Answer:
Step-by-step explanation:
From the information given:
Tank's Capacity = 600 gal
Original content of water = 200 gal
Salt solution = 100 lb
In the tank:
Suppose x(t) = amount of salt at time (t); &
V(t) = volume of water
Then,
V(t) = 200 + t
and [tex]x'(t) = 3 - \dfrac{2x(t)}{200+t}[/tex]
From the above linear equation, the integrating factor can be computed as:
[tex]x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}[/tex]
[tex]= e^{2 \ log (200+t)}[/tex]
= (200 + t)²
The general solution can now be expressed as:
[tex]x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)[/tex]
We know that C = integrating factor, thus taking the integral:
[tex]x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}[/tex]
At the initial condition, x(0) = 100
∴
[tex]100= \dfrac{(200)^3 +C}{(200)^2}[/tex]
C = ((200)²×100) - 200³
C = -4 × 10⁶
Hence, at any time t, the amount of salt is:
[tex]x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}[/tex]
What's the area of this yellow surface? pick one of the options.
please help! asap!! function A and function B are linear functions, which statement is true?
Answer:
A
Step-by-step explanation:
Equation of the line A
(y+7)/(17+7) = (x+3)/(3+3)
(y+7)/24 = (x+3)/6
y+7 = 4x + 12
y = 4x + 5
y intercept = 5
Function B
y intercept = -2
help..............................................................
Answer:
This will now be ⁴√(7^9)
Step-by-step explanation:
c=4
a=7
b=9
Using only an addition, how do you add eight 8’s and get the number 1000?
Answer:
8
8
8
8 8
8 8 8
-------------------
1 0 0 0
Step-by-step explanation:
In the context of communication, which of the following statements is true of people from high-context cultures? a) They prefer the use of the direct, get-down-to-business conversation style.
b) They focus on the use of precisely written legal contracts.
c) They give importance to the position, age, and seniority of parties in a conversation.
d) They focus on the actual spoken and written word.
The measure of the angle of depression from the top of a 270 m building tweet park bench on the ground is 63° 43’.How far Where is the park bench from the building? round to the nearest whole number
Answer:
547 m
Step-by-step explanation:
Given :
Angle of depression, θ = 63°43' ; 43/60 = 0.7167 = 63 + 0.7167 = 63.7167°
The height, h = 270
The distance of park bench from the building, d is given by :
Tan θ = opposite / Adjacent
Tan 63.7167 = d / 270
d = 270 * Tan 63.7167
d = 546.70459
d, distance of Park bench from building is 547 m
a deli employee can make a sandwhich in 6 minutes.she works for 84 minutes.how many sandwhiches can she make
Answer:
14
Step-by-step explanation:
84/6
Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king and then, without replacement, a face card? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
0.0181 probability of choosing a king and then, without replacement, a face card.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of choosing a king:
There are four kings on a standard deck of 52 cards, so:
[tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]
Probability of choosing a face card, considering the previous card was a king.
12 face cards out of 51. So
[tex]P(B|A) = \frac{12}{51}[/tex]
What is the probability of choosing a king and then, without replacement, a face card?
[tex]P(A \cap B) = P(A)P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{1*12}{13*51} = 0.0181[/tex]
0.0181 probability of choosing a king and then, without replacement, a face card.
which of the following best describes the slope of the line below? pls help asap
Answer:
Step-by-step explanation:
Undefined.
Can someone graph this quick plsssss
Answer:
x = 0.529 and y = 3.882
Step-by-step explanation:
The given equations are :
[tex]y=\dfrac{5}{3}x+3\ ......(1)\\\\y=\dfrc{1}{3}x-3\ .......(2)[/tex]
We need to solve the equations by graphing.
The attached figure shows the solution of the given equations. We can see that, the intersecting points are :
x = 0.529 and y = 3.882
Hence, this is the required solution.
How much interest will be earned on a $1600 investment at 7.72% compounded
quarterly for 9 years?
Question 1 of 25
Calculate the sum or difference. Enter the answer as a fraction in lowest
terms, using the slash (/) as the fraction bar.
2.5
tom
Answer here
Answer:
5/2 improper, 2 1/2 proper
PLZ DONT LEAVE IN BLANK I WILL DO ANYTHING!!!! PLZ PLZ PLZ PLZ PLZ PLZ PLZ PLZ 20 Xp
The data below shows the scores of some students on a test:
29, 31, 27, 20, 25, 34, 24
Which box-and-whisker plot represents the data?
Answer: The answer is C.
Step-by-step explanation:
It is definitely not B because the average of the numbers compared to what that shows don't make sense.
The biggest number that you gave us is 34 but on option A, it looks like its 30 or 31. So that's not correct.
Finally, it can't be D because the biggest number shown there is 35 when it actually is 34.
I hope I was able to help!
Good luck and have a great day :)
LA=
Round your answer to the nearest hundredth.
С
7
A
?
8
B
Answer:48.81
Step-by-step explanation:
Hope it helps
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
17 cm
a
a
b
8 cm
12 cm
5 cm
Answer:
No solution is possible since you failed to provide the necessary information
Step-by-step explanation:
Which equation would have the steepest graph? Explain how you know?
Answer:
y = 3/8 x
Step-by-step explanation:
the smaller the number the steeper the graph
find measure of indicated arc please!
Answer:
94 degrees
Step-by-step explanation:
You might need: Calculator
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these
flowers rapidly increases as the trees blossom.
The relationship between the elapsed time t, in days, since the beginning of spring, and the number of locusts,
L(t), is modeled by the following function:
5.9
L(t) = 750.
(1)
Complete the following sentence about the rate of change in the locust population.
2
The population of locusts gains of its size every
3
days.
Answer:
5.9
Answer directly from Khan
Candice works at a grocery store. She works 35 hours a week and
gets paid $8.50 an hour. For every hour over 35, Candice gets
paid $10 an hour. If she was paid $357.50 last week, how many
hours over 35 did Candice work?
9514 1404 393
Answer:
6
Step-by-step explanation:
For 35 hours, Candice is paid ...
($8.50/h)(35 h) = $297.50
Any amount in excess of that is paid at $10 per hour. The amount of excess pay is ...
$357.50 -297.50 = $60.00
Then the number of overtime hours was ...
$60/($10/h) = 6 h
Candice worked 6 hours over 35 last week.
Can y’all help me on question 13?!
Answer:
85 cm2
Step-by-step explanation:
Separate the figure into sections and add the product
Sam asks five of his friends in his accelerated ELA class.
He finds that the average number of books read for this sample was 6.
Give two reasons why this sample might not be representative of the population that Sam is
trying to study
Answer:
1) Sam only interviewed five people out of his entire ELA class, so he doesn't have a very wide demographic to study
2) All of these people were Sam's friends, so they might all have similar interests or only enjoy certain things, and that doesn't allow for a wide range of data collection
ASAP PLEASE!M DUE TODAY!
Terrance rolled a bowling ball 5 feet and 2
inches before it hit a bowling pin. If 1 inch is
equal to 2.54 centimeters, how many centimeters
did the bowling ball roll before hitting the pin?
Answer:
157.48cm
Step-by-step explanation:
5feet 2inches
=(5×12) +2in.
=62in. [ 1ft = 12in.]
= 12in. = 2.54cm
=62in. = (2.54 × 62)
=157.48cm
Explain why the set of polynomials is closed under subtraction
Answer:
Polynomials are closed under addition. When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials.
Step-by-step explanation:
Which data set has an apparent negative, but not perfect, linear relationship between its two variables
A)Chris and Alex Were Building a sand Castle. They Decided to make it into a cone shape. After some time, the diameter of the the sand shaped cone was 12in and the height was 7in. What is the exact volume of the sand cone?
B) the kids kept adding sand, ten minutes later the volume of the sand cone had increased by 30%. what is the exact volume of the sand cone now?
Answer:
A.) 84π | B.) 546π/5
Step-by-step explanation:
A.)
V(Cone) = πr²(h/3) where r = radius and h = height.
r = d/2 where d = diameter.
r = 12/2 = 6
V(Cone) = π(6)²(7/3) = π(36)(7/3) = 84π
B.)
84π · 0.3 = 126π/5
84π + 126π/5 = 546π/5
Shana has three pets, a dog, a cat and a bird. One of them is named Sammy. Noodles is younger than both the bird and the dog. Fluffy is green. Which pet has the name Sammy?
Answer:
The dog has the name Sammy.
Step-by-step explanation:
A cat and dog cannot be green, therefore the bird is Fluffly.
Noodles must be the cat since it's younger than the bird and the dog.
The only one that doesn't have an explanation is the dog, therefore the dog must be named Sammy.
On a number line what nomber is 3 units to the left of 3
Answer:
Hello There!!
Step-by-step explanation:
The answer is 0. The number is 3 and you move 3 units to the left which is toward the negative numbers sides below zero which equals the answer as 0. [3-3=0.]
hope this helps,have a great day!!
~Pinky~
Step-by-step explanation:
7On a number line what nomber is 3 units to the left of 3
which of the following is true because of the commutative law of multiplication
15*3=45
15*3=40+5
15*3=3*15
15*3=3*3*5
Explanation:
The commutative law of multiplication says that A*B = B*A, for any real numbers A,B. The order of multiplication doesn't matter.
That's why 15*3 is the same as 3*15.
This is because having 15 groups of 3 leads to 3+3+3+...+3 = 45 (imagine adding 15 copies of '3' together), and having 3 groups of 15 gets us 15+15+15 = 45 as well.
Or you could picture a rectangular table that has 15 rows and 3 columns. It has 45 inner cells. If the table had 3 rows and 15 columns, then we'd still have 45 inner cells.
A rectangle has sides of 9 cm and 12 cm long. What is the perimeter of the rectangle?
21 cm
42 cm
оооо
72 cm
108 cm
A rectangle has sides of 9 cm and 12 cm long. What is the perimeter of the rectangle?
Answer:-42 cm
Answer:42cm
Step-by-step explanation:
formula=2l+2w
2 (9)+2 (12)
18+24= 42cm
The diameter of a circle is 15 in. Find its circumference in terms of \piπ
Answer:
15π in
Step-by-step explanation:
In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...
Circumference = dπ (where d is the diameter of the circle)
Therefore the circumference equals...
Circumference = dπ = 15π in
[tex]\boxed{Given:}[/tex]
Diameter of the circle "[tex]d[/tex]" = 15 in.
[tex]\boxed{To\:find:}[/tex]
The circumference of the circle (in terms of π).
[tex]\boxed{Solution:}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]
[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]
Therefore, the circumference of the circle is 15 π in.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]