Answer:
2.14
Step-by-step explanation:
Answer:
2.14
Step-by-step explanation:
hope this helps
Plz mark brainliest :)
A constant volume of cookie dough is formed into a cylinder with a relatively small height and large radius. When the cookie dough is placed into the oven, the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t, the height of the dough is 8 mm, the radius of the dough is 18 mm, and the radius of the dough is increasing at a rate of 2 mm per minute.
Part A: At time t, at what rate is the area of the circular surface of the cookie dough increasing with respect to time? (5 points)
Part B: At time t, at what rate is the height of the dough decreasing with respect to time?
Answer:
a) dA/dt = 125,42 mm/min
b) dh/dt = - 1,78 mm/min
Step-by-step explanation:
The volume of the cylinder is:
V(c) = π*r²*h ( r and h radius of the base and heigh respectively )
Then the surface area is: Area of the base : π*r²
Plus lateral area : h*2*π*r
A(c) = π*r² + 2*π*r*h
With the help of differentials we obtain:
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt (1)
In this equation and at time t we know:
r = 18 mm dr/dt = 2 mm/min h = 8 mm dh/dt = ??
dA/dt = increasing rate of the surface area ( with respect to time)
To find dh/dt we know:
V(c) is constant, then
V(c) = π*r²*h then h = V(c) / π*r²
dh/dt = - [V(c)*2*π*r*dr/dt ] / π²*r⁴
By subtitution of V(c)
dh/dt = - [ π*r²*h *2*π*r*dr/dt ] / π²*r⁴
dh/dt = - [2*π²h*r³*dr/dt ] /π²*r⁴
dh/dt = - [2*h* dr/dt ] / r
dh/dt = - 2*8*2 / 18 mm/min
dh/dt = - 1,78 mm/min
By subtitution in equation (1)
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt
dA/dt = 2*π*18*2 + 2*π*8*2 + (- 2*π*18*1,78 )
dA/dt = 226,20 + 100,53 - 201,31
dA/dt = 125,42 mm/min
Following are solutions to the given points:
Formula:
Cylinder volume [tex]v = \pi r^2 h...............(i)[/tex]
[tex]\to \frac{dr}{dt} = 2 \frac{mm}{min}\\\\ \to \frac{dh}{dt} = -2 \frac{mm}{min}\\\\ \to h=8\\\\ \to r=18 \\\\[/tex]
Part A:
Calculating the circular area of the surface:
[tex]\to A=\pi r^2\\\\[/tex]
So, [tex]\frac{dA}{dt}=2 \pi r \frac{dr}{dt}.........(ii)[/tex]
Therefore
[tex]\to \frac{dA}{dt}= 2\pi \times 18 \times 2= 72 \pi \ \frac{mm^2}{min}\\\\[/tex]
Part B:
[tex]\to \frac{dh}{dt}= - 2 \frac{mm}{min}[/tex]
Learn more:
brainly.com/question/19667963
[tex]2 log_{2}(x) + \frac{1}{2} log_{2}(x - 1) - log_{2}( x + 3) [/tex]
solving these problem
I'm putting here a picture of the working out
5. Ellen wants to rent a bike. They charge a $12 service
fee plus $16 per hour and she can spend at most $140,
how many hours can she rent the bike?
Answer:
5
Step-by-step explanation:
cuz 12 +16 is 28, 140÷28 is 5
Answer:
16h + 12 = 140
Step-by-step explanation:
She can ride the bike for 8 hours.
PLS HELP. It’s question 18
Answer:
no
Step-by-step explanation:
Plzzzzz help right answer gets a brainly!
Answer:
3
Step-by-step explanation:
i think because that what's between
What is the equation of this line?
Please Help
y=1/2x -2
y=-2x -2
y=2x -2
y=-1/2x -2
Answer:
the first option
Step-by-step explanation:
the slope is the rise over run (up over across) and the line meets the y axis at -2 so that is your intercept
this is due in a few hours can yall help me
Answer:
18%, 34%, 9/25, 0.25
Step-by-step explanation:
36% = 18%
17/50 = 34%
0.18 = 9/25
1/4 = 0.25
I have 8 Twix bar that I want to share with 6 students how much of the Twix bar will each student get
Answer:
1.3
Step-by-step explanation:
8 divided by 6 = 1.3
BRAINLIEST PLEASE
Answer:
1.3
Step-by-step explanation:
Hope this helped have an amazing day!
30 POINTS PLEASE help
Answer:
m= -1/7
b=2
Step-by-step explanation:
which of these is not a linear graph.
Answer:
D
Step-by-step explanation:
It isn't linear
Answer:
D)
Step-by-step explanation:
Linear graphs are straight they can be positive or negative but they do not have bending points in them.
I added a picture to help you
what is -3 exponent 2 in expanded form?
Answer:
-3 times -3 that is -4 exponent two in expanded form
Step-by-step explanation:
-3²
= -3 • -3
eg. Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression. 5,325 in expanded notation form is 5,000 + 300 + 20 + 5 = 5,325.
How to cross multiply for sin
Answer:
What do you mean sin?
Step-by-step explanation:
An adult ticket for hypnotist's show cost $15. A children's ticket for the hypnotist's show cost $9. The number of adult tickets sold 5 more times the number of children's ticket sold. A total of $1512 is taken in for ticket sales. How many of each type of ticket is sold.
1. 21 adult tickets and 110 children's tickets
2. 110 adult tickets and 22 children's tickets
3. 10 adult tickets and 90 children's tickets
4. 10 adult tickets and 18 children's tickets
Answer:
The answer is B, or the second one.
90 Adult tickets and 18 Children's tickets
Step-by-step explanation:
(90 x 15) + (18 x 9)
1/3 + a = 5/4
A=? ..........................................................
You hear that tuition is going to increase by 3% next year. If tuition
this
year is $7,200 this year, what will the tuition be next year?
Answer: $7416
Step-by-step explanation:
You look up 3% of $7200 ($216) and add that to the original price to get $7416 :)
How is Triangle ABC similar to DBE?
Answer:
Triangle ABC is similar to triangle DBE: ∆ABC~∆DBE. ... Therefore, in conformity with first sign of the similarity of triangles, if two angles of one triangle are equal to two angles of another triangle, they are similar to each other. ∠BDE=∠BAC,∠BED=∠BCA ⇒ ∆ABC~∆DBE
The first line of the passage includes a
to introduce a
section and help readers locate it easily,
that
CELL PHONE POLICY
Devices Supplied by the Company
The use of company supplied devices must be limited to
work-related correspondence. They should not be used
for personal communication.
Personal Cell Phones and Devices
Employees are encouraged to limit their use of personal
cell phones and other devices during business hours.
The passage also includes
introduce more specific topics.
The passage is organized according to a
y sequence
Answer:
Step-by-step explanation:
Answer: 1. heading and subheading
2. subheading
3. point-by-point
Step-by-step explanation:
What is the length of segment DA?
Answer:
Step-by-step explanation:
The length of this line segment is the distance between its endpoints A and B. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
Answer: DA = 6
====================================================
Explanation:
The triangles are similar, allowing us to make the proportion below
DB/DA = DA/DC
Plug in the given values. Cross multiply and solve for x
DB/DA = DA/DC
9/DA = DA/4
9*4 = (DA)*(DA)
36 = (DA)^2
(DA)^2 = 36
DA = sqrt(36)
DA = 6
The length of DA is exactly the geometric mean of the lengths BD and DC
geometric mean of x and y = sqrt(x*y)
It’s not b!!!! Help me please
Answer:
D maybe? im not sure
Step-by-step explanation:
I am so stressed can someone please help me
It’s 53 points
Answer:
(3,1)
Step-by-step explanation:
Solve the following system of equations.
5x+4y = 10
5x + 8y = 30
Answer:
(-2, 5), x = -2, y = 5
Step-by-step explanation:
When x = -2 and y = 5 on both equations, the equations become true.
What is the value of the expression when a = 5, b = 4 , and c = 6?
4a/2b−c
2
5
9
10
Step-by-step explanation:
9 +6=15-6=9
so your answer should be 9
mark me brainliest lol
Answer:
now you can say as brainliest to other person :)
Help me plz. I’ll give good points.
Answer:
A is the answer because the -T is right at 0
How much is 3/5 of 31/8 ?
Answer:
2.325
Step-by-step explanation:
i used a calculator ,i think i did it right lol
Which of these isn't a proportional relationship? 15:30 & 1:2 3:9 & 9:27 05.10 & 10:20 2:4 & 4:2
Answer:
4:2
Step-by-step explanation:
Please help geometry
The price of milk increased from $2 to $2.50. What is the percent of change for the price of milk?
25.00%
Or
25c
Have a Merry Christmas!
Simplify 16 – 1.42 + (–1.5)
Answer:
13.8 is the answer ...............
There are 32 females cast in the school play. The ratio of male roles is 3:8. How many males are cast in the school play
what is 1/4(8+x+4) simplified using the distributive property
Answer:
x4+3
Step-by-step explanation:
i think this is the answer i aint sure tho
