Answer:
1.857 minutes
Step-by-step explanation:
From the given information:
Consider the amount of salt present in the tank as x(t) at a given time (t); &
The volume of the solution = V(t)
At t = 0 i.e. (at initial conditions) x(0) = 30; and V(0) = 50
However, the overall increase taken place for 1 gallon per minute is:
V(t) = 50 + t
The amount of salt x(t) at any given point for time (t) is;
[tex]\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}[/tex]
After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:
[tex]\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}[/tex]
Taking the integral of what we have above, we get:
In x(t) = - 5 In(t + 50) + In (C)
In x(t) = In (t+ 50)⁻⁵ + In (C)
In x(t) = In C ( t + 50)⁻⁵
x(t) = C(t + 50)⁻⁵ (General solution)
To estimate the required solution; we apply the initial conditions x(0) = 30;
Thus;
x(0) = C(50)⁻⁵ = 30
⇒ C = 30 × 50⁵
Hence; x(t) = 30 × 50⁵ × (t + 50)⁻⁵
The above expression can be re-written as:
[tex]x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25[/tex]
i.e.
[tex]\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}[/tex]
[tex]\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}[/tex]
[tex]\dfrac{50}{t+50}= 0.964192504[/tex]
[tex]{50}= 0.964192504(t+50)[/tex]
50 = 0.964192504t + 48.2096252
50 - 48.2096252 = 0.964192504t
1.7903748 = 0.964192504t
t = 1.7903748 / 0.964192504
t ≅ 1.857 minutes
We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.
Which relation is a function?
a.
{(5,3), (2,8), (-5, -1),(4,7), (2, 1)}
b. {(5,3), (2,8), (-5,-1), (4,7), (-2, 1)}
{(5,3), (2,8), (-5, -1), (4,7), (5,7)}
d. {(-5,3), (2,8), (-5, -1), (4,7), (
2, 2)}
Answer: b
Step-by-step explanation:
You can determine which is a function by looking at the x values. If an x value repeats, it is not a function. In A, the x variable 2 repeats so it is not a function. In C, the x variable 5 repeats. In D, the x variable -5 repeats. The only answer choice where none of the x values are the same is B, so the answer is B. Hope this helps!
1. What is an equation of the line through (7, -1) with slope -3?
Find equation of this line.
Answer:
Step-by-step explanation:
(-4, 2) (3, -4)
(-4 - 2)/(3 + 4) = -6/7
y - 2 = -6/7(x + 4)
y - 14/7 = -6/7x - 24/7
y = -6/7x - 10/7
Madeline has two different candles made by two different companies. The length in centimeters of the first candle depends on its burning time t (in hours) according to the formula f(t)= 20-1.5t. The length (in centimeters) of the second candle over time
Answer:
I needed help with this answer well, because im on it right now.
Step-by-step explanation:
I'm in algebra and I don't understand how to solve this equation or problem :(
2)
Mike went to the doctor and was found to be 20 pounds overweight.
The doctor discovered that Mike ate an average of 2000 calories per
day. He said for Mike to lose weight and meet his goal, the maximum
amount of calories he could eat per day was 1750. How many calories
will Mike be cutting out each week (7 days)?
Answer:
1750 Calories
Step-by-step explanation:
2000-1750=250
250x7=1750
Water flows from a faucet at a constant rate. Kian
measures 8 cups of water in 6 seconds.
What is the constant of proportionality for the relationship of cups of water to minutes?
Answer:
4 cups every 3 second which means so 80 cuos in one minute
Step-by-step explanation:
hope this helps
The constant of proportionality for the relationship of cups of water to minutes is 80
Represent cups with c and time with t.
So, the given parameter can be represented using the following ratio
c : t = 8 : 6
Multiply by 10
c : t = 80 : 60
60 seconds = 1 minutes.
So, we have:
c : t = 80 : 1
Express as fractions
[tex]\mathbf{\frac ct = \frac{80}1}[/tex]
Multiply both sides by t
[tex]\mathbf{\frac ct = 80}[/tex]
Multiply both sides by 6
[tex]\mathbf{c = 80t}[/tex]
A proportional equation is represented as:
[tex]\mathbf{c= mt}[/tex]
Where m represents the constant of proportionality
By comparison:
[tex]\mathbf{m = 80}[/tex]
Hence, the constant of proportionality is 80
Read more about the constant of proportionality at:
https://brainly.com/question/18707816
The following measurements were added: 5.45 + 6.1 + 2.84. what should
the answer be reported as *
1)14.39
2)14.3
3)14.4
4)14
Evaluate the expression.
(14 +17) - 6-12
Answer:
(14+7)-6-12
31-18
13
.............
Jimmy bought a pair of jeans for $50 and a shirt for $25. He has a coupon to save 1/10 of the total on his purchase. How much does Jimmy pay for the jeans and shirt after the discount?
Answer:
$67.5
Step-by-step explanation:
50+25=75. Then, it's 1/10 of 75 which is $7.5. Then, 75-7.5 which is $67.5
Hope this helps :D Please mark brainliest
what is the volume
Answer:
The volume is 227.5
Step-by-step explanation:
The volume for a triangular prism, such as this is, (lxwxh)/2. Because in all shapes volume equals the area multiplied by the height or depth. And an area of a triangle is l or base multiplied by the altitude or w, divided by 2. So the area would be 5x7/2, 35/2, 17.5. And the volume would be 17.5x13, 227.5
Joe worked 8 hours less then Lou. Together they worked 72 hours. How many hours did each work?
Answer:
Joe=32 Lou=40
Step-by-step explanation:
72-8=64
64/2=32
32+8=40
Joe=32
Lou=40
Hope this helped:)
Roberto wants to display his 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different ways can Robert display his figures?
Answer:
3 is an odd number, so we need an even number of sets of 3 cards because 18 is an even number.
So we need 0, 2, 4 or 6 sets of three.
0 2-card + 6 3-card, 3 2-card+4 3-card, 6 2-card+2 3-card, 9 2-card+0 3-card. There are only 4 combinations:
(2-card, 3-card)=(0,6), (3,4), (6,2), (9,0).
Grade 10 Math, I need help fast!
Given the function f(x) = 2x. What is the value of f(-3)?
A. -6
B. 8
C. -8
D. 1/8
f(x)=2x
f(-3)=2(-3)
f(-3)=-6
Answer:
A. -6
Step-by-step explanation:
Just plug in -3 to where x is.
can u find all the angles plz?
Answer:
The two sides we know are O pposite (300) and A djacent (400).
SOHCAH TOA tells us we must use T angent.
Calculate Opposite/Adjacent = 300/400 = 0.75
Find the angle from your calculator using tan-1
:)
Answer:
1 = 88 2 = 42 3 = 113
Step-by-step explanation:
2 is 42 because it is the opposite angle and then you subtract 42 and 50 from 180 to get 88 for #1 and you subtract 42 and 25 from 180 to get 113 for #3.
please
help i’ve been stuck on
this all day
Answer:
CPB
Step-by-step explanation:
acute is less than 90 degrees and right is 90 degrees and obtuse is over 90 degrees
Answer: The answer is CPB
Question 4
Measure the length of your selected line segment using the tools available in GeoGebra. Include measurements for both the image and the
prelmage, and enter your values in the table. Compare the measured values with the values you calculated in Question 3. Are the values equal?
Type an X in the appropriate box.
Answer:
Edmentum.
Step-by-step explanation:
God bless and enjoy. :)
Correct answer only
Answer:
Step-by-step explanation:
y=2x+1
Answer:
y=2x+1
Step-by-step explanation:
Which of the following is a factor of the polynomial 6x^2-x-15
2. Which of the following statements is true?
A. The sample size should be 50% of the population for an effective statistical study.
B. Stratified sampling is when every nth individual is selected.
C. Surveys should be designed so as to get as much private information from people as possible.
D. To determine if a conclusion is valid, you must consider the sampling technique, the sample size and the data gathering technique.
4y + x = 12, 2x = 24 - 8y
Solve by Substitution
Answer: Undefined
Step-by-step explanation:
4y+x=12, 2x=24-8y
Isolate x by subtracting 4y
4y+x=12
x=12-4y
Plug the equation for x in to anywhere you see the variable x in the other equation
2(12-4y)=24-8y
Distribute 2
24-8y=24-8y
Get the variables on one side so add 8y (cancels out)
24=24
Can’t solve its undefined
Write the next three terms: 2,4,6,8,.
Answer:
10, 12, 14
Step-by-step explanation:
even numbers, just add 2 to previous answer
10, 12, 14............
2. Determine the scale factor of a drawing if the scale is 1 inch = 4 feet.
Answer: Therefore the scale factor is 48 times.
Step-by-step explanation: Since the drawing is in inches, the scale will be 1/4
the scale is 1 inch to 4 FEET.
Convert feet to inches
1 inch to 48 inches
So the ratio is 1:48
Line l was mapped to Line m as shown in the graph below. please help
What transformation was applied to Line l to produce the result shown?
Line l was translated up 5 units.
Line l was reflected over the x-axis.
Line l was reflected over the y-axis.
Line l was translated 6 units to the right.
ΔABC is dilated using a scale factor of 12 to produce ΔA'B'C'. Select all of the statements that apply to the transformation.
Answer:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of [tex]\frac{1}{2}[/tex] to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = [tex]\frac{1}{2}[/tex] of the sides of ΔABC
Area of ΔA'B'C' = [tex]\frac{1}{2}(\text{Area of triangle ABC})[/tex]
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
Answer: The Third option and the sixth option.
Step-by-step explanation: I have had this question on a test before and i got the answer correct. i hope this helped.
4th Grade Unit 3 Assessment Part D ohn has 200 buttons. He has 5 times as many buttons as How many buttons do John and Markie have all together? Enter your answer in the space provided.
Answer:
1200
1. X represents the number of buttons Markie has: 200 times 5 = x
2. 200 X 5 = 1000, so Markie has 1000 buttons
3. Add Markies Buttons and Johns buttons: 200 + 1000 = 1200
4. Sentence: John and Markie have 1200 buttons all together.
look at the picture please
Answer: the last one is the right answer
Step-by-step explanation:
4/9 equals 0.444444 or 0.4 with the dash on top
Factor the common factor out of this expression.
25u^2+20v^2+5v
Answer:
Hi Answer Is 5(5u^2+4v^2+v)
Find three consecutive integers whose sum is 57????
Answer:18 19 20
Step-by-step explanation:"Consecutive" means that the integers will follow each other in value, for example: 1, 2, 3 or 4, 5, 6. Also, no decimals are needed here because "integers" are whole, counting numbers. Here is the set up: Let x= the first integer Then X+1= 2nd consecutive integer and x+2= 3rd .
Suppose that x=1 x+1= 1+1=2 and x+2=1+2=3 However, you need specific consecutive numbers whose sum is 57. Remember that sum means to add:
x+ (x+1) + (x+2) = 57 Addition of all 3 consecutive numbers Now solve for x
and substitute into each part to come up with the three integers:
3x + 3= 57 3x=54 x=54/3 = 18 x=18, x+1= 18+1=19 x+2=18+2=20
Check your answer: 18+19+20=57 57=57 Check
Please help i’ll give brainliest and please dont say this is east im in 6th and just learned this
Answer:
C
Step-by-step explanation:
1/3 is .3 repeating
and you need to move decimal over twice for a percentage so should be 15%
System of Equations in Three Variables Word Problem
Answer:
i think the answer is a number or multiple number and maybe a decimal.
Step-by-step explanation:
go to Tiger Algebra Solver