I think this might be the correct answer
The number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
We have:
In a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty time.
Total = 70 pupils
Number of like tasty time = 36
Number of like ice cream = 34
Number of like both = 6
Let x be the total number of pupils that like neither tasty-time nor ice cream
The number of pupils that like ice cream only = 34 - 6 = 28
The number of pupils that like tasty-time only = 36 - 6 = 30
From the Venn diagram:
28 + 30 + 6 + x = 70
x = 70 - 64
x = 6
Thus, the number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
Learn more about the Venn diagram here:
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2. About how much is 123.1 do you weigh in pounds? Estimate if you don't know☺ Find an online converter and find out how many kilograms that is.
Answer:
123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.
Step-by-step explanation:
If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.
if 25 liters of milk can make 8 tin of cheese how many liters of milk would b needed to make 11 tin of cheese?
Answer:
Step-by-step explanation:
34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.
