I'm assuming all the numbers here mistakenly got copied twice.
Let A(t) denote the amount (in kg) of salt in the tank at time t. The solution starts with 70 kg of salt, so (a) A(0) = 70.
I also assume there is more to the question, so I'll just go ahead and build the differential equation to model this situation, and solve it.
Pure water is flowing into the tank, so no salt is being introduced. The concentration of salt at time t is A(t)/2000 kg/L, and solution is drained from the tank at a rate of 4 L/min, which means salt is being removed at a rate of
(4 L/min) (A(t)/2000 kg/L) = A(t)/500 kg/min = 0.002 A(t) kg/min
Thus the amount of salt (ignoring units now) in the tank changes according to the DE,
dA(t)/dt = -0.002 A(t)
which is easy to solve because it's linear with constant coefficients.
Without going into too much detail:
dA(t)/dt + 0.002 A(t) = 0
exp(0.002t ) dA(t)/dt + 0.002 exp(0.002t ) A(t) = 0
d/dt [exp(0.002t ) A(t)] = 0
exp(0.002t ) A(t) = C
A(t) = C exp(-0.002t )
Given A(0) = 70, solve for C :
70 = C exp(0) = C
Hence
A(t) = 70 exp(-0.002t )
z= 8i – 172
Re(z) =
Im(z)
A formula for finding the perimeter of a rectangle is P=2L+2W. If you know the perimeter (P) and width (W) of a rectangle, which formula can you use to find the length (L)?
Step-by-step explanation:
→ P = 2L + 2W
→ P = 2(L + W)
→ P ÷ 2 = L + W
→ (P ÷ 2) - W = L
We can use this formula to to calculate the length.
What should be added to 7/12 to get -4/15 ?
Answer:
-17/20
Step-by-step explanation:
7/12 + x = -4/15
Subtract 7/12 from both sides
x = -4/15 - 7/12
Use 60 as common denominator
x = -16/60 - 35/60
x = -51/60
Reduce
x = -17/20
PLS HELP WITH 4 and 5 ASAPPP FOR BRAINLIEST
Answer:
4. SAME SLOPE, SAME Y INTERCEPT.
When this happens... The system of Equations has an Infinite Number of solutions.
A IS YOUR ANSWER
5.
A system of Equations has no solution when the graph of the system are PARALLEL LINES.
OPTION D IS YOUR ANSWER.
Use the given information to find the exact value of a.sin 20, b.cos
Answer:
Step-by-step explanation:
[tex]sin(2\theta)=2sin\theta~cos\theta\\\\cos(2\theta)=cos^2\theta-sin^2\theta\\\\cos\theta=\frac{24}{25}\\\\sin^2\theta+cos^2\theta=1~=>sin\theta=\pm\sqrt{1-cos^2\theta}\\\\we ~will~ use~ the ~minus~ sign~because~sin\theta~is~negative~in~IV~cuadrant\\sin\theta=-\sqrt{1-{(\frac{24}{25})}^2}=-\frac{7}{25}[/tex]
Now we cal calculate the quantities requested
[tex]sin(2\theta)=2sin\theta cos\theta=2(-\frac{7}{25})\frac{24}{25}=-\frac{336}{625}\\\\[/tex]
[tex]cos(2\theta)=cos^2\theta-sin^2\theta=(\frac{24}{25})^2-(-\frac{7}{25})^2=\frac{527}{625}[/tex]
[tex]tan(2\theta)=\frac{sin(2\theta)}{cos(2\theta)}=\frac{-\frac{336}{625}}{\frac{527}{625}}=-\frac{336}{527}[/tex]
What is the next number in the sequence?
3,12, 21, 30,?
A. 39
B. 33
C. 51
D. 42
HELP? You put $1000 into an investment yielding 6% annual interest; you left the
money in for two years. How much interest do you get at the end of those
two years?
Answer:
$120
Step-by-step explanation:
as long as the interest is not being compounded, use the simple interest formula of:
Interest = Principal x Interest Rate x Time (in years)
I = 1000(.06)(2)
I = 120
How can I do this one?
Answer:
(x2+1)(x+1)(x−1)
Step-by-step explanation:
Thats the answer
What is the surface area of the right cylinder below?
Answer:
Ok to find the surface area of this cylinder first we need the circumference to find this we do C=πd
C=3.14*18
C=56.52
now we have to multiple this by the height of two
113.04
now we have to find the area of the bottom to do this we do A=πR^2
A=3.14*81
A=254.34
multiple this by two for the two sides we get
508.68
now we add this to 113.04 we get
621.72
since I used 3.14 instead of more digits of pie we can round this up so the answer is C.
Your Welcome
BIFFY OUT!!!
-4 + -2 =
Hurry it’s a test
hope it helps you ♡♡
i need help please on this question
Help PLSSS I will give brainlyest I suck at math this should be easy
Answer:
36
Step-by-step explanation:
Least Common Multiple of 9 and 12
Factor each into prime factor
9 = 3 * 3
12 = 2 * 2 * 3
LCM is the greatest number of different prime factors from each
LCM = 3 * 3 * 2 * 2
LCM = 36
Answer:
36 hotdogs
Step-by-step explanation:
36 ÷ 9 = 4
36 ÷ 12 = 3
Hope this helps!
-kiniwih426
Multiply and simplify.
Sqrt of 15(3+5)=
Sqrt of 3 +
Sqrt of 5
Answer:
Please post the actual question
Step-by-step explanation:
Thanks
URGENT?!?!!!!!!
What is the missing reason in step 5
A. Corresponding parts of congruent triangles are congruent
B. Corresponding parts of similar triangles are congruent
C. Diagonals of a kite are congruent
D. Adjacent sides of a kite are congruent
11 15 24 33 10 35 23 25 40. What is P45 of the given data?
Answer:180 u
Step-by-step explanation:
I need the answer plsss
Answer: 12.5
Step-by-step explanation: Well 50 diviedby 4 = 12.5
Can someone help me with this question please.
Answer:
multiply by 2
Swings to track
20in = 40 yards
Track to bb court
8 in = 16 yards
how much further is the track from the swings
than from the bb court
40 - 16 = 24 yards
Solve for x in IJK Algebra
Answer:
x = 60
Step-by-step explanation:
The sum of the angles in a triangle is 180
40 + x+20 + x = 180
Combine like terms
2x+60 =180
Subtract 60 from each side
2x+60-60 =180-60
2x =120
Divide by 2
2x/2 =120/2
x = 60
Step-by-step explanation:
option 2 is the answer....
how do u find 10% of 300
Answer:
30
Step-by-step explanation:
10/100 = x/300
10x300=3000
3000/100 = 30
Please help fill in the blanks! Worth 45 points
Answer:
Answer is as follows
Step-by-step explanation:
The probability distribution is a statistical function that describes all the possible values and likelihood’s that a random variable can take within a given range.
Answer:
Region I is n(A)
There's 21 elements there.
Region II is the intersection or the region shared by A and B. Denoted by (AnB)
From the data given again.
There are 13 elements in Region II
Region III
Thats part B of the venn diagram
Denoted by n(B)
There's 24 elements in this region.
Region IV
This is the intersection of A and C or the part of the diagram shared by A and C
Denoted by (AnC)
There's 11 elements in this section.
Region VI
This is region shared by B and C
or (BnC)
There's 12 elements in this section.
Region VII
Thats the C part of the Venn diagram
Denoted as n(C)
There's 21 elements here
Region VIII
This part is Empty.
There's no Elements outside the Diagram
There's 0 elements here.
Hope this helps.
Have a great day!
please help, I'll give brainlist who answers my questions ax+by=2x-3y
Answer:
a=4, b=-3
Step-by-step explanation:
If it is vertical, then the y coefficient must be equal to zero, which means b = -3. When y is 0, a*3=2*3+6, which means a=4.
Answer:
a=4
b=-3
Step-by-step explanation:
ax+by=2x-3y+6 is vertical and passes through (3,0) which means the equation should be equivalent to x=3.
If we want the y's to cancel we need -3y on lefy since we have it on right so b=-3.
So now the equation is ax=2x+6
If ax=2x+6 and x=3, by substitution property we have a(3)=2(3)+6.
Let's solve for a.
3a=6+6.
3a=12
a=12/3
a=4.
a=4
b=-3
Question 6 (Essay Worth 5 points)
The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples!
Answer:
a^2+b^2=c^2 A and b need to add upp to c^2
Step-by-step explanation:
3^2+4^2=5^2
9+16=25
25=25
8^2+15^2=17^2
64+225=289
289=289
HELP PLEASE.. Which of the following functions is graphed below?
Help anyone? Please hurry
pls I need this last question someone help
Answer:
n= 2x-6y
Step-by-step explanation:
So we might look at this and have an immediate panic attack, but if there is one thing we might look to to help us, it would be logarithms. Logarithms have many wonderful properties that will help us solve this equation. Let's get started:
1. This is the starting equation. [tex](2^{\frac{1}{2} } )^{n} =\frac{2^x}{8^y}[/tex]
2. Let's use the power to power rule on the left and multiply 1/2 by n:
a. [tex]2^{\frac{1}{2}n } =\frac{2^x}{8^y}[/tex]
3. Next, lets take the log of both sides and use the properties of logarithms:
a. [tex]2^{\frac{1}{2}n } =\frac{2^x}{8^y}[/tex]
b. [tex]log(2^{\frac{1}{2}n }) =log(\frac{2^x}{8^y})[/tex]
c. One property we are allowed to use is bringing down the exponent on the left, and another property we can use is when you have the log of a fraction, that is the same thing as the log(numerator)-log(denominator)
d. [tex]\frac{1}{2}n *log(2) =log(2^x)-log(8^y)[/tex]
e. After we do this, we can use the same property of bringing down the exponent on the right side:
f. [tex]\frac{1}{2}n *log(2) =x*log(2)-y*log(8)[/tex]
g. After this, because log(2) and 1/2 are both numbers and are multiplied by n, we can divide them from both sides, and simplify:
h. [tex]\frac{1}{2}n =\frac{x*log(2)-y*log(8)}{log(2)}[/tex]
i. [tex]2(\frac{1}{2})n =2\frac{x*log(2)-y*log(8)}{log(2)}[/tex]
j. [tex]n =2\frac{x*log(2)-y*log(8)}{log(2)}[/tex]
k. After this, we must simplify the fraction because log(2)/log(2)=1, and log(8)/log(2)=3, these are both because 2^1=2 and 2^3=8 respectively:
l. [tex]n =2(\frac{x*log(2)}{log(2)}-\frac{y*log(8)}{log(2)} )[/tex]
m. Lastly, let's cancel and distribute:
n. [tex]n =2(x-3y)[/tex]
o. [tex]n=2x-6y[/tex]
Tomando como referencia que los ángulos opuestos por el vértice son iguales. Obtén el valor de los ángulos que se te solicitan
a = 143o
b=
c=
d=
e=
f=
g=
Answer:
??
Step-by-step explanation:
Find the measure of each acute angle
Answer:
x = 18
Step-by-step explanation:
The sum of interior angles in a triangle = 180 degrees
The given is a right triangle which means one of the angle is = 90
so the sum of 3x + 2x = 90
5x = 90 divide both sides by 5
x = 18 to find the measure of angles replace x with 18
Let X = the number of nonzero digits in a randomly selected 5-digit PIN that has no restriction on the digits. What are the possible values of X? Give three possible outcomes and their associated X values
Answer: there are total 100,000 5-digit PINs.
Three Possible outcomes Associated X values
12345 5
04555 4
00001 1
Step-by-step explanation:
Here, X = the number of nonzero digits in a randomly selected 5-digit PIN that has no restriction on the digits.
Possible number of outcomes = 10 x 10 x 10 x 10 x 10
= 100,000
Possible outcomes Associated X values
12345 5
04555 4
00001 1
Hence, there are total 100,000 5-digit PINs.
Three Possible outcomes Associated X values
12345 5
04555 4
00001 1
7. Suppose you roll a fair, six-sided die 2000 times and then make a histogram of your results. Which of the following would most likely be characteristics of the histogram you would obtain?
a. Skewed-right
b. Symmetric, with a central peak
c. Skewed-left
d. Uniform
Uniform would most likely be characteristics of the histogram obtain.
What is histogram?A histogram is a rough representation of the distribution of numerical data. The term was first coined by Karl Pearson.
The histogram is the width of the area covered by the x-axis bars. These are approximate values because the histograms show the bin values instead of the original data values.
If a histogram is bell-shaped, it can be modestly described by its center and width. The center is the location of its axis of symmetry. The spread is the distance between the center and one of its inflection points.
To learn more about histogram, refer;
https://brainly.com/question/16819077
#SPJ2
The solution to the system of equations is (0, 4).
(PIC 1)
TRUE or FALSE
The solution to the system graphed below is (1, -2).
(PIC 2)
TRUE OR FALSE
Answer:
1 is false
2 is true
Step-by-step explanation:
The solution is the coordinate where the two lines intersect
For the first image the two lines intersect at (3,5) therefore (0,4) is not a solution to the system of equations
For the second image the lines intersect at (1,-2) therefore the statement is true