Answer:
[tex]A(t) = 1400(1 - e^{\frac{-t}{50}})[/tex]
Step-by-step explanation:
The net mass flow rate dA/dt = mass flow rate in - mass flow rate out
mass flow rate in = concentration of brine in × brine flow rate in = 4 lb/gal × 7 gal/min = 28 lb/min
Let A(t) be the amount of salt at time t. The concentration of salt in the tank at time, thus C = amount of salt/volume of tank = A(t)/700 lb/gal.
Since the well mixed solution is pumped out at a rate of 14 gal/min, the mass flow rate out = concentration of salt in tank × volume flow rate out = A(t)/700 lb/gal × 14 gal/min = m(t)/50 lb/min
So, dA/dt = mass flow rate in - mass flow rate out
dA/dt = 28 lb/min - A(t)/50 lb/min
dA/dt = 28 - A(t)/50
dA/dt = [1400 - A(t)]/50
separating the variables, we have
dA/[1400 - A(t)] = dt/50
integrating both sides, we have
∫dA/[1400 - A(t)] = ∫dt/50
-1/-1 × ∫dA/[1400 - A(t)] = ∫dt/50
1/-1 × ∫-dA/[1400 - A(t)] = ∫dt/50
-1 × ㏑[1400 - A(t)] = t/50 + C
-㏑[1400 - A(t)] = t/50 + C
㏑[1400 - A(t)] = -t/50 - C
taking exponents of both sides, we have
[tex]1400 - A(t) = e^{\frac{-t}{50} - C} \\1400 - A(t) = e^{\frac{-t}{50}}e^{-C}\\1400 - A(t) = Be^{\frac{-t}{50}} ( B = e^{-C}) \\A(t) = 1400 - Be^{\frac{-t}{50}}[/tex]
when t = 0, A(0) = 0. So,
[tex]A(t) = 1400 - Be^{\frac{-t}{50}}\\A(0) = 1400 - Be^{\frac{-0}{50}}\\0 = 1400 - Be^{0}\\0 = 1400 - B\\B = 1400[/tex]
So,
[tex]A(t) = 1400 - 1400e^{\frac{-t}{50}}\\A(t) = 1400(1 - e^{\frac{-t}{50}})[/tex]
Can someone please help.
Answer:7-10
Step-by-step explanation:
In this question it is asking what is the biggest change in the temperature that happened "next to the other one" on the table
And the change from 7-10 is the highest change that is "next to each other"
What is the value of (5 2– 10) ÷ 5 × 2 3 ?
CORRECT ANSWER PLEASE?!!
Answer:
210
Step-by-step explanation:
(52-10)
42÷5
8.4×25=210
Answer:
BEODMASS
( 52 - 10 ) ÷ 5 × 23
42÷5 ×23
8.4 x 23
193.2
¿Existen o no existen los números?.
si existen pero que tipo de números? porque si existen
Explain the meaning of probability. What does it mean if an event has a probability of 0? Give an example. What does it mean if an event has a probability of 1? Give an example. What does it mean if an event has a probability of 1/2? Give an example. (LONG ANSWERS ONLY)
Answer:
If an event has a probability of 0 it means that it is impossible. For example when they say there is 0% of rain. It is very unlikely it is going to rain. If an event has a probability of 1 it means that it is certain. For example, if they say there is a 100% chance it is going to rain. It is very certain that it's going to rain. If an event is 1/2 then it means there it is likely as it is unlikely. For example, if they say there is a 50% chance of rain. Then it might not rain, but there is a chance that it might rain as well.
Step-by-step explanation:
Hope this helps!
Probability can simply be defined as the chances of an event a, occuring with respect to event b, with respect to event n, given an nth number of possible outcomes.
Probability can be calculated using the following expression:
[tex] \frac{freq \: of \: event \: n}{freq \: of \: total \: number \: of \: events} [/tex]
When an event has a probability of 0, it means that by no chance or condition will the event be true. For example, the probability of a person who is a boy has 0 probability that he is a girl.
When an event has a probability of 1, it means that with every chance or condition, the event will be true. For example, the probability that a person who is a boy has a probability of 1 that he is a boy.
An event that has a probability of 1/2 means that the event could either return a probability of 0 or 1 on different chances or conditions. For example, the probability of a fuetus whose gender is not known has a probability of 1/2 for being a boy and 1/2 for being a girl.
Portia has purchased a new aquarium for her fish. It is in the shape of a hexagonal prism. 3a) How much water can Portia’s new aquarium hold? * 1 point a) 166.28 cubic inches b) 790.28 cubic inches c) 956.56 cubic inches d) 3120 cubic inches e) 6240 cubic inches
Answer:
D. 3120
Step-by-step explanation:
How many sides does a hexagon have? Six. Let's begin our equation with 6. The area of a triangle formula would be: 1/2 bh. And a hexagon is just six triangles put together. Now our equation is: 6 (1/2 bh) What's bh then? B (base)= 8in. The base is usually always at the bottom. Now we take 10 and add it into the equation. Next we would multiply this by 13. Our equation is now: 6(1/2*8*10)*13. What do you get then? 3120.
For Part B: Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?
Now, we're dealing with surface area. What is surface area, anyway? Surface area is the sum of all faces. There are 2 hexagonal faces and 6 sides.
What is 6*1/2 *8? 24! Now what's 10*24? That's right, 240!
8*13=104
6(104)=624
624+240=864
Was Thomas Jefferson a federalist or anti-federalist?
Answer:
He was an Anti-federalist
Step-by-step explanation:
Answer:
Anti-federalist
Step-by-step explanation:
The Federalists, led by Secretary of Treasury Alexander Hamilton, wanted a strong central government, while the Anti-Federalists, led by Secretary of State Thomas Jefferson, advocated states' rights instead of centralized power.
PLS HELP!!!
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
6 yd
13 yd
17 yd
Answer:
36
Step-by-step explanation:
2. If an older television with an aspect ratio of 4:3 has a screen area of 1550 square inches, but the image displayed has an aspect ratio of 16:9, how much area does the image actually occupy? First determine what percent of the screen does the image occupy?
a. 825.5 sq. in.
b. 1162.5 sq. in.
c. 1181.5 sq. in.
d. 1375.5 sq.in.
Which Which value of x makes this equation true? -3x+10=5x-8
value of x makes this equation true? -3x+10=5x-8
Answer:
9/4
Step-by-step explanation:
-3x+10=5x-8
or, -3x-5x = -8-10
or, -8x=-18
or, 8x=18 (i.e. - is cancelled)
or, x=18/8
i.e. x=9/4
Hence, the value of x is 9/4
Answer:
The value of x is 9/4
Step-by-step explanation:
-3x+ 10 = 5x - 8
Add 3x both side
-3x + 3x + 10 = 5x + 3x - 8
10 = 8x - 8
Now, Add 8 both side
10 + 8 = 8x - 8 + 8
18 = 8x
8x = 18
Now, Divide by 8 from both side
8x/8 = 18/8
x = 9/4
Thus, The value of x is 9/4
FOR VERIFICATION ONLY:-3x + 10 = 5x - 8
-3(9/4) + 10 = 5(9/4) - 8
-27/4 + 10 = 45/4 - 8
-27 + 4 × 10/4 = 45 - 8 × 4/4
-27 + 40/4 = 45 - 32/4
13/4 = 13/4
Hence, L.HS = R.H.S
-TheUnknownScientist
Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
Step-by-step explanation:
you can get simply V= ABh πr^2 h π3.14^2 x 17.9 then you get the answer Ihope I can help you
The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?
Step-by-step explanation:
Area=2(L+W)
A=2(6+3)
A=2(9)
A=18in²
therefore, 7500/18
=416.66in²
38°
24 in
A restaurant owner plans to install this bicycle rack in front of her restaurant. In order to meet city safety requirements, the base
of the bicycle rack cannot exceed 20 inches so as to not obstruct pedestrians. Will this bicycle rack be approved by the city?
Answer:
39
Step-by-step explanation:
Yes, the base of the bicycle rack measures about 15 inches.
Whta is the sin angle?The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.
A restaurant owner plans to install this bicycle rack in front of her restaurant.
In order to meet city safety requirements, the base of the bicycle rack cannot exceed 20 inches so as to not obstruct pedestrians.
The base of the bicycle is ;
In the right angle triangle;
[tex]\rm = sin38 \times 24\\\\ =0.61 \times 24\\\\=14.77[/tex]
Yes, the base of the bicycle rack measures about 15 inches.
Hence, Yes, the base of the bicycle rack measures about 15 inches.
Learn more about sin angle here;
https://brainly.com/question/18597026
#SPJ2
find 11/25 of a liter
Answer:
0.44l
Step-by-step explanation:
a litre=1l
11/25 of it=11/25×1l
=0.44l
Answer:
A litre=1 l
Or, 1/25×1
=0.44.
In a grocery store, a $12 case of soda is labeled, "Get a 20% discount." What is the discount? What is the sale price of the case of soda?
4x+(3x+2)=3x(4+2)................................
50 POINTS
Solve by linear combination
2x-4y=4
x-4y=10
Write your answer as an ordered pair with no spaces (x,y)
Answer:
(1/2,1/4) because m= 1/5 and m= 1/2 and te equation is y=1/4x - 5/2 and y= 1/2x - 1
Substracting both
[tex]\\ \sf\Rrightarrow x=4-10=-6[/tex]
Putting in eq(2)
[tex]\\ \sf\Rrightarrow -6-4y=10[/tex]
[tex]\\ \sf\Rrightarrow -4y=16[/tex]
[tex]\\ \sf\Rrightarrow y=-4[/tex]
Hence our solution is
(x,y)=(-6,-4)HELP ASAP!!!!!!
Colin saved $30 in July, $21.50 in August, and $50 in September. He spent $18 on video games and $26.83 on books. How much money does Colin have left?
If the graph of f(x) = |x| is shifted up 5 units, what would be the equation of the new graph?
A. g(x) = |x + 5|
B. g(x) = |x| + 5
C. g(x) = |x| - 5
D. g(x) = |x - 5|
Answer:
B. g(x)= |x| + 5
Step-by-step explanation:
-5 represents a vertical shift down, so that narrows it down to either A or B. A shows a shift across the horizontal (X) axis, so it must be B.
Please help me solve these questions
S(x)=5x+5
T(x)=_3x +4
The value of t(s(2))
Answer:
Step-by-step explanation:
This is a composite function, in which we will first evaluate the s function at a value of 2, then we will use that value in the t function.
s(2) = 5(2)+ 5 so
s(2) = 15. Now we evaluate the t function at 15:
t(15) = 3(15) + 4 so
t(15) = 49
help me pls! PLS PLS PLS I NEED IT
20 points
options are x, x^9, x^4, and x^6
Answer:
x^4
Step-by-step explanation:
The expression can be simplified to (x^2)^2. Using an exponent rule, you multiply the two exponents together to get 4. The answer is x^4
Can some explain how to do this?
Answer:
Exact Area = 210.25pi - 210Approximate Area = 450.185The units for the area are in square inches or in^2. The approximate value shown above is when using pi = 3.14
=============================================================
Explanation:
Use the pythagorean theorem to find the length of the hypotenuse
a = 20b = 21c = unknowna^2 + b^2 = c^2
20^2 + 21^2 = c^2
400 + 441 = c^2
c^2 = 841
c = sqrt(841)
c = 29
The hypotenuse is 29 inches long. This is the diameter of the circle. Half of that is the radius at r = d/2 = 29/2 = 14.5 inches.
The area of the circle is...
A = pi*r^2
A = pi*(14.5)^2
A = pi*210.25
A = 210.25pi
Which is exact in terms of pi
We'll subtract off the triangular region as this isn't shaded in. The area of the triangle is base*height/2 = 20*21/2 = 420/2 = 210 square inches.
So the shaded region is therefore 210.25pi - 210 square inches
This approximates to 210.25*3.14 - 210 = 450.185 when using the approximation pi = 3.14; use more decimal digits of pi to get a more accurate value.
Please show steps, 100 points and Brainliest
Convert vertex form f(x)=(x+2)^2-25 to factored form.
Answer:
f(x)=x^2+4x-21
Step-by-step explanation:
Answer:
f(x) = (x + 7) (x - 3)
Step-by-step explanation:
f(x)=(x+[tex]2)^{2}[/tex]-25
(x + 7) (x - 3) we put the 2 x's because of the (x+2)^2
now the + 7 and - 3, multiply the 2 numbers = -21 then use those 2 in
(x+2)^2 to add for the answer = -25
Paula needs to replace the floor in her family room since her cat peed in several places. She wants to put down both vinyl flooring and carpet in the room. The carpet she selected costs $2 per sq. foot. The vinyl floor covering costs $1 per sq. foot. She has $500 to spend on materials and must cover an area of 300 sq. feet. How much carpet and vinyl flooring will she buy to meet her requirements?
Answer:
c = amount of carpet flooring; v = amount of vinyl flooring2c + 1v = $500v = 100 sq. ft.c + v = 300c = 200 sq. ft.
Step-by-step explanation:
the anwser
Arianna earns $15 for doing yard work for 3 hours. If Arianna charges at the same rate, how many hours will it take her to
earn $35? hours
Answer:
7 hours
Step-by-step explanation:
15 dollars +15 dollars 30 dollars=2 hours. 5 dollars left 15 divided by 3, 5 dollars. 3 divided by 3 = 1 so 1 hours is 5 dollars. My explaining is not good.
Answer: 7 hours
Step-by-step explanation:
She earns 5 dollars per hour because 5x3=15
and then you do 15x2=30
then 3x2=6
then just add 1 to 6
6+1=7
so there's your answer
7 hours
A riddle for the day
I am less than 7 tens and more than 4 tens I am a odd number if you add both my digits you will get 11 which number am I?
47
65
67
74
Answer:
two of them are possible which one is the correct
Please i need help over here
Two dice are tossed simultaneously, what is the probability that?
1. sum oc the out come is more than 7?
2. the sum of the square of individual outcome is less than 20?
Answer:
5 / 12
11 / 36
Step-by-step explanation:
The sample space for 2 dice = 6² = 36
Number of outcomes where sum is less than 7 = 15
Probability = required outcome / Total possible outcomes
P(obtaining a sum less Than 7) = 15 / 36 = 5/12
Number of outcomes where Sum of individual outcome is less than 20 = 11
P(sum of individual outcome less than 20) = 11/ 36
help pls what is he surface area measured in square centimeters, of the shape
below do not include units in your answer
Answer:
Solution given:
l=8cm
b=8cm
h=3cm
now
total surface area=2(lb+bh+lh)
=2(8*8+8*3+8*3)=224cm²
224 cm² is a required volume.
3/4-2/3=what does it equal
Answer:
1/12
Step-by-step explanation:
[tex] \frac{3}{4} - \frac{2}{3} = \frac{9 - 8}{12} = \frac{1}{12} [/tex]
12. Which statement best describes the effects on the graph of f(x) = log2 xwhen f(x) is replaced by
f(x-2) + 1?
a. The graph is vertically stretched by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
b. The graph is vertically compressed by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
c. The graph is horizontally stretched by a factor of 3, horizontally translated 2 units left, and
vertically translated 1 unit up
d. The graph is vertically compressed by a factor of , vertically translated 2 units down, and
horizontally translated 1 unit left.
Answer:
B.
Step-by-step explanation:
Hope it helps thx#CARRYONLEARNING!