Answer:
The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.
Step-by-step explanation:
The statement is incomplete: The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min. ¿At what rate is the volume changing at the instant when r = 1 cm and h = 7 cm?
The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is expressed by the following formula:
[tex]V = \frac{\pi}{4}\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
The rate of change of the volume ([tex]\frac{dV}{dt}[/tex]), measured in cubic centimeters is obtained by deriving (1) in time:
[tex]\frac{dV}{dt} = \frac{\pi}{2} \cdot r\cdot h\cdot \frac{dr}{dt} + \frac{\pi}{4}\cdot r^{2}\cdot \frac{dh}{dt}[/tex] (2)
Where:
[tex]\frac{dr}{dt}[/tex] - Rate of change of the radius, measured in centimeters per minute.
[tex]\frac{dh}{dt}[/tex] - Rate of change of the height, measured in centimeters per minute.
If we know that [tex]r = 1\,cm[/tex], [tex]h = 7\,cm[/tex], [tex]\frac{dr}{dt} = 2\,\frac{cm}{min}[/tex] and [tex]\frac{dh}{dt} = -7\,\frac{cm}{min}[/tex], then the rate of change of the volume is:
[tex]\frac{dV}{dt} = \frac{\pi}{2}\cdot (1\,cm)\cdot (7\,cm)\cdot \left(2\,\frac{cm}{min} \right) + \frac{\pi}{4}\cdot (1\,cm)^{2}\cdot \left(-7\,\frac{cm}{min} \right)[/tex]
[tex]\frac{dV}{dt} \approx 16.493\,\frac{cm^{3}}{min}[/tex]
The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.
HELP ASAPPPPPP pls solve step by step!!!
Answer:
X=18
Step-by-step explanation:
6x=108
swap sides
6x/6
108/6
divide each side by 6
x=18
Y-intercept for y=2(x-3)^2+4
Answer:
The y-intercept for this equation is 22.
Step-by-step explanation:
You can solve this quite easily by assigning a zero value to x and solving for y. That is where the curve will intersect the x-axis:
y = 2(x - 3)² + 4
y = 2(x² - 6x + 9) + 4
y = 2x² - 12x + 18 + 4
y = 2x² - 12x + 22
EDIT
Note that the expression above is in standard form, though it can also be factored if needed:
y = 2(x² - 6x + 11)
Now we can solve for an x value of zero:
y = 2(0)² - 12(0) + 22
y = 22
So the y-intercept is 22.
Examine the diagram.
The mZ1 is
the 63° angle.
What is the measure of angle 1?
v degrees
1
63°
Answer:
1. the supplement of
2. 117
Step-by-step explanation:
got it right
Answer:
The m∠1 is
the supplement ofthe 63° angle.
What is the measure of angle 1?
117degrees
The perimeter of a rectangular atrium is 300 yards. The length of the garden is ninety-six yards more than the width. Find
the length and the width.
Answer:
27 yards 123 lenght..think answer is this
Answer: L is 123 and W is 27
Step-by-step explanation:
Just did it
The total cost of a $83.15 meal after a 20% tip
Answer: $99.78
Step-by-step explanation:
If am being honest I just copied the other person :)
7 1/2 divided by 5/6
Answer:
(7 1/2 / 5) / 6 = 0.25
Step-by-step explanation:
{x/x es un número primo par}
(14-27 divided by 3) x 3
Answer:
-13
Step-by-step explanation:
{(14-27)/3}×3
-13/3×3=-13
5 beetles out of 45 insects.
1:9 is the answer
Answer:
I suppose that this question is about ratios.
When we have A elements of one type, for every B elements of another type.
The ratio between these elements is A:B
In this particular case, we have:
5 beetles out of 45 insects (the 5 beetles do not belong to the group of 45 insects, if that where the case, we would not get the value 1:9 seen in the question)
Then there are 5 beetles and 45 insects.
The ratio is 5:45
Now, whit those we can divide both numbers by the same number and the ratio will be the same, then if we divide both by 5, we get:
(5/5):(45/5)
1:9
cake batter poured into a pan creates a circular batter pattern whose radius increases at a constant rate of 1 in/sec. at what rate is the total batter area increasing at the end of 4 second
Answer:
8 π .
Step-by-step explanation:
radius increases at a constant rate of 1 in/sec.
dr / dt = 1
where r is radius .
radius after 4 sec
r = 1 x 4 = 4 in
area A = π r²
differentiating both sides
dA / dt = 2 π r dr / dt
Putting dr / dt = 1 , r = 4 in
dA / dt = 2 π x 4 x 1
= 8 π sq in per sec.
Area increases at the rate of 8 π per sec.
If the edge length of a cube is 11 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
Answer:
11 because i fed you mom and eat her boot
Find the discount on a pair of jeans that originally cost $35 with 20% off coupon
Answer:
I think it's $28
a letter or symbol that is used to represent a number is called
Answer:
variable. a variable is like the x in 3x and it represents a numbe
Step-by-step explanation:
Need ASAP. Only answer if ur confident in ur answer
Answer:
360 m²Step-by-step explanation:
surface area = 2(12)9 + 12²
= 216 + 144
= 360 m²
Given that a = 24 cm and b = 7 cm, work out x
Please help me with problems one through four and show work. (Preferably on paper)
Step-by-step explanation:
I hope you can understand my steps and hope you all the best in matematic. There are various type of calculation, i try my best to do in easy way
The table shows locations on a map. Place Location park (–2, 2) farmers market (–2, –3) post office (2, 2) bus stop (6, –3) Which places on the map are 4 units apart? the park and the farmer’s market the farmers market and the bus stop the post office and the park the post office and the bus stop
Answer:
B
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Aulani was working and conpleted 40% of her 50 question assignment. How many questions did Aulani complete?
Answer:
20 questions
Step-by-step explanation:
First find 10% dividing by 10
50 / 10 = 5
Now multiply by 4 to get 40%
5 x 4 = 20
So Aulani completed 20 questions.
hope this helps :)
Answer:
She completed 20 questions.
Step-by-step explanation:
Dan invests £18790 into his bank account. He receives 4.9% per year simple interest. How much will Dan have after 3 years?
Answer:
£21,552.13
Step-by-step explanation:
A = P(1 + rt)
P = £18790
r = 0.049 (rate in percent form)
t = 3 years
A = £18790(1 + (0.049)(3))
A = £18790(1 + 0.147)
A = £18790(1.147)
A = £21,552.13
Lucy says that the product of 80 ×50 should have two zeros. brock says the product should have three Zeros.
Calculate the area of trapezium CDEF:)
In the diagram shown
. CDEF is a trapezium
.ABCF is a rectangle
. BD = 9cm
.AB = 6cm
.EF = 3cm
Perimeter of ABCF = 20cm
Answer:
6+6=12
20-12 = 8
8/2 = 4
BC = 4 cm
9 - 4 = 5
CD = 5
5 + 3 = 8
8/2 = 4
4 X 6 = 24
A florist just received a shipment of 1308 roses. How many bouquets of a dozen roses can the florist make using the shipment of roses?
Answer: 109
Step-by-step explanation:
1308 divided by 12 = 109
Answer:
109
Step-by-step explanation:
1,308 divided by 12 equals 109
What is the slope of line j?
Answer:
45 degrees glad to Help would like brainliest
Step-by-step explanation:
Yooo help. I attached a pic of the question
Answer:
will it will be D because That the y - intercept
Write an expression for the sequence of operations described below.
raise 2 to the 5th power, then find the product of the result and w
Do not simplify any part of the expression.
Answer:
2x2x2x2x2, 32
Step-by-step explanation:
Basically just multiplying 2 by itself 5 times.
2x2=4
2x2x2=8
2x2x2x2=16
2x2x2x2x2=32
Higher Order Thinking. Explain how to add 3+3+4. Use pictures,numbers, or words.
Answer:
Step-by-step explanation:
3 + 3 + 4
!!! + *** + &&&&
!!!***&&&&
10 symbols in all
Hope this Helps!!!
What is the place value of 7 in 74,310,892?
Answer:
10 million place
Please help me I don’t know y but it’s hard
Answer:
6
Step-by-step explanation:
hope this helps
1 sorry ceds to the person who commented under me
PLEASE HELP!! WILL MARK BRAINLY
Answer:
arc length = 84.82 cm
Step-by-step explanation:
arc length = 36 * 3π/4
arc length = 3π * 9
arc length = 84.82 cm
Hope this helps!
What is four hundred and nineteen ten thousandths in a decimal
Answer:
419/1000 = 0.0419
Hope this helps!