Answer:
h ≅ 16.29 cm
[tex]\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}[/tex]
Step-by-step explanation:
From the conical funnel;
Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)
Then;
[tex]tan \theta= \dfrac{r}{h}[/tex]
[tex]tan \theta= \dfrac{8}{16}[/tex]
[tex]tan \theta= \dfrac{1}{2}[/tex]
∴
[tex]\dfrac{r}{h} = \dfrac{1}{2}[/tex]
[tex]r = \dfrac{h}{2}[/tex]
The volume (V) of the cone is expressed as:
[tex]V = \dfrac{1}{3}\pi r ^2 h[/tex]
[tex]V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h[/tex]
[tex]V = \dfrac{\pi h^3}{3\times 4}[/tex]
[tex]\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}[/tex]
[tex]\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}[/tex]
Given that:
[tex]\dfrac{dv}{dt} = 12 \pi[/tex]
Then:
[tex]-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}[/tex]
[tex]- \int 48 \ dt = \int h^2 \ dh[/tex]
[tex]\dfrac{h^3}{3}= -48 t + c[/tex]
[tex]At \ t = 0 \ ; h = 0[/tex]
∴
[tex]\dfrac{0^3}{3} = -48(0) + c[/tex]
c = 0
So;
[tex]\dfrac{h^3}{3}= -48 t + 0[/tex]
[tex]\dfrac{h^3}{3}= -48 t[/tex]
t = 30
[tex]\implies h = (-48(30))^{1/3}[/tex]
h = 16.2865
h ≅ 16.29 cm
Thus;
from [tex]-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}[/tex]
[tex]\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}[/tex]
[tex]\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }[/tex]
[tex]\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }[/tex]
[tex]\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}[/tex]
complete the similarity statement relating the three triangles above. (pls help me out ill even mark u as brainlest :))
ASAP determine whether the polygons are similar
Answer:
Not similar
Step-by-step explanation:
For two triangles to be similar , their sides should be in the same ratio. Here the sides are ,
First ∆ = 5 , 5 & 3 Second ∆ = 6 , 6 & 4Ratio of first sides :-
= 6/5 = 1.2
Ratio of second sides :-
= 6/5 = 1.2
Ratio of third sides :-
= 4/3 = 1.33
Since the ratio of all three sides are not same , Hence the two triangles are not similar.
Hence the two triangles are not similar .integers
(4×5)-10-2(1-2)+5
Answer:
12
Step-by-step explanation
PEMDAS is key to solving. First you multiply 4*5 because its the first parenthesis we see, to get 20. Next we see that 1-2 is in a different parenthesis, so we get -2. So our current equation is 20-10-2-1+5. You just add/subtract in that order. 20-10=10 10-2=8 8-1=7 7+5=12 So your final answer is 12.
Under her cell phone plan, Lily pays a flat cost of $55.50 per month and $4 per
gigabyte. She wants to keep her bill at $63.10 per month. Write and solve an equation
which can be used to determine x, the number of gigabytes of data Lily can use while
staying within her budget.
equation:
answer x=
Answer:
Equation : y = 4x + 55.50
x = 1.9 gigabytes
Step-by-step explanation:
Given that:
Flat fee per month = $55.50
Cost per gigabyte = $4
Let,
x be the number of gigabytes.
y be the total cost
y = 4x + 55.50
Lily wants to keep her bill $63.10
63.10 = 4x + 55.50
63.10 - 55.50 = 4x
4x = 7.60
Dividing both sides by 4
[tex]\frac{4x}{4} = \frac{7.60}{4}\\x=1.9[/tex]
Hence,
Equation : y = 4x + 55.50
x = 1.9 gigabytes
Answer:
Equation: 4x+55.5=63.1
Answer: x=1.9
find slope of the graph 9x-3y=15
[tex]y = mx + b[/tex]
where m = slope and b = y-intercept.
What we have to do is to make the y-term as the subject of equation.
[tex]9x - 3y = 15 \\ 9x - 15 = 3y \\ \frac{9x - 15}{3} = y[/tex]
Simplify[tex] \frac{9x}{3} - \frac{15}{3} = y \\ 3x - 5 = y \\ y = 3x - 5[/tex]
From y = mx+b, the slope is 3.
Answer[tex] \large \boxed {slope = 3}[/tex]
6) A jet travels 480 miles in 2 hours. At this rate, how far could the jet fly in
8 hours? What is the rate of speed of the jet?
please help me!
Answer:
1,920 is how far the jet travels in 8 hours, the rate of the jet is 240 meaning it would travel 240 miles in 1 hour,
An airline conducts a survey to determine customer
satisfaction.
Which of these methods will produce the most representative sample of the
population of airline customers?
Answer:
B
Step-by-step explanation:
After the passengers have reached their destination they will provide their honest feedback on the survey because they have just experienced the airline.
Answer:
the answer is (C)!!!
Step-by-step explanation:
1. factor: 8x + 16
2. 5 is 40 % of what number
3. Write an equivalent expression for 3(2a - 5b + 1)
is this 8 I will mark you as Braiylist
Answer:
Yes it is.
Step-by-step explanation:
2 2/3 as a fraction.
Answer: 8/3
Step-by-step explanation:
Explanation:
2
2
3
Split them,
2
+
2
3
Convert the first term into a fraction of denominator
3
,
6
3
+
2
3
Combine,
8
3
Answer:
8/3
Step-by-step explanation:
1. Sewing patterns recommend buying extra fabric in case of mistakes.
Jessica bought 5 yards of fabric, plus 25% extra fabric. Derek bought 7
yards of fabric, plus 30% extra. Who bought more fabric? How much
more?
Answer:
derek bought 8.5 more yards of fabric
Step-by-step explanation:
Answer:
?
Step-by-step explanation:
I need help plzzzzzzzz
Answer:
B and 7
Step-by-step explanation:
because 9 minus 2 is 7
How many lines of symmetry does a smiley face have
Answer:
1
Step-by-step explanation:
Which describes the intersection of planes A and B?
O line CD
O line ED
O point C
O point D
Step-by-step explanation:
° The intersection of two planes is a line. looking in your diagram, line ED is where planes A and B intersect; this means line ED is Our answerI hope it's helpSolve for a and b. 40 30 5
James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3500 for the reception. If the reception hall charges a $50 cleanup fee plus $34 per person find the greatest number of people that they may invite and still have within their budget.
Answer: See Below
Step-by-step explanation:
Create the equation:
$34 times the number of people plus the $50 cleaning fee has to be less than or equal to $3500
Or
34p + 50 <= 3500
34p <= 3450
p <= 101.470588....
We can have a part of a person attending the reception so we have to drop the remainder/decimal. Therefore the most amount of people that can attend the party and stay within budget is 101.
Cane buys candy in bulk and sells it at a 25% markup. It represents the original cost of the candy which expression represents the marke price? A. 25c.
B. 0.75
C. 1.250
D. 1.250 -1.25
Answer:
1.25c
Step-by-step explanation:
Given that :
Original cost of candy = c
Markup percentage = 25%
Markup price will be = original price(1 + markup percentage)
Marked up price = c(1 + 0.25)
Marked up price = c + 0.25c
Marked up price = 1.25c
me
Use inductive reasoning to predict the next line in the
conjecture is correct.
ts
1 = 1x1
1 + 5 = 2 x3
1 + 5 + 9 = 3 x 5
The next equation is
(Type an equation. Do not perform the calculation. U
intents
Find three consecutive integers such that the sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.
Answer:
12,13 and 14
Step-by-step explanation:
Let the three consecutive integers be n, n+1 and n+2
ATQ,
The sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.
[2(n+1)+4(n+2)] = 7n-2
or
2n+2+4n+8=7n-2
Taking like terms together,
6n-7n = -2-8-2
n = 12
So,
First integer = 12
Second integer = 12+1 = 13
Third integer = 12+2 = 14
Hence, three consecutive integers are 12,13 and 14.
I need help!! It is due today!! It’s Geometry !!!
Answer:hi the answer is x=6
hope this helped
Step-by-step explanation:
When Sandy and Allen's mother decorates the house for a holiday by herself, it takes her 5 hours. When both Sandy and Allen help, the three can finish the job in 2.5 hours. When only Allen helps his mother decorate, it takes the two 3.5 hours. How long would it take Sandy to decorate the house by herself?
Answer:
Step-by-step explanation:
Mother=5hrs
Sandy and Allen and mother=2.5
Allen with mother=3.5
It would take sandy 5hrs coz she decorates the house herself so if u think logically it took her mother 5 hrs so it would take her.Coz its only her doing it no one else is helping!
Choose the graph that represents a linear function.
Answer:
the graph that represents a linear are right and a
The price of gas started at 2.30 per gallon and increased at a rate of 5% per year what is the function ? How much will gas be in 4 years?
It takes 50 pounds of seed to completely plant a 6-acre field. How many acres can be planted per pound of seed?
Would you be breaking the speed limit in a 40 mi/h zone if you were traveling at 60km/h?
Since 40 mi/h is greater than 60 km/h. Therefore, 60 km/h is not breaking the speed limit given.
We need to check if would you be breaking the speed limit in a 40 mi/h zone if you were travelling at 60 km/h.
What is the speed?The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
To check whether the speeds are the same, make their units the same.
As we know, 1 mile = 1.60934 km
So, 40 miles = 64.3736
≈64
Then, the speed =64 mile/h
Since 40 mi/h is greater than 60 km/h. Therefore, 60 km/h is not breaking the speed limit given.
To learn more about the speed visit:
https://brainly.com/question/7359669.
#SPJ2
The expanded form of 2^3
Answer:
2*2*2
Step-by-step explanation:
i think it prob wrong or its 8
Make 1/5 a fraction with a denominator of 45
Please show work
12 points
Step-by-step explanation:
1/5
45÷5=9
so if 9 ×5 is 45 we need to times the whole fraction by 9.
1/5 ×1/9=1/45
hope this helps
Which function is not a linear function?
Answer: upper left corner
This is an absolute value function. It is a piecewise function composed of two different linear equations (they are glued together at the vertex), but it is not overall a single straight line compared to the other graphs.
The bakers at healthy bakery can make 340 bagels in 5 hours
Answer:
nice how many cals is one
Step-by-step explanation:
Answer:
cool
Step-by-step explanation:
they can make 68 bagels per hour if that was what you wanted to know
Y is between X and Z. XY = 7x + 1, YZ = 2x + 7 and XZ = 98. Find
the value of 'x'.
Step-by-step explanation:
the value of x is 4.
Answer:
4
Step-by-step explanation:
i am, a master of the diareah
