Answer:
4:2
Step-by-step explanation:
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
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 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
According to the graph below, what percent of the Simpsons’ annual expenses is Federal taxes? A circle graph titled Simpson's Annual Expenses. Federal taxes, 24 percent; State/local taxes, 10 percent; Housing and household, 23 percent; Food, 6 percent; Medical care, 8 percent; Transportation, 11 percent; Recreation, 3 percent; Clothing, 5 percent; Other, 10 percent. a. 10% b. 14% c. 24% d. 34%
According to the graph, the percentage of the Simpsons’ annual expenses that is Federal taxes is 24%
What is a circle graph?A circle graph also known as pie chart has a shape of a circle and each section are represented in percentages or degrees
From the question, we have:
Federal taxes = 24%State/local taxes = 10%Housing and household = 23%;Food = 6%Medical care = 8%Transportation = 11%Recreation = 3%Clothing = 5%Other = 10%The above means that the percentage of the Simpsons’ annual expenses that is Federal taxes is 24%
Read more about circle graphs at:
https://brainly.com/question/24461724
Answer:
10%
Step-by-step explanation:
Please help geometry
a bakery sold 208 chocolate cupcakes in a day,which was 25%of the total number of cupcakes sold that day. How many cupcakes did the bakery sell that day
Answer:
832
Step-by-step explanation:
multiply the 25% by 4
Answer:
Coryxkenshin
Step-by-step explanation:
I am so stressed can someone please help me
It’s 53 points
Answer:
(3,1)
Step-by-step explanation:
- 4(6 + 5g) equivalent expressions
Answer:
the awnser is 4g because if you multiply the -4 by 6 and 5 g you get the equation: -24+-20g.. subtract -24 from -20 you will get 4g
You have $500, sale price is $435. How much change will you get
Answer:
go to sleep its 11:23 also u will get
$65 dollars pls mark me brainleist
Step-by-step explanation:
(1 point) A pond contains 100 fish, of which 40 are carp. If 20 fish are caught from the lake, what are the mean and variance of the number of carp among those 20
Answer:
E(X) = 6
Var(X) = 3.394
Step-by-step explanation:
Let X represent the number of carp caught out of the 20 fishes caught. Now, if we are to assume that each
of the (100, 20) ways to catch the 20 fishes will be equally likely.
Thus, we can say that X fulfills a hypergeometric
distribution with parameters as follows;
n = 20, N = 100, k = 30
Formula for expected mean value in hypergeometric distribution is;
E(X) = nk/N
E(X) = (20 × 30)/100
E(X) = 6
Formula for variance is;
Var(X) = (nk/N) × [((n - 1)(k - 1)/(N-1))) + (1 - nk/N)]
Var(X) = ((20 × 30)/100) × [((20 - 1)(30 - 1)/(100 - 1)) + (1 - (20 × 30/100)]
Var(X) = 6 × 0.5657
Var(X) = 3.394
Simplify 16 – 1.42 + (–1.5)
Answer:
13.8 is the answer ...............
What is 1.452 rounded to the nearest hundredth
Answer:
1.450
Step-by-step explanation:
what grade ar4e you in I'm guessing 4th or 5th
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)
please answer this :(
Answer:
X+2 metres. Just use a^+2ab+b^2
PLZZ SOMEONE GIVE ME THE EQUATION!! You have $20 to buy snacks for yourself and 4 friends. If you buy a bag of chips for each person, and still have $13.75 left, how much did you spend on each bag of chips?
Answer:
1.56
Step-by-step explanation:
Answer:
1.25
Step-by-step explanation:
20-13.75 = 6.25
6.25 / 5 = 1.25
What’s the common factor for 72 and 84
Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
Now each number has at least two 2s
Each number has at least one 3
The highest common factor is 2 * 2 * 3 = 12
1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
Timed!! Answer hurry!
[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
Ms. cooper goes to Panera Bread for dinner and orders the Green Goddess salad. Her total was $8.79. Ms. cooper gave the cashier $10, how much change did she receive?
HELP!! It’s question 8
Answer:
the answer is 1.25 or 5/4
Answer:
Actual kitchen area equals 108 feet
Step-by-step explanation:
room turns into 12 ft. by 9 ft.
to find area: 12 x 9
Actual kitchen area equals 108 feet
Abbey receives a $40 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $2.89 a. Let m represents the number of songs downloaded. Write an inequality that represents this given situation? b. What is the maximum number of songs Abbey can download?
Answer:
A. $2.89(m)=$40
B. 13 songs
Step-by-step explanation:
$2.89(m)=$40
m=$40/$2.89
m=13.84
She can download a maximum of 13 songs
Check:
$2.89 (13 songs)=$37.57
$40-$37.57=$2.43 left on her gift card
m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43
Answer:
13 songs
Step-by-step explanation:
40 divided by 2.89 is 13.84. DO NOT ROUND TO 14
So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs
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.
During the summer, 1.3% of the water in the kiddie pool evaporates every day. If the kiddie pool holds 8,000 gallons of water and is not
refilled for 10 days, how many gallons of water will be in the pool? Round your answer to the nearest gallon enter the amount
Answer:
7019 gallonsStep-by-step explanation:
Initial volume of water = 8000 galDaily reduction = 1.3% Time = 10 daysRequired equation:
8000*(1- 0.013)^10 =8000*0.987^10 =7018.7781 ≈ 7019 rounded to the nearest gallonIn an election for school president, the loser received 70% of the winner's votes. If 969 votes were cast, how many did each receive?
Answer:
The ans would be 291 (however we can round this off to 290 as no can partially vote as 0.1)
Step-by-step explanation:
We can easily find the loser's vote by-
70% of 969= 678.9
now, all we need to do is find the winners vote
we know that the total no. of votes= 969 & we know the no. of votes loser got
so, subtracting the losers vote from 969 would give us the remaining no. of votes (the winner's votes)....so,
969-678.9=290.1
we can round this off to 290
hey , can you help me with this thanks !!
Answer:
16
Step-by-step explanation:
the sides may not seem to help but it dose go to the other side and try to meser it it would be 4. add 8+4+4 or 8+8=16
Answer:
18.6cm (rounded to 3 s.f.)
Step-by-step explanation:
You can actually figure out the two bases of the triangles based on the Pythagoras theorem where the slant length of a 90° triangle is [tex]\sqrt{a^{2} + b^{2} }[/tex] where a is one of the bases and b is the other length that is 90° perpendicular to a.
So this means:
[tex]\sqrt{6^{2} + base^{2} }[/tex] = 8cm
6² + base² = 64cm
36 + base² = 64
base² = 64-36
= 28
base = [tex]\sqrt{28}[/tex]
≈ 5.2915 (5 s.f.)
So the two bases are roughly 5.2915, and the middle base is part of a rectangle, so it has the same length as the rectangle's length, which is 8cm.
Thus, x = 5.2915 + 5.2915 + 8
= 18.6cm (rounded to 3 s.f.)
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
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
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.
HELP NOW
Write an equation of the parabola that passes through the point (62,−490) and has x-intercepts −8 and 72. Then find the average rate of change from x=−8 to x=2.
Answer:
y = 0.7(x^2 - 64x - 576)
Average rate of change = -49.
Step-by-step explanation:
As the x intercepts are -8 and 72 we can write the equation
y = a(x + 8)(x - 72) where a is some constant to be found.
As it passes through point (62, -490) we have, substituting:
-490 = a(62+8)(62-72)
-490 = - 700a
a = 0.7
So the equation of the parabola
y = 0.7(x + 8)(x - 72) or
y = 0.7(x^2 - 64x - 576).
Average rate of change between x = -8 and x = 2
= [0.7(2+ 8)(2 - 72) - 0.7(-8+8)(-8-72)] / (2 - -8)
= -490 - 0 /10
= -49
