A vat holds 100 cubic feet of liquid and is initially full. Liquid which is salt water with 1 gram of salt per 2 cu ft of liquid is being added at a rate of 2 cu ft per minute. It is mixed immediately, and the mixture is draining at 2 cu ft per minute, so the vat stays exactly full. Let y(t) denote the number of grams of salt in the vat at time t. Write the differential equation for y. Use the graphical method to plot two substantially different solutions for y, depending on the initial amount. Explain the difference. Then use the formula for solution of first-order linear DE to write the explicit solution if the vat is initially filled with pure water (i.e., no salt).
Answers
Answer:
explicit solution : y(t) =49 t
Step-by-step explanation:
Given : The vat holds 100 cubic feet of liquid and it is initially full
with salt water that contained 1 gram of salt per 2 cu ft of liquid
attached below is the detailed solution
Related Questions
What is the area of the square? A square with the left side labeled 4 units.
Answers
4^2 = 16
the area is 16 units
Answer:
Area = 16 units
Step-by-step explanation:
Area = length * width Length = x Width = w
A = (x) (w)
Because the shape is a square we know all 4 sides are equal, the lenth and width are the same sizes.
x = 4 units
w = 4 units
A = 4*4
A= 16 units
Pls help me with this
Answers
hope this helps! sorry if i’m wrong:)
The perimeter of a rectangle is 96 feet, and the width is 22 feet. What is the length of the rectangle?
Answers
Answer:
26 feet
Step-by-step explanation:
The perimeter of a rectangle is 2 times its length and 2 times its width, or [tex]2l+2w=P[/tex]. Let's plug in the given values for the width and perimeter and solve.
[tex]2l+2(22)=96[/tex]
Simplify.
[tex]2l+44=96[/tex]
Subtract 44 on both sides.
[tex]2l+44-44=96-44[/tex]
Simplify.
[tex]2l=52[/tex]
Divide by 2 on both sides.
[tex]\frac{2l}{2} =\frac{52}{2}[/tex]
Simplify again to find the value of [tex]l[/tex].
[tex]l=26[/tex]
The length is 26 feet.
Good luck <3
Find an equation for the line below?
Please help I’m not very good with figuring out graphing
Answers
Answer:
y = 1/3x + 8/3
Step-by-step explanation:
To find an equation use two points to gather the slope and y-intercept.
(1, 3) (-5, 1)
Slope:
y2 - y1 / x2 - x1
1 - 3 / -5 - 1 = -2 / -6
-2 / -6 = 1 /3
y = 1/3x
y intercept is 8/3
Equation: y = 1/3x + 8/3
hope this helps and is right. p.s. i really need brainliest :)
Answer:
y=1/3x+8/3
Step-by-step explanation:
[SOLVED]
Lin took 75 boxes of carrots and 80 boxes of potatoes to the market. She sold 68 boxes of carrots and 71 boxes of potatoes. How many boxes of vegetables did she take home?
How many boxes of carrots are left?
7
How many boxes of potatoes are left?
9
How many boxes altogehter are left?
16
Answers
Answer: 16 vegetables
Step-by-step explanation:
Answer:
7 carrots 9 potatoes and 16 all together
Step-by-step explanation:
help me please :(*****
Answers
Answer:
54
dcutvihvihvtuutcigciyvihvihvo
Answer:
Step-by-step explanation:
The area of the figure below is ___ft2. Round to the nearest hundredth where necessary. Please help ! Will mark brainlist!
Answers
Answer:
A=467.61 ft^2
Step-by-step explanation:
This is a trapezoid. The area of this trapezoid is [tex]A=\frac{1}{2}(25+33)h[/tex] . 33-25 is 8, so that is the base of the little traingle if we break up the slanted end into a triangle. Now we can use the pythagoreum theorem to find out that the height is 16.125 .
Now the Area equation is [tex]A=\frac{1}{2}(25+33)16.125[/tex]
That gives us our final answer of 467.61 ft^2
i need help guys plsss
Answers
Answer:
6. r = 21 cm
7. A = 155.5 m²
Step-by-step explanation:
7: Formula for arc length is;
S = (θ/360) × 2πr
We are given;
S = 51 cm
θ = 139°
Thus;
51 = (139/360) × 2π × r
Making r the subject;
r = (51 × 360)/(2π × 139)
r ≈ 21 cm
8) Area of sector is gotten from the formula;
A = (θ/360) × πr²
A = (220/360) × (π × 9²)
A = 155.5 m²
Divide the rational expressions
(X/x+1)(2/x)
Answers
( 1 + 1 )( 2/x )
(2)(2/x)
4/x
that's basically it
geometry/ trigonometry. please help!!!!
Answers
Answer:
Sin A= 5/13, Cos A= 12/13, Tan A= 5/12
Step-by-step explanation:
Answer and Step-by-step explanation:
Trig functions:
sin(Angle) = [tex]\frac{Opposite.side}{Hypotenuse}[/tex]
cos(Angle) = [tex]\frac{Adjacent.side}{Hypotenuse}[/tex]
tan(Angle) = [tex]\frac{Opposite.side}{Adjacent.side}[/tex]
C = 26 because of Pythagorean theorem
sin(A) = [tex]\frac{10}{26} = \frac{5}{13}[/tex]
cos(A) = [tex]\frac{24}{26} = \frac{12}{13}[/tex]
tan(A) = [tex]\frac{10}{24} = \frac{5}{12}[/tex]
#teamtrees #PAW (Plant And Water)
Write the slope-intercept form of the equation that goes through the point (0,0)
and is parallel to the line that has a slope of -6.
Answers
Answer:
y = -6x
Step-by-step explanation:
slope-intercept form: y = mx + b
slope↑ ↑y-intercept
parallel lines have the same slope, thus the slope is -6
substitute the y in (0, 0) and the slope of -6 into the equation y = mx + b:
=> y = -6x + 0
=> y = -6x
After a snowball fight, Ethan wanted to warm up with a cup of hot chocolate. He decided to make enough to share with his friends. First, he heated 6 cups of milk and 1 pint of cream in a large pot. Then, he stirred in 4 cups of melted chocolate. How many cups of hot chocolate did Ethan make?
Answers
Answer:
12 cups
Step-by-step explanation:
1 pint is 2 cups
Answer:
Step-by-step explanation:
Are all isosceles triangles similar? Are all right triangle similar? Are all isosceles right triangles similar? Explain.
Please don't answer with one answer, blank or a ridiculous response. This is serious please.
And don't send links that are viruses
Please explain each one.
Answers
9514 1404 393
Answer:
a) no
b) no
c) yes
Step-by-step explanation:
a) Isosceles triangles can have a third angle (the one that is not part of the pair of equal angles) with any value in the range 0 < α < 180°. Triangles with different angle values will not be similar.
Not all isosceles triangles are similar.
__
b) The smallest acute angle of a right triangle can have any measure in the range 0 < α ≤ 45°. Right triangles having different smallest angles will not be similar. The attachment shows dissimilar right triangles.
Not all right triangles are similar.
__
c) If the smallest acute angle of a right triangle is 45°, then both acute angles are 45°, and the right triangle is an isosceles triangle. Each such triangle will be similar to every such triangle.
All isosceles right triangles are similar.
The diameter of one circle is 12 inches long. The
diameter of a second circle is 25% longer than the
diameter of the first circle. To the nearest square inch,
how much larger is the area of the second circle than
the arca of the first circler
Answers
Answer:
9.42 in.²
Step-by-step explanation:
12 × 25% = 3
12 + 3 = 15
2πr
2 × 6 × 3.14 = 37.68 in.²
2 × 7.5 × 3.14 = 47.1 in.²
47.1 in.² - 37.68 in.²
9.42 in.²
The area of the second circle larger than the area of the first circle will be 63.585 square inches.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the diameter of the circle. Then the area of the circle will be
A = (π/4) d² square units
The width of one circle is 12 inches long. The width of a subsequent circle is 25% longer than the measurement of the primary circle.
The diameter of the second circle is given as,
⇒ 1.25 x 12
⇒ 15 inches
The area of the first circle is given as,
A₁ = (π/4) (12)²
A₁ = 113.04 square inches
The area of the second circle is given as,
A₂ = (π/4) (15)²
A₂ = 176.625 square inches
The area of the second circle larger the area of the first circler is given as,
A = A₂ - A₁
A = 176.625 - 113.04
A = 63.585 square inches
The area of the second circle larger than the area of the first circle will be 63.585 square inches.
More about the area of a circle link is given below.
https://brainly.com/question/11952845
#SPJ2
X^2/3 •5x =5x^5/3
Can someone explain how the exponent is 5/3?
Answers
If the area of a triangle is 150 square cm, and the height is 10, what is the length of the base?
Answers
Answer:
cf cvgbhv
Step-by-step explanation:
xcvbn
Answer:
Step-by-step explanation:
150=10*Base*1/2
15=Base*1/2
Base=30cm
Find the length of side a in the right triangle below.
17
a
15
The length of the side, a, is approximately
Answers
Answer:
I'm assuming that a is the hypotenuse (Longest side)
Step-by-step explanation:
22.67 is the answer
If a isn't the hypotenuse (Longest side) then let me know in the comments then I will comment the right answer for you <3
Which is a formula for the area of a triangle?
Group of answer choices
A = 1/2 X b X h
A = Base X Height
A = L X W
A = bh
Answers
Tricia looked at a map of an amusement park that used the scale 1 inch = 1 meter. On the map the roller coaster was 5 inches from the ice cream stand. When Tricia gets off the roller coaster, how far will she have to walk to get to the ice cream stand?
A. 3 inches
B. 6 inches
C. 4 meters
D. 5 meters
Answers
Answer:
D = 5 meters
Step-by-step explanation:
1 inch = 1 meter
5 inch = 5 meter
Whatever you do to one side you do the same to the other.
Tim says 1/8 of this model is shaded. Lucy says 8/8 of this model is shaded.
Answers
Answer:
Step-by-step explanation: Lucy is correct because all of the squares are filled, and therefore instead of 1 square filled, 8 are, this is why lucy is correct :)
Answer:
Lucy is correct.
Step-by-step explanation:
We can see that the ENTIRE model is shaded ( all eight squares).
So Lucy is correct since she stated that 8 out of 8 (8/8) squares are shaded.
8/8 = 1, so whole.
1/8 would mean that only one out of eight squares is shaded, so Tim is NOT coorrect.
When driving in England, Brian drove through several speed cameras. On one drive, Brian left his hotel and after 7 minutes he was 2.5 km away and at that moment was measured going 0.5 kpm (kilometers per minute). Later, 18 minutes after he started driving, he was 14.8 km from the hotel and at that moment was measured going 0.8 kpm.
A. Find the linearization at 7 minutes.
B. Find the linearization at 18 minutes.
C. Compute two approximations for Brian's distance from his hotel at 14 minutes, using the linearizations from parts a and b.
D. Which approximation do you think is better? Why?
Answers
Solution :
The formula for the linearization of a function [tex]$f(x)$[/tex] at a point [tex]$x$[/tex] = a is given as
[tex]$L(x)=f(a)+(x-a)f'(a)$[/tex]
Assuming the time is t and the distance travelled is [tex]$f(t)$[/tex], that makes the speed as [tex]$f'(t)$[/tex].
So substituting them in the linearization formula,
A. At t = 7 minutes
f(7) = 2.5 km
f'(7) = 0.5 kpm
∴ [tex]$L_7(t)=f(7)+(t-7)f'(7)$[/tex]
[tex]$=2.5+(t-7)0.5$[/tex]
[tex]$=2.5+0.5t-3.5$[/tex]
[tex]$=0.5t-1$[/tex]
B. At t = 18 minutes
f(18) = 14.8 km
f'(18) = 0.8 kpm
∴ [tex]$L_{18}(t)=f(18)+(t-18)f'(18)$[/tex]
[tex]$=14.8+(t-18)0.8$[/tex]
[tex]$=14.8+0.8t-14.4$[/tex]
[tex]$=0.8t-0.4$[/tex]
C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get
[tex]$L_7(14)=0.5(14)-1.0$[/tex]
= 7 - 1
= 6 km
[tex]$L_{18}(14)=0.8(14)+0.4$[/tex]
= 11.2 + 0.4
= 11.6 km
D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km
= 3.5 km
And between the 14 minutes and 18 minutes is = 14.8 km - 6 km
= 8.8 km
This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.
Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km
= 9.1 km
And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km
= 3.2 km
This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.
Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.
There are 4 triangles and 16 squares.what is the simplest ratio of triangles to square
Answers
The ratio of triangles to squares is 4:16 unsimplified because there are 4 triangles and 16 squares. To simplify the ratio, think of it as a fraction:
4/16
The fraction can be simplified to 1/4, meaning that the simplest ratio is 1:4.
PLEAASEE HELP ITS ALREASY LATE AND I DK WHAT TO DO
Answers
Answer:
A
Step-by-step explanation:
we can find out by writing its equation;
9-(-3) / (14-4) = 12 / 10 = 6 / 5
so its equation gonna be y = 6/5x - 7.8
.
now we can grid in the answer choices:
-9 = -6/5 -7.8 so (-1 , -9) is the correct answer
.
First what you can do is find the eq of the line where you need the slope(m) and a point on the line
To find slope (m)
(Y2-y1)/(x2-x1)
(4,-3)=(x1,y1)
(14,9)=(x2,y2)
(9-(-3))/(14-4)
=(9+3)/10
=12/10
m=1.2
Sub this information into the formula
y-y1=m(x-x1)
y-(-3)=1.2(x-4)
y+3= 1.2x -4.8
y=1.2x -7.8
Now sub each point a - d into this to see if they are true
y=1.2x -7.8
a.(-1,-9)
-9=1.2(-1)-7.8
-9=-1.2-7.8
-9=-9
TRUE -POINT IS ON LINE
b.(-2,-8)
-8=1.2(-2)-7.8
-8=-2.3-7.8
-8=-10.1
NOT TRUE -POINT ISNT ON LINE
c.(29,27)
27=1.2(29)-7.8
27=34.8-7.8
27=27
TRUE -POINT IS ON LINE
d.(28,18)
18=1.2(28)-7.8
18=33.6-7.8
18=25.8
NOT TRUE -POINT ISNT ON LINE
ANSWER= a) & c)
Find the slope of the line.
Answers
order the numbers 0.3, 2/5, -0.85, 0.09, 3/4, 3/20 least to greatest
Answers
Answer:
-0.85, 0.09, 3/20, 0.3, 2/5, 3/4
Step-by-step explanation:
Turn all the fractions into decimals
2/5 -> .4
3/4 -> .75
3/20 -> .15
Then order them
-.85, 0.09, 0.15, 0.3, 0.4, 0.75
A child weighing 59 lb has a bad infection and is to be given Cefaclor.
The dosage is 15 mg per kg.
The drug will be delivered in an oral suspension with concentration 250 mg/5 mL.
How many mL will she receive?
Round to the nearest whole number.
You will need to convert her weight to kg, using 1 kg = 2.2 lb.
Answers
Answer:
Step-by-step explanation:
59:2,2=26,81
15*26,81:250=1,6086
Which is the correct vertical cross section through the vertex of the figure?
Answers
Classify the following triangle, Check all that apply A Equilateral B, Acute C. Scalene D. Obtuse E. Isosceles. F.Right
Answers
Answer:
D) obtuse
Step-by-step explanation:
Answer:
the answer is D. Obtues
which of the following equations fits the data shown in the table?
Answers
Answer:
y=2x+3 C
Step-by-step explanation:
The first point (0,3) tells us the y intercept of 3 and we can use the slope formula to figure out that the slope is 2.
If x=7-4 √3 then find the value of (x+1/x)^2
Answers
Answer:
29.03703703
Step-by-step explanation:
7-4 √3 = 5.196152423
(5.196152423 + 0.19245009)^2