Answer:
Step-by-step explanation:
From the given information:
[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]
Given that the solution is pumped at a slower rate of 4gal/min
Then:
[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]
[tex]R_{out}= \dfrac{2A}{50+t}[/tex]
The differential equation can be expressed as:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]
Integrating the linear differential equation; we have::
[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]
[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]
multiplying above integrating factor fields; we have:
[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]
[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]
[tex](50 + t)^2 A = (50 + t)^3+c[/tex]
A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]
A(35) =69.6193 pounds
A(35) [tex]\simeq[/tex] 70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
Find the slope-intercept equation of the line that passes through (0,-1) and has a slope of -2/3 .
Answer:
y= -2/3x-1
Step-by-step explanation:
Hope this helps!
write "yes" or "no" to state whether or not the given side lengths would form a right triangle.
25, 16, 12
A) Yes
B No
Answer: No
Step-by-step explanation:
To find out if it is a right triangle then use the formula a^2 + b^2 = c^2 where a and b are the legs which are the two small sides and c is the hypotenuse the longest side. Input the values for a, b, and c and solve.
a = 12
b = 16
c= 25
12^2 + 16^2 = 25^2
144 + 256 = 625
400 = 625
This means that it is not a right angle because 400 does not equal to 625.
whats nine and 5 tenth in standard form
what's the way to finding a solution?
f (x) = x squared What is f(x) + f(x) + f(x)?
Answer:
Step-by-step explanation:
fx^3
(HELP 50 POINTS)
In the figure above, point O is located at the centroid of triangle ABC. What is the combined lengths of segments DO and BO?
Select one:
A. 22
B. 25
C. 26
D. 29
Answer:
c
Step-by-step explanation:
help plz and it’s not 61.6 because that’s what someone has said
Answer: 250 total kids and 140 girls
Step-by-step explanation:
%56=girls that means %44= boys that means 110 is %44 of the number of kids is 110/44*100= 2.5*100=250kids 56%=girls that means %56 of 250 which is 140 girls
Which sequences are geometric? Check all that apply.
–2, –4, –6, –8, –10, …
16, –8, 4, –2, 1
–15, –18, –21.6, –25.92, –31.104, …
4, 10.5, 17, 23.5, 30, …
625, 125, 25, 5, 1, …
B) 16, -8, 4, -2, 1
C) -15, -18, -21.6, -25.92, -31.104
E) 625, 125, 25, 5, 1
==================================================
Explanation:
Part (A)
Divide each term over its previous term. If each result is the same, then we have a geometric sequence.
(term2)/(term1) = (-4)/(-2) = 2
(term3)/(term2) = (-6)/(-4) = 1.5
We can stop here since we got a different result.
This sequence is not geometric.
--------------------------------------
Part (B)
Same idea as part (A)
(term2)/(term1) = (-8)/16 = -0.5
(term3)/(term2) = 4/(-8) = -0.5
(term4)/(term3) = (-2)/4 = -0.5
(term5)/(term4) = 1/(-2) = -0.5
We get the same result each time. The common ratio is r = -1/2 = -0.5. This sequence is geometric.
--------------------------------------
Part (C)
(term2)/(term1) = (-18)/(-15) = 1.2
(term3)/(term2) = (-21.6)/(-18) = 1.2
(term4)/(term3) = (-25.92)/(-21.6) = 1.2
(term5)/(term4) = (-31.104)/(-25.92) = 1.2
This sequence is geometric since each result is the same. The common ratio is r = 1.2
note: 6/5 = 1.2
--------------------------------------
Part (D)
(term2)/(term1) = (10.5)/4 = 2.625
(term3)/(term2) = (17)/(10.5) = 1.619
We don't get the same result, so we can stop here. This sequence is not geometric.
--------------------------------------
Part (E)
(term2)/(term1) = (125)/(625) = 0.2
(term3)/(term2) = (25)/(125) = 0.2
(term4)/(term3) = (5)/(25) = 0.2
(term5)/(term4) = (1)/(5) = 0.2
The common ratio is r = 0.2 or r = 1/5
This sequence is geometric.
Answer:
C) -15, -18, -21.6, -25.92, -31.104
E) 625, 125, 25, 5, 1
Step-by-step explanation:
Find the slope of a line that passes through the given two points
(2,4) and (3,6).
Answer:
The slope is 2.
Step-by-step explanation:
hope that helps
y²-y¹/x²-x¹
6-4/3-2
2/1
=2
Colin weighs himself at 60kg to the nearest kg.
What is the least he could weigh?
An oil well produces 159 gallons of oil every day. A standard oil barrel holds 42
gallons of oil. About how many barrels of oil will the well produce in one day? Estimate.
Answer:
there are 2 full barrels and one that is almost full so intotal there are 3 barrels.
Step-by-step explanation:
HELP ASAP PLZZZZ, I’m begging!
Answer:
I think it's B
Step-by-step explanation:
I believe the answer is C
Which describes all decimals that are rational numbers?
Tbo dod
Answer:
Step-by-step explanation:
For starters, rational numbers are any numbers that has the capability to be written as a fraction.
For example, 0.5 is a decimal, and can also be written in form of a fraction, as 1/2
A recurring decimal can be written as a fraction. For example, we have 0.167 which can be written as 1/6
In the example, for the decimal 0.36425, we find the place value of the last digit. The last digit here is 5 placed in the hundred-thousandths place. On simplifying further into a fraction, we have 36425/100000.
Josie bikes 40 miles each month for five months she multiplies 40×5 what unit should she use for the product miles or months?
Answer:40x5 are the factors of every miles times each month so the units she should use is months
Step-by-step explanation: 40= (miles)
5=(months)
I just need an answer
Answer:
Step-by-step explanation:
The similar things between the two is that they both to through the y-intercept and x-intercept, but one graph is positive and the other is negative and also have different slopes.
both the domain and range of the graph shown above is all real numbers.
true or false
True or false the sum of two negative numbers is always negative explain why or why not this is true or false
Answer:
true
Step-by-step explanation:
Let's say you have -7 dollars in your bank account, and then you go and spend 5 more, which is -5, now you have -12 bucks in your account
Answer:
true!
Step-by-step explanation:
if you add negative numbers together, it will have to be negative because you are not adding positive numbers. same thing with positive numbers, if you add two positive numbers together, the sum will be a bigger positive number!
When Solving Quadratics, What questions should I ask myself?
Answer:
Step-by-step explanation:
In as much as I might give a warning on not to doubt oneself, I also need to put out what one should take note of when solving quadratic problems.
Using the general formula, it's of utmost importance to not mix the variables together. Remember, making "a", "b" and "b", "a" will lead to an entirely different answer, which is most likely wrong anyway.
It's important to take note of the signs too. Remember, the formula say,
-b ± √(b² - 4ac) / 2a
The first b is negative, and that means a negative value will turn positive there. These are very trivial steps, but they can also make or mar our efforts in getting the correct answer
Select the correct answer.
Which system of equations is satisfied by the solution shown in the graph?
Answer:
i think letter D because it's same
Answer:
one solution
Step-by-step explanation:
Jill walked 2 1/3 miles to the
treasure and then 1 3/4 miles back
to the boat. How many miles did
Jill walk in all?
The perimeter of the triangle is 350 units. Find the measure of each side (label your answers).
Answer:
125, 105, 120
Step-by-step explanation:
You would first make an equation with what you know:
x + 45 + x + 25 + x + 40 = 350.
Now, you would simplify and add like terms.
3x + 110 = 350
Now, you would subtract 110 from both sides.
3x = 240
Now, you would divide both sides by 3.
x = 80
Now that you know what x is, simply plug it in to the respective equations for all three sides.
x + 45 would become 80 + 45, and add up to 125.
x + 25 would become 80 + 25, and add up to 105.
x + 40 would become 80 + 40, and add up to 120.
To check your work, you would now add the three totals.
125 + 105 + 120 = 350.
please help me for a question
Answer:
there is no question??
f(x)=4x^2+2x+6
What is the value of the discriminant of f?
How many distinct real number zeros does f have ?
Answer:
It has ZERO distinct real number zeros.
(QUICK DUE IN 50 MINUTES)
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Drag and drop the constant of proportionality into the box to match the table.
If the table is not proportional, drag and drop "not proportional" into the box.
x 0 2 4 6
y 0 3 6 9
Answer: it is NOT proportional
Step-by-step explanation: it doesn’t stick to 1 number going up if that makes sense, it’s adding 1 each time it goes up but it has to stick to one number going up making this NOT proportional
Answer:
2/3
Step-by-step explanation:
x adds by 2's: 0 2 4 6...
y adds by 3's: 0 3 6 9...
Given the point and slope write the equation of the line (6, -6); slope = 5/6
Answer:
y=5/6x-11
Step-by-step explanation:
Slope intercept form: y=mx+b
With slope: y=5/6x+b
Replace x with 6 and y with -6
[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]
-6=5/6(6)+b
Simplify:
-6=5+b
Subtract 5 on both sides:
-11=b or b=-11
Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)
Hope this helps!
Which table represents a linear function?
Please help?
Answer:
I think its the fourth one sorry if I am wrong
Step-by-step explanation:
The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity.
tan(x)sin(2x)
= tan(x)∙[2sin(x)cos(x)]
= StartFraction sine (x) Over cosine (x) EndFraction times 2 sine (x) cosine (x)
= 2sin2(x)
= 1 – cos(2x)
What are the correct justifications, listed in proper order?
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity
Double Angle Identity, Simplify, Double Angle Identity, Quotient Identity for Tangent
Double Angle Identity, Simplify, Quotient Identity for Tangent, Double Angle Identity
Double Angle Identity, Quotient Identity for Tangent, Double Angle Identity, Simplify
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity
The following steps show how the right side of 1 – cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity is option A
Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity.
What is double angle identity?The sin2x formula is the double angle identity used for sine function in trigonometry. Trigonometry is a branch of mathematics where we study the relationship between the angles and sides of a right-angled triangle. The formula for sin2x: sin2x = 2 sin x cos x (in terms of sin and cos)
Given
1 – cos(2x) = tan(x)sin(2x)
Taking R.H.S
tanx.sin2x
= tanx(2 sinx cosx)
2 sinx cosx is a double angle identity
= [tex]\frac{sinx}{cosx} .(2 sinxcosx)[/tex]
[tex]\frac{sinx}{cosx}[/tex] is a quotient identity for tangent
= [tex]2sin^{2} x[/tex]
We have simplify by cancelling out cosx.
= 1 - cos(2x)
It is a double angle identity.
Find out more information about double angle identity here
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Pete wants to buy a new bike that costs $120 before any discount. Which offer should he choose to pay the least amount for the bike? NEED HELP PLEASE
Jordan was asked to convert 345,000,000 to scientific notation. His response was 34.5 x 10^7. His teacher told him he was incorrect. Explain Jordan’s mistake and determine the correct answer
Answer:
345,000,000 =3.45 x 10^8
Step-by-step explanation:
To convert a number to scientific notation, place or move the decimal point of a number until the coefficient of the number is greater than 1 and less than 10. This is Jordan mistake, 34.5 is greater than 10. Which is incorrect!
explanation:
you have 345,000,000
Keep moving the dot till you have 3.45
Then count how many spaces you've moved
To get to 3.45, it took you 8 moves so you would have 3.45*10^8 as your answer