The inflow rate of water is given by the function of the volume of the
tank derived from the shape of the tank.
Response:
The rate water is being pumped into the tank is approximately 286,253 cm³/minWhich method can be used to find the rate at which water is pumped into the tank?
The given parameter are;
Shape of the tank = Conical
Rate at which water is leaking out of the tank = 7,000 cm³/min
Height of the tank = 6 m
Diameter of the tank = 4 m
Solution:
We have;
[tex]\dfrac{D}{h} = \mathbf{\dfrac{2 \cdot r}{h}}[/tex]
[tex]r = \mathbf{\dfrac{D}{2 \cdot h}}[/tex]
Which gives;
[tex]\dfrac{r}{h} = \dfrac{4}{6 \times 2} = \dfrac{1}{3}[/tex][tex]r= \mathbf{\dfrac{h}{3}}[/tex]
[tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h = \dfrac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{3} \right)^2 \cdot h = \mathbf{ \pi \cdot \dfrac{h}{27} ^3}[/tex]
Which gives;
[tex]\dfrac{dV}{dh} = \mathbf{\pi \cdot \dfrac{h}{9} ^2}[/tex]
By using chain rule of differentiation, we have;
[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \times \dfrac{dh}{dt}}[/tex]
Which gives;
[tex]\dfrac{dV}{dt} = \mathbf{\pi \cdot \dfrac{h}{9} ^2\times 20}[/tex]
[tex]\dfrac{dV}{dt} = \pi \cdot \dfrac{200}{9} ^2\times 20 \approx 279,252.68[/tex]
[tex]\dfrac{dV}{dt} = \mathbf{Inflow \ rate - Outflow \ rate}[/tex]
Therefore;
[tex]Inflow \ rate = \mathbf{\dfrac{dV}{dt} + Outflow \ rate}[/tex]
Which gives;
Inflow rate ≈ 279,252.68 + 7000 = 286,252.68 ≈ 286,253
The inflow rate = The rate water is being pumped into the tank ≈ 286,253 cm³/minLearn more about rate of change of a function here:
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49.98 ÷ 17 = ? (show ur work)
Answer:
2.94
Step-by-step explanation:
In the picture below
3. Mr. James told Jill he would charge her $15 per hour, plus parts, to fix her bicycle.
The parts ended up costing $32, and
it took Mr. James 3 hours to fix the bike. Write
and evaluate an expression to determine how much Jill owes Mr. James.
Answer:
512
Solution:
so first you multiply 15 times 32 and get 480 than you add 32 and get 512.
How do I solve this using Substitution??
Answer:
-1
Step-by-step explanation:
so -x-6 and x-4 are both = to y so that means they are both = to each
other so -x-6=x-4 add x to both sides -6=2x-4 add 4 to both sides 2x = -2 simplify by divide by 2 so x=-1
Answer:
Take the second equation and add 4 to both sides, this gives you x=y+4. The plug in y+4 on the first equation, so y=-(y+4)-6, distribute the negative to everything inside the parentheses, and you get y=-y-4-6. Combine like terms and you get y=-y-10, then add y to both sides, you get 2y=-10, divide both sides by 2 and you get y=-5.
Then plug -5 into the second equation and you get -5=x-4, add 4 to both sides and you get -1=x.
If you want to check your answer, just plug in x and y to either of the equations and see if it makes a true statement.
In Newport, the library is 66 miles due south of the courthouse and 88 miles due west of the community swimming pool.
What is the distance between the courthouse and the community swimming pool?
Answer:
110
Step-by-step explanation:
Use the pythagorean theorem (a^2 + b^2 = c^2) to solve it. 66 is a and 88 is b. The distance between them is c.
When is simplified, what is the resulting expression?
Answer:
A. -0.8x + 4.8y + 16
Step-by-step explanation:
Solved using distributive property
Let's find out
[tex]\\ \tt\Rrightarrow 4(0.5x+2.5y-0.7x-1.3y+4)[/tex]
a(b+c)=ab+ac[tex]\\ \tt\Rrightarrow 4(-0.2x+1.2y+4)[/tex]
[tex]\\ \tt\Rrightarrow -0.8x+4.8y+16[/tex]
Option A
please help with these 2 questions!! (9 and 10) please show with solution needed!!
If X is any real number other than 0, then X^0= ------------; 0^0 is not a number.
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1
what should be added to (-5 a2b - 9 ab) to get
a2b + 3 ab?
Based on given conditions,
[tex]a²b + 3 ab - (-5 a²b - 9 ab) [/tex]
[tex]→a²b + 3 ab + 5 a²b + 9 ab[/tex]
[tex]→(a²b + 5 a²b) + (3ab + 9 ab[/tex]
Now collecting the coefficients and adding them,
[tex](1 + 5)a²b + (3 + 9)ab[/tex]
[tex]→6 {a}^{2}b + 12ab[/tex]
Hence, the 6a²b + 12ab should be added.
simplify 16/5 +30/7+3/2-13/5
Answer:
Simplifying the same denominators first:
16/5 - 13/5 = 3/5
So, we're brought down to:
3/5 + 30/7 + 3/2
35 goes into 5 and 7, so I'll simply 3/5 + 30/7 next -
7 x (3/5) to get 21/35
5 x (30/7) to get 150/35
Now add the two to get 171/35
(150+21=171)
Finally find a common denominator for 35 and 2.
(35x2=70)
2 x (171/35) --> 342/70
35 x (3/2) --> 105/70
Add up 342+105 to get 447 & put over 70.
Answer is 447/70
(It can't be simplified any further than this.)
Hope this helps!
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS NO BOTS PLEASE THANKS
Answer: The answer is BC=6 and EF=3
Step-by-step explanation: because BC =6 and EF=3 which will be 6/3 =2/1. so divide 6 by 3 to get 2 then anything divided by one gives itself 2=2. Then compare 2 and 2.
What expression shows 4 less than a number
PLEASE! HELPPPPPPP!!!!!!!!
Answer:
15
Step-by-step explanation:
24/8=3
16/8=2
24/16=3/2
3/2*10=15
I hate IXL
What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x 2y = 4 x 2y = 8 2x y = 4 2x y = 8.
The equation of the line that is parallel to the given line and passes through the point (2, 3) is,
[tex]x+2y=8[/tex]
What is the equation of line?The equation of the line is the way of representation of a line in the equation form.
The equitation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.
Given information-
The points through which the line passes is (2, 3).
The points of the line shown in the image attached below is (-4, 0) and (4, -4).
The slope of the line shown in the image which passes through the point (-4, 0) and (4, -4) is,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{-4-0}{4-(-4)}\\m=\dfrac{-4}{8}\\m=\dfrac{-1}{2}[/tex]
As the line which passes through the point (2, 3) is parallel to the line shown below. Hence, the slope of it must be equal to that line.
Therefore the equation of the line which passes through the point (2, 3) and has a slope of -1/2, is,
[tex](y-y_1)=m(x-x_1)\\(y-3)=-\dfrac{1}{2}(x-2)\\2(y-3)=-x+2\\2y-6=-x+2\\x+2y=8[/tex]
Thus the equation of the line that is parallel to the given line and passes through the point (2, 3) is,
[tex]x+2y=8[/tex]
Hence, the option 2 is the correct option.
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Answer:
y = –4
Step-by-step explanation:
Please help me find the answer
Answer:
[tex]x = 28 {}^{o} [/tex]
Step-by-step explanation:
hopefully this helps you
please mark me as brainlist
Answer: 28 degrees D
Step-by-step explanation: The whole angle is 90 and the other angle (not x) is 62 so 90 minus 62 is 28
What is the radius of this circle?
A) 3.14 inches
B) 5 inches
C) 10 inches
D) 20 inches
Answer:
C
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
im very c0nfused help
Answer:
x = 13°
Step-by-step explanation:
The left base angle of the triangle with x as the vertex is vertically opposite 85° and are congruent.
left base angle = 85°
the angle below the right base in the triangle is corresponding to 98° and are congruent.
right base angle = 180° - 98° = 82° ( adjacent angles on a straight line ) , then
x = 180° - (85 + 82)° = 180° - 167° = 13° ( sum of angles in a triangle )
What is the coefficient of 4
Answer:
4 is the coefficient of x
A ribbon 4 m long is cut into 8 equal pieces.
What is the length of each piece?
Give your answer as a fraction in its simplest form.
Answer:
1/2 m
Step-by-step explanation:
It is because 4 = 4/1, 8 = 8/1 and 4/1 divided by 8/1 is also equal to 4/1 times by 1/8 which equals 4/8.
4/8 is simplified to make 1/2m
hope this helps mark brainliest
Solve for y
1160
S
15y - 4
w
Answer:
17400y2S-4w
Step-by-step explanation:
Osama starts with a population of 1,000 amoebas that increases 30% in size every hour for a number of hours, h. The expression 1,000(1 0. 3)h finds the number of amoebas after h hours. Which statement about this expression is true?.
Answer:It is the product of the initial population and the growth factor after h hours.
Step-by-step explanation:
this for ttm/im
Which is the most accurate way to estimate 48% of 127?
Answer:
60.96
Step-by-step explanation:
127 times 0.48
Find the mZMNI.
M
15x – 12
L
6x
12x+2
N I
Step-by-step explanation:
sum of two interior angles is equal one exterior angle....this implies that,
6x + 15x-12 = 19x+2.....make X the subject
6x+15x-19x = 2+12
2x = 14..... divide both sides by 2
x = 7
this implies that, 19x + 2 where x is 7,
= 19(7) +2
=135°
therefore,<MNI = 135°
The angle MNI is 135 degree.
What is angle?An angle is the figure formed when two rays cross at a common endpoint, according to the definition of angles.
The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is remote Interior Angle.
Sum of two interior angles is equal one exterior angle.
Here:
(6 x) + (15 x-12) = (19 x+2)
6 x + 15 x - 19 x = 2 + 12
6 x - 4 x = 14
2 x = 14, x =7
Putting the value of x in (19 x + 2).
19 * 7 + 2 = 133 + 2 = 135.
Therefore, the value of 19 x + 2 is 135 degree.
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Consider the set of rational numbers to solve the problem.
What is the inverse of 43 under the operation of addition?
Answer:
-43
Step-by-step explanation:
The additive inverse of 43 is its opposite, -43.
The sum of a number and its additive inverse is the additive identity element:
43 + (-43) = 0
Is (x-3) a factor of (x3 - 3x2 + 2x + 2)?
SHOW FULL WORK
Answer:
No
Step-by-step explanation:
If (x - 3) is a factor then x = 3 is a root and the polynomial will equal zero for x = 3 , that is
3³ - 3(3)² + 2(3) + 2
= 27 - 3(9) + 6 + 2
= 27 - 27 + 8
= 8
since the polynomial ≠ 0 for x = 3 then (x - 3) is not a factor
PLS HELP ME PLS
In this activity, you will express mass in standard rotation and in scientific notation. Search the Internet to find the mass in grams for each atom
or molecule listed
Express the mass of the stars and molecules in both standard notation and scientific notation. If necessary, round the numbers so the first factor
goes only to the hundredths place
• one iron atom
• One water molecule
• one silver atom
• one gold atom
• one platinum atom
• One orarium atom
Answer:
iron- 9.28 * 10-23
silver- 1.79 * 10-22
gold- 3.27 * 10-22
platinum- 3.25 * 10-22
uranium- 3.95 * 10-22
water- 2.99 * 10^-23
I need help
Which of the following is an irrational number?
Daniel is playing on the swings at the playground. At the top of his swing, he will have _____.
neither potential nor kinetic energy
some potential energy and some kinetic energy
no potential energy and all kinetic energy
all potential energy and no kinetic energy
big points
Answer: all potential energy and no kinetic energy
Step-by-step explanation:
please help me find the total surface area
Answer:
Area of the figure = 64 cm²
Step-by-step explanation:
To find the total surface area (TSA) of the figure, we must add the areas of the 4 triangles along with the area of the square.
Given,
Altitude of triangle (h) = 6 cmBase of triangle (b) = 4 cmSide of the square (h) = 4 cmBy using these values,
Area of the triangle = ½ bhArea of the triangle = ½ × 6 × 4Area of the triangle = ½ × 24Area of the triangle = 12 cm²Now,
Area of the square = s²Area of the square = 4²Area of the square = 16 cm²So, from this,
Area of the figure = (4 × Area of the triangle) + Area of the square Area of the figure = (4 × 12) + 16Area of the figure = (48) + 16Area of the figure = 64 cm²•°• The TSA of the figure is 64 cm².
_________________________
Hope it helps!
[tex]\mathfrak{Lucazz}[/tex]
MAFS.5.NBT.1.4
5. Usain Bolt holds the record for the fastest time in
the 100 meter dash. He first broke the record in
2008 when ran the 100 meter dash in 9.683 seconds.
In 2009, he ran the 100 meters in 9.572 seconds.
Tell whether each sentence is True of False.
5a. Rounded to the nearest tenth, O True False
both times are the same.
5b. Rounded to the nearest whole O True False
number, both times are the same.
5c. Usain's time in 2009 was O True False
faster than his time in 2008.
Step-by-step explanation:
5a- rounding to nearest 10th 9.683 = 9.7
rounding to nearest 10th 9.572 = 9.6 both times are not same so false
5b rounding to near est whole no
9.683 and 9.572 become 10. both are same. true.
5c he is faster in 2009 true
Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?
Answer:
[tex]\frac{x^2}{12}-\frac{y^2}{4}=1[/tex]
Step-by-step explanation:
Since our foci are located on the x-axis, then our major axis is going to be the horizontal transverse axis of the hyperbola:
Formula for hyperbola with horizontal transverse axis centered at origin
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Directrices -> [tex]x=\pm\frac{a^2}{c}[/tex]Foci -> [tex](\pm c,0)[/tex] where [tex]a^2+b^2=c^2[/tex][tex]a>b[/tex]Since we are given our directrices of [tex]x=\pm3[/tex] and foci of [tex](\pm4,0)[/tex], then we can set up the directrices equation to solve for [tex]a^2[/tex]:
[tex]x=\pm\frac{a^2}{c}\\ \\\pm3=\pm\frac{a^2}{4}\\ \\12=a^2[/tex]
Now we can determine [tex]b^2[/tex] to complete our equation for the hyperbola:
[tex]a^2+b^2=c^2\\\\12+b^2=4^2\\\\12+b^2=16\\\\b^2=4[/tex]
Therefore, our equation for our hyperbola is [tex]\frac{x^2}{12}-\frac{y^2}{4}=1[/tex]