Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]
[tex]R_{in} =3 \ lb/min[/tex]
At a slower of 4 gal/min, the solution gets pumped out;
So,
[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]
[tex]R_{out} = \dfrac{2A}{50+t }[/tex]
The differential of the equation is:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]
For the linear differential equation, the integrating factor is determined as:
[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]
[tex]= (50+t)^2[/tex]
Multiplying [tex](50+t)^2[/tex] with the above integration factor;
[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]
[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]
[tex](50+t)^2 A = (50 +t)^3 + c[/tex]
[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]
[tex]A(30) = 76.09 \ pounds[/tex]
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
Inverse function of y=1-x/7
Answer:
x = (7,0)
y = (0,1)
Step-by-step explanation:
-9/2, -3.14, -4, -1.365
in greatest to least
Answer:
-1.365, -3.14, -4, -9/2
Step-by-step explanation:
How do you write 8.2 × 102 in standard form?
Answer:
If this is supposed to be scientific notation then it is 820. if it is 8.2 times one hundred and two then it is 836.4.
Step-by-step explanation:
Hope this helps. :)
12x+5y=95
find the x-intercept
Answer:
(95/12,0)
Step-by-step explanation:
Answer:
(7.916, 0)
Step-by-step explanation:
In order to find the X-intercept, let y=0
12x + 5(0) = 95
12x = 95
95/12x = 7.91666...
Therefore, the x intercept is (7.916, 0)
Whats the Standard form of 3-7i/2+6i
Answer:
[tex]3+\frac{5i}{2}[/tex]
Step-by-step explanation:
Simplify and write the answer in the standard form, a+bi. Hope this helps!
What is the density of the glass in 2.5 g/cm in kg/m
We are given:
Density of glass in g/cm³ = 2.5
Finding the density in kg/m³:
In converting 2.5 g/cm³ to kg/m³, we will first convert the g to kg
Converting the g to kg:
2.5 g/cm³ * 1
Since 1kg = 1000g, 1kg/1000g = 1
2.5 g/cm³ * 1kg / 1000g
the g in the numerator and the denominator will cancel out and we will get:
2.5 kg / 1000 cm³
Converting the cm³ to m³:
We know that 1 m³ = 10⁶ cm³
So, 10⁶ cm³ / 1 m³ = 1
Multiplying the density by 1
2.5 kg / 10³ cm³ * 1
2.5 kg / 10³ cm³ * 10⁶ cm³ / 1 m³
the cm³ in the numerator and the denominator will cancel out
2.5 * 10⁶ kg / 10³ m³
2.5 * 10³ * 10³ kg / 10³ m³
2.5 * 10³ kg / m³
2500 kg/m³
A pole that is 2.8 m tall casts a shadow that is 1 m long. At the same time, a nearby building casts a shadow that is 39.5 m long. How tall is the building? round youre answer to the nearest meter
Answer:
110.6 meters
Step-by-step explanation:
39.5 x 2.8 = 110.6
1.9t-5 simplify using commutative property
Pls help lolll
Answer:
There is nothing to be further simplified. It is how you wrote it. Let me know if it was a mistake I'll edit my answer.
Step-by-step explanation:
Joshua finished the mile race in 22.7 minutes. Blake finished the race 8 3/10 minutes sooner than Joshua finished it. How many minutes did it take Blake to finish the race?
Answer:
31 mins
Step-by-step explanation:
22.7+8 3/10=31 mins
How many inches are in 4 1/2 yards of fabric?
Answer: 162 inches
Step-by-step explanation: 4 yards are 144 inches and 1 yard alone is 36 when you divide it by half it’s 18. (144+18=162)
To convert [tex]4 \dfrac{1}{2}[/tex] yards of fabric to inches, multiply by 36.
Therefore, there are 162 inches in [tex]4 \dfrac{1}{2}[/tex] yards.
For the measurement, we know
1 yard = 36 inches
The given measurement is: [tex]4 \dfrac{1}{2}[/tex] yards
Convert it into an improper fraction,
[tex]4\dfrac{1}{2} = \dfrac{4 \times 2 + 1}{2} \\\\ = \dfrac{9}{2}[/tex]
Thus, [tex]4 \dfrac{1}{2}[/tex] yards can be written as [tex]\dfrac{9}{2}[/tex] yards.
Since 1 yard = 36 inches
Therefore,
(9/2) yards = (9/2)x36 inches
= 9 x 18 inches
= 162 inches
Hence,
The measurement [tex]4 \dfrac{1}{2}[/tex] yards are equivalent to 162 inches.
To learn more about the measurement unit visit:
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I need help ASAP!!,!
Which of the following would be in the solution set to the system of inequalities given below?
Answer:
(-4,0)
Step-by-step explanation:
Solve for please X/2+6=-2
Answer:
x = -16
Step-by-step explanation:
what is 5 quarts converted to liters
Answer:
1 quart = 0.95 liters. with this said, we can conclude that 5 quarts equals 4.73 liters
Answer:
4.73176
Step-by-step explanation:
okay so this is the exact decimal but you can just write you answer as 4.73
hope this helps
Which number is the opposite of -3? Starting at -3, how many steps does it take to get to the opposite of -3? What does this number of steps represent?
Answer: 3 is the oppos ire of -3 and it takes 6 steps to get to it
Step-by-step explanation:
Answer:
"Which number is the opposite of -3?": The number that is opposite of (-3) is 3
"Starting at -3, how many steps does it take to get to the opposite of -3?": It takes 6 steps to get to the opposite of -3.
" What does this number of steps represent?": This number represents the distance between -3 and 3.
Step-by-step explanation:
Find the volume of a cone with a height of
9in and a diameter of 12in.
Answer:
339.12 in³
Step-by-step explanation:
volume of cone: v = Bh/3 = πr²h/3
v = (3.14 * (12/2)² * 9 )/ 3 = 339.12
Hello :)
Please help me solve this
Explain answer
Answer:
[tex]Scale\ Factor = \frac{1}{2}[/tex]
ABC dilated
Step-by-step explanation:
Given
Triangles ABC and DEF
Required
Determine the scale of dilation
First, we pick a side on ABC
[tex]AB = 6[/tex]
Pick a corresponding side on DEF
[tex]DE = 3[/tex]
The scale factor is then calculated as:
[tex]Scale\ Factor = \frac{DE}{AB}[/tex]
[tex]Scale\ Factor = \frac{1}{2}[/tex]
i.e. ABC was dilated by 1/2
3 Write an expression
to represent:
"Twice a number 51
increased by 51"
Answer:
51x 3+51 is the answer from my side
There are 99 females and 121 males participating in a marathon. What percent of the participants are male
Answer:
0.55 = 55%
Step-by-step explanation:
total people: 220
121/220 = 11/20 = 55%
brainileist pweeeeeez
Answer:
55%
Step-by-step explanation:
121/99+121
0.55
55%
Sunflower we haved renewed your helper thank you with working with our business
Answer: wdym? do u need any help
Step-by-step explanation:
Hello can someone please help me with this. I'll give 50 points.
A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. How many of each type of computer should the business buy?
a. 9 laptops and 21 tablets
b. 11 laptops and 19 tablets
c. 19 laptops and 11 tablets
d. 21 laptops and 9 tablets
Answer:
I think it's A because that's only 10,620
Answer: b. 11 laptops and 19 tablets
Step-by-step explanation:
The radius of a circle is 16.3 millimeters
Answer:
I think the equation is C=r/2 but I haven't done this math in a while
Find the value of X. Show your work.
Congruent triangle
Answer:
x = 3
Step-by-step explanation:
exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
97 + x = 64 + 27
x = 97 - 64 - 27 = 6
Answer: x=-6
you know that the interior angles of a triangle equal 180°. so lets find the remaining angle measure
64 + 27 = 91
180 - 91 = 89
so 89 is the third interior angle of the triangle. now let's find the exterior angle.
you know that the extended angle is supplementary; which means it will equal 180° as well. so lets add the third interior angle we just found and let's add it to the unknown expression:
89 + 97 + x = 180
186 + x = 180
-186 -186
x = -6
now it might seem wrong because x is negative and it feels like it should be positive. but let's check our answer.
64+27+89 does equal 180
and 97+(-6)+89 does equal 180
i hope this helps!
explain the steps that you would use to explain the equation -2x+10>50 to solve for x.
Step-by-step explanation:
make it braintliest please
What step can be taken to solve the equation 10x = 6 + 9x?
Answer:
subtract 9x from both sides
Step-by-step explanation:
10x = 6 + 9x
9x 9x
19x = 6
0.315789474 = x
.315 = x
Answer:
Subtract 9x from both sides of the equation.
Step-by-step explanation:
To put x by itself, you need to first put all like terms together. So in order to do this, you need to put 10x and 9x together. Since 9x is positive, you need to subtract 9x from both sides of the equation.
Here is how you completely solve the equation:
10x=6+9x10x-9x=61x=6x=6Helppppp pleaseeeeeeeeeeeeee
Which function is represented by the graph?
Answer:
f(x) = -2|x| + 1 aka the first option
Step-by-step explanation:
sam can make 10 bracelets in 4 hours. how many bracelets can he make in 1 hour. 2 hours. and 3 hours.
Answer:
1 hour- 2 bracelets ; 2 hours 2 bracelets; 3 hours 4 bracelets
Step-by-step explanation:
i dont know if correct
When simplifled, the value of the expression (15 - 11) 2 + 64 +4 is equal to
10
4
24
18
Answer:
I genuinely dont see the answer lol
Step-by-step explanation:
P - Parenthesis
E - Exponent
M - Multiply
D - Divide
A - Add
S - Subtract
[tex](15 - 11)2 + 64 + 4 \\ (4)2 + 64 + 4 \\ 8 + 64 + 4 \\ 72 + 4 \\ 76[/tex]
Write 6 wholes and 2 tenths as a decimal.
Answer: 6.2
Step-by-step explanation:
A whole number is behind the decimal point.
The tenth is right in front of the decimal point.
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Write an equation in point slope form for the line that passes through each point with the given slope.
(1,4), m=6
Answer:
y = 6x -2
Step-by-step explanation:
Answer:
y = 6x - 2
Step-by-step explanation:
pass (1,4)
y = mx + b
b = y - mx = 4 - 6 x 1 = -2
y = 6x - 2