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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]
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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!
a square number never end with 7 true or false
Step-by-step explanation:
true
hope it helps!
.......
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
How to cross multiply for sin
Answer:
What do you mean sin?
Step-by-step explanation:
what does x equal?
4x+7=31
Answer:
x = 6
Step-by-step explanation:
First, subtract 7 from both sides to get x alone. That will give you 4x = 24 .
Then divide both sides by 4 to remove the coefficient of x. That means x = 6.
4x+7=31
-7 -7
4x=24
÷4 ÷4
x = 6
Miguel bought a shirt for $13.95, a pair of pants for $16.87, and a hat for $7.79. What was the total amount of money Miguel spent?
Answer:
they did not pay the same rate.
2 pairs for $50
50÷2=25
Miguel spent $25 on each pair of jeans
4 pairs for $90
90÷4=22.5
Han spent $22.50 on each pair of jeans
Therefore these two did not pay the same rate.
Step-by-step explanation:
Wanna chat add me as a friend OR COME TO Snap (ADAMBELAL839)
Answer:
38.61
Step-by-step explanation:
Each value added to gether to achieve your final value
Bouncing Baby Company sells their cribs for the following amounts to stores:
Number of Cribs Price
10 $1320
50 $6600
Which of the following statements about the price of the cribs are true if the price remains proportional to the number of cribs? Select TWO that apply.
A
6 cribs cost $660
B
22 cribs cost $2640
C
40 cribs cost $5280
D
55 cribs cost $7920
E
80 cribs cost $10,560
F
250 cribs cost $11
Answer:
C and E
Step-by-step explanation:
Ik u prolly dont care about the explanation but ill just say it
the ratio is 1:132 or 1 crib is $132. So 40 x 132 = 5280 and 80 x 132 = 10560
For the test im doing the answer is C and D yw ;D
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 :)
Please help geometry
Plzzzzz help right answer gets a brainly!
Answer:
3
Step-by-step explanation:
i think because that what's between
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
I needddddddddd helppppppppp
Answer:
[tex]\frac{2}{-3}[/tex]
Step-by-step explanation:
To find the slope you only need two points from the table, and the equation [tex]\frac{y1-y2}{x1-x2}[/tex]
(1,-2) (4,-4)
[tex]\frac{-2+4}{1-4}[/tex] = [tex]\frac{2}{-3}[/tex]
please help UwU
if correct you get Brainiest
Answer: C
Step-by-step explanation:
A tire manufacturer believes that the life of its tires follow a normal distribution with a mean of 46,000 miles and a standard deviation of 4,000 miles. What mileage can he guarantee each tire to last so that 99% of the tires last longer than the guaranteed lifetime?
Answer:
Guarantee of Tyre = 36,680 miles
Step-by-step explanation:
Given:
Mean = 46,000 miles
Standard deviation = 4,000 miles
Computation:
Assume;
x = guaranteed lifetime
P(X > x) = 99%
So,
P(X > x) = 0.99
So,
P(Z > z) = 0.99
So,
1 - P(Z > z ) = P(Z < z)
P(Z < z) = 0.01
So, in z table value of z = -2.33
x = μ + [z x σ]
x = 46,000 + [-2.33 x 4000]
x = 36,680
Guarantee of Tyre = 36,680 miles
Solve for x. Round to the nearest tenth.
Answer:
x = 9.6
Step-by-step explanation:
Please help me with ptomblem
Answer:
When [tex] p^2 - 4p [/tex] is subtracted from [tex] p^2 + p - 6 [/tex], the result is [tex] 5p - 6 [/tex]. To get [tex] p - 9 [/tex], subtract [tex] 4p + 3 [/tex] from the result.
Step-by-step explanation:
✔️Subtracting [tex] p^2 - 4p [/tex] from [tex] p^2 + p - 6 [/tex]:
[tex] (p^2 + p - 6) - (p^2 - 4p) [/tex]
[tex] p^2 + p - 6 - p^2 + 4p [/tex] (Distributive property)
Collect like terms
[tex] p^2 - p^2 + p + 4p - 6 [/tex]
[tex] 5p - 6 [/tex]
✔️Subtracting [tex] p - 9 [/tex] from [tex] 5p - 6 [/tex]:
[tex] (5p - 6) - (p - 9) [/tex]
[tex] 5p - 6 - p + 9 [/tex] (distributive property)
Add like terms
[tex] 4p + 3 [/tex]
Find the arc length of AB to the nearest tenth.
90°
B
A
70 m
The arc length is
meters.
90 is a fourth of 360, so the a fourth of the total circumference is between those two radii. This means that, if you find the circumference and divide it by 4, the resulting number is that length.
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)
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.
1/3 + a = 5/4
A=? ..........................................................
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
[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
which shape has sides that are straight and connected?
Answer:
The first shape
Step-by-step explanation:
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:
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
I am so stressed can someone please help me
It’s 53 points
Answer:
(3,1)
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
convert 15 °C to Fahrenheit, use the formula F = 9/5 C + 32
Answer:
59
9/5(15)+32 =59
Step-by-step explanation:
It’s not b!!!! Help me please
Answer:
D maybe? im not sure
Step-by-step explanation:
