The conic water vessel of height 40 cm and radius 8 cm filled at 20 cm^3/s gives;
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.How can the water level rate be found?The volume of the vessel, v = π•r^2•h/3
[tex] \frac{h}{r} = \frac{40}{8} = 5[/tex]
h = 5•r
Therefore;
v = π•r^2•(h)/3 = π•(h/5)^2•h/3
v = π•h^3/75
By chain rule of differentiation, we have;
[tex] \frac{dv}{dh} = \frac{dv}{dt} \times \frac{dt}{dh} [/tex]
Which gives;
[tex]π• \frac{ {h}^{2} }{25} = 20 × \frac{dt}{dh} [/tex]
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {h}^{2} }{25} } [/tex]
When the height is 12 cm from the vertex, we have;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {12}^{2} }{25} } = 1.1 [/tex]
The rate at which the water level is rising when the water level is 12 cm from the vertex is approximately 1.1 cm/s.When the vessel is one-quarter filled, we have;
v = π•h^3/75
π•(40)^3/(75×4) = π•h^3/75
10•(40)^2 = 16,000 = h^3
h = (16,000)^(1/3) = 25 (approx)
Which gives;
[tex] \frac{dh}{dt} = \frac{20}{\pi \frac{ {25}^{2} }{25} } = 0.21 [/tex]
When the vessel is one-quarter filled the rate at which the water level is rising is approximately 0.21 cm/s.
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Solve w2 + 2 w - 24 = 0.
Answer:
w= -6
w= 4
Step-by-step explanation:
w= -b sqrt(b^2-4ac)
2a
let
a=1
b=2
c= -24
substitute values~
[tex]==========================================[/tex]
In order to solve this equation for w, we need to factor it.
First, let's think of 2 numbers that multiply to -24 and add to 2.
These numbers are -4 and 6.
Check:
6×(-4)=-24 ✓
6+(-4)=6-4=2✓
Now, factor:
( ) ( )
That's how it should look like:
(w+ )( w- )
Now, instead of the blanks, plug in -4 & 6:
(w-4)(w+6)
Now, set each factor equal to 0:
w-4=0
w=4
w+6=0
w=-6
[tex]====================================[/tex]
Notes:-Hope everything is clear.Let me know if you have any questions!Enjoy your day!Always remember: Knowledge is power!Answered by:-Nickname:-
[tex]\rule{1}{1}~\rule{2}{2}\mathbb{DiAmOnD}[/tex]pls help me pls I have to turn in tonight and if u answer this can you draw and send it pls
Answer:
see attached
Step-by-step explanation:
(i) F' shown in red = Rotation 180° about point (2, 1)
(ii) F'' show in blue = Reflection of F' in x-axis
if there are 12 cookies and you ate 1/2 how many cookies will you have left
Answer:
6 cookies
Step-by-step explanation:
half of twelve is 6
12/2=6
Which best describes the range of the function f(x) = 2(3)x?
y > 0
y ≥ 0
y > 2
y ≥ 2
Answer:
y > 0
Step-by-step explanation:
if x = 0, y = 2
if x > 0, y > 0
if x < 0 , y > 0
The option that describes the range of the function f(x) = 2(3)x is A. y > 0.
How to illustrate the function?It should be noted that a function whose value us constant raised to the power of the argument especially the function where the constant is e.
The range of the value of y depends on x. Here, the option that describes the range of the function f(x) = 2(3)x is y > 0.
In conclusion, the correct option is A.
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10 points !!!!!!!!!!!!
Step-by-step explanation:
the numbers are a bit cut off at the top.
do I understand it correctly that the question is when the balloon loses 6/8 of a cubic foot of air ?
if so, I need to point out that the balloon loses 1/8 of a cubic foot per day.
so, how many days until it loses 6/8 if a cubic foot ?
well, 6 times that of 1/8 of a cubic foot = 6 days.
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
area = 4x² +210x + 2250
Step-by-step explanation:
Area of a rectangle = width × length
Given:
width = 2x + 30length = 2x + 75⇒ area = (2x + 30)(2x + 75)
= 4x² +150x + 60x + 2250
= 4x² +210x + 2250
Randall makes chilli for a cold winter night. To make 7 servings, he uses 12 1/4 cups of diced tomatoes. How many cups of diced tomatoes are needed to make one serving of chili? Answer in decimal form.
Answer:
1.25 cups of diced tomatoes
Step-by-step explanation:
1. 12 1/4 ÷ 7
2. = 49/4 x 1/7
3. =49/28
4. =7/4
5. =1 1/4 or 1.25
I hope this was helpful
Dalvin's family took a road trip to Mount Rushmore. Dalvin fell asleep 44% of the way through the trip. If Dalvin fell asleep after they had traveled 176 miles, what was the total length of the trip?
Ignore this I deleted my answer cause I missread the question...
please help. please help.
Answer:
A. $3960
B. r=40x^2+400x+3000
C. $200
Step-by-step explanation:
A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write . R=PC
Per price increase is $20. So four price increase is $20x4=80. Hence, price per dive is 100+80=$180.
Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4x2=8 customers are reduced. Hence, total customers is 30-8=22
So Total Revenue is: R= 180 x 22= 3960
B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.
Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.
Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.
R= (100+2x)(30-2x) = -40x^2+400x+3000
C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y).
That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5 x 20= 100. So the price that gives the greatest revenue is 100+100 = 200
roblem #7
A system of linear equations is shown.
2y=6x+ 4
y = 3x-4
Explain how many solutions this system of equations has.
Answer:
no solution.
Step-by-step explanation:
1) in order to explain, the given system should be resolved:
[tex]\left \{ {{2y=6x+4} \atop {y=3x-4}} \right. \ < = > \ \left \{ {{y=3x+2} \atop {y=3x-4}} \right.[/tex]
2) the both equations have the same slope (it is 3), it means the given lines are parallel, then no solution.
"the square of y decreased by
quotient of 36 and 6"?
Here's your answer, folks! ↓
[tex]y^2 - (36 * 6)[/tex]
Can somoene help me with this question please
Answer:
About 260 seconds
Step-by-step explanation:
Tha rate is:
A: 8L/1.66666m
b: 10L/1m (converted to litres)
Divide 2400 by those rates above which:
2400 / (8/1.66666) = 500
2400 / (10/1) = 240
500 - 240 = 260
Julio watched a movie that started at 11:30 am and ended at 2:12 pm how long was the movie
Is my answer correct?
Answer: yes there are just delete the last one and replace it with the sixth one start from the start also does this happen to be K12 7th grade?
Step-by-step explanation:
Y= x + 6
y= -x+2
solve each system of equations by substitution
Answer:
x= -2
y=4
Step-by-step explanation:
Since we have an equation set equal to y, we can plug it in for either value of y.
I will be using y= x+6 in this case.
Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2
Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2
Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4
Divide both sides by 2 to get x= -2
Not plug x= -2 in back for the top (or bottom) equation and get that y=4
Hope this helps and isn't too complicated!
What is 3 inches converted to feet?
Write your answer as a fraction in simplest form. 6
3 in=3 x 1 in
Answer:
1/4 feet
Explanation:
12 inches = 1 feet1 inches = (1/12) feet3 inches = (1/12)*3 feet3 inches = 1/4 feetSo
1in=1/12ftHence.
3in3(1/12)3/121/4ft0.25ftWhat is the quotient? X^2-11x+24/(x-8)(x+2)
Answer:
D
Step-by-step explanation:
[tex]\frac{x^2-11x+24}{(x-8)(x+2)}[/tex] ← factorise the numerator
= [tex]\frac{(x-8)(x-3)}{(x-8)(x+2)}[/tex] ← cancel the common factor (x - 8) on numerator/ denominator
= [tex]\frac{x-3}{x+2}[/tex]
The quotient of the given division problem is D. (x - 3) / (x + 2).
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given expression is,
(x² - 11x + 24) / (x - 8)(x + 2)
We have to first factor the numerator.
x² - 11x + 24 can be factored as (x - 8) (x - 3).
This is done using the factorization method.
Now the expression becomes,
(x² - 11x + 24) / (x - 8)(x + 2) = (x - 8) (x - 3) / (x - 8)(x + 2)
= (x - 3) / (x + 2)
Hence the quotient is option D.
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Rebecca is calculating her expected expenses for her week long trip to Thailand. Her plane ticket costs 22,885 baht, her lodging costs 15,307 baht, and she has set aside 29,071 baht for food and spending money. What is Rebecca’s total expense? a. 128,071 baht b. 67,263 baht c. 21,493 baht d. 9,121 baht.
Answer:
The answer is B because you add up the 3 expenses
Step-by-step explanation:
Add the three expenses
The total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
How to calculate total expense?Total expense shows the overall expense for the thing we're expending for. We add all the expenses to get the total expense.
For this case, we're given that:
Cost of plane tickets = 22,885 bahtCost of lodging = 15,307Cost for food and other expenses = 29,071So, total expected expense is sum of all these expenses.
Total expected expense = 22885 + 15307 + 29071 = 67263 baht
Thus, the total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
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Consider the figure below: (DE and BC are parallel)
I need more help it would be so nice + it is 100 points.
Answer:
8/3 < 8/2
D
Step-by-step explanation:
8/3 = 2.67
8/2 = 4
So, when fractions have equivalent (same) numerators, the one with the lesser denominator is the greater fraction.
There is more left if 8 is divided by 2 than when it is divided by 3
[Answer]8/3 < 8/2
[Answer] D
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Answer:
8/3 < 8/2
Step-by-step explanation:
D. When fractions have equivalent numerators, the one with the lesser denominator is the greater fraction.
8/2 = 4
8/3 = 2.667
Please help me with this problem
Evaluate (-½·3)³
Answer: -27/8
Step-by-step explanation:
[tex]\left(-\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}[/tex]
[tex]\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]=-\left(\frac{1}{2}\cdot \:3\right)^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]
[tex]\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]
[tex]=-\left(\frac{1}{2}\right)^3\cdot \:3^3[/tex]
[tex]=-\frac{1}{8}\cdot \:3^3[/tex]
[tex]=-\frac{1}{8}\cdot \:27[/tex]
[tex]=-\frac{27}{8}[/tex]
6. A line passes through the points (-2,5) and (6,9). Calculate the gradient of this line.
Answer:
d 2.5 line is 6.9 which is 9.4
Step-by-step explanation:
because
Which expression has a value of 13? (2 points)
a
(20 ÷ 4) − 4 + 3 x 2
b
(18 ÷ 2) + 6 ÷ 6 + 3
c
(16 ÷ 4) + 3 x 4 − 1
d
(10 ÷ 2) − 3 + 4 x 2
Answer:
it is option B that is correct
Step-by-step explanation:
use BODMAS
B- Brackets
O-order
D-division
M-multiplication
Addition
Subtraction
This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show your work.
Answer:
area of the figure: 29.92 m²
formula's:
area of rectangle: length * widtharea of sector: ∅/360 * πr²solving steps:
area of rectangle + area of sector
5.5 * 4 + 30/360 * π(5.5)²
22 + 7.919
29.92 m²
Answer:
Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.
Rectangle
Area of a rectangle = width × length
= 4 × 5.5
= 22 m²
Sector
[tex]\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}[/tex]
[tex]=\dfrac{30 \cdot\pi\cdot5.5^2}{360}[/tex]
[tex]=\dfrac{121}{48}\pi \textsf{ m}^2[/tex]
Total area
total area = area of rectangle + area of sector
[tex]=22 +\dfrac{121}{48}\pi[/tex]
= 29.91943148...
= 29.9 m² (nearest tenth)
Please help me with this math question attached below.
Answer: 12 outcomes
Step-by-step explanation:
When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.
7x^2+16-8
Solve using the Quadradic Formula, and round to the nearest hundredth as needed.
Someone please help-
Answer: 0.45 and -2.74
Step-by-step explanation:
You're going to want to use the Quadratic Formula, so (-b±√(b^2-4ac))/2a.
When you plug in you should get -16 ± √16^2-4(7)(-8)/2(7)
-16± √(256+224) all divided by 2 x 7 or 14
(-16 ± 22.3607)/14
0.45 and -2.74 are your answers
is this correct or no if not what the answer
Answer:
A.
While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.
FGH and PQR are vertical angles. If FGH is 29 what is the measure of PQR?
< PGR = 61°
Step-by-step explanation:[tex]< FG4\ and\ < PQR\ are\ vortical\ angles.[/tex]
[tex]< FG4=29[/tex]°
[tex]< PQR=90\ - < FG4[/tex]
[tex]=90\ -29[/tex]°
[tex]=61[/tex]°
I hope this helps you
:)
1. A house which cost £96000 appreciated in value each year by 1.6%
Calculate the value of the house after 4 years.
Give your answer to 3 significant figures
Answer:
£102,000
Step-by-step explanation:
A growth rate of 1.6% corresponds to an annual growth factor of ...
1 +1.6% = 1.016
The house value is multiplied by this factor each year for 4 years, so the final value is ...
£96000 × 1.016⁴ ≈ £102,293
To 3 significant figures, the house value after 4 years is £102,000.
Answer:
answer : 102293.04
3 significant figures : 102000
Step-by-step explanation:
the height of a cylinder is 5 centimeters. The circumference of the base of the cylinder is 16 centimeters. which measurement is closest to the volume of cylinder in cubic cintemeters
a: 251.3
b: 4,021.2 cm
c:251.3 cm
d:628.3 cm
Answer:
Should be 251.3 cm^3
Step-by-step explanation:
Use the formula for volume of cylinder