The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm
Answer:
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by the following equation:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In which r is the radius.
Implicit derivatives:
This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 4 mm/s.
This means that [tex]\frac{dr}{dt} = 4[/tex]
How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?
This is [tex]\frac{dV}{dt}[/tex] when [tex]r = \frac{d}{2} = \frac{60}{2} = 30[/tex]. So
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi*(30)^2*4[/tex]
[tex]\frac{dV}{dt} = 1508[/tex]
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
need help geometry be serious
Division of Labor:
There were 4 hobos that arrived in town looking for work. They met with a business owner who said he could pay them for 200 hours of work. However, there was a catch. They could divide up the work anyway they wanted, but each hobo had to work the same number of days as he/she worked hours in 1 day. For example, If a hobo worked 8 hours a day, he/she had to work for 8 days. The other catch is that the laziest hobo of all did the negotiations with the business owner and then went back to present the plan to his/her pals.
The question is how many hours a day did each hobo work?
(please be asap lol i need help on this )
Answer:
16
Step-by-step explanation:
answer please show work
Answer:
That's too small for me
Step-by-step explanation:
Solve the equation.
с/8 = 9
c =
What number do you multiply to find this partial product 8×56
Answer: 8*56 is 448
you could also multiply 2⁶ x 7 to get 448
The number that you can multiply to find this partial product 8×56 is 8 and (50+6).
What is the partial product?The partial product method involves multiplying each digit of one integer by each digit of another, while each digit retains its position. For example, 23 x 42 becomes (20 x 40) + (20 x 2) + (3 x 40) + (3 x 2).
The number that you can multiply to find this partial product is,
8×(50+6)
= (8×50) + (8×6)
= 400 + 48
= 448
Hence, the number that you can multiply to find this partial product 8×56 is 8 and (50+6).
Learn more about the Partial Product:
https://brainly.com/question/24716925
#SPJ2
I’m confused how do you know where to put the plus and minus signs when rearranging the equation?
karen works for 85 hours throughout a two-week period. She earns $2,891.25 throughout this period. How much does karen earn for 8 hours
pls help me giving 33 points! enjoy <3
f(x) = x^2. What is g(x)?
Answer:
D. g(x) = (1/4 x)^2
Step-by-step explanation:
We have to choose a solution in which the point (4, 1) works.
A) g(x) = 1/4(x^2) = 1/4(4^2) = 1/4(16) = 4 ≠ 1
B) g(x) = (1/2 x)^2 = (1/2 * 4)^2 = 2^2 = 4 ≠ 1
C) g(x) = 4(x^2) = 4(4^2) = 4(16) = 64 ≠ 1
D) g(x) = (1/4 x)^2 = (1/4 * 4)^2 = 1^2 = 1
A fruit shop bought 500 kg of apples for R900 and sold them R2.80 per kg.What is the profit per kg?
Answer:
total cost= RS.4050
Total SP= 75*45+25*47.5
TOtal SP= 4562.5
PRofit= 512.5
Profit %= 512.5/4050*100
Profit%=12.7%
Step-by-step explanation:
if the sales are $680 and the commission rate is 9% what is the commission
Answer:
61.2
Step-by-step explanation:
What is the product of 3x(x2 + 4)?
O x2 + 3x + 4
O 3.3 + 4
O 3.3 + 12x
O 3.x2 + 12x
Answer:
The fourth option
you made a 12 minute call using a calling card. The call costs $0.66. there is a $1.21 left on your card. if the rate stays the same, how many more minutes can you talk for using the card
I need to find the width of the rectangle
Scott is getting balloons for his uncle's birthday party. He wants each balloon string to be 6 feet long. At the party store, string is sold by the yard. If Scott wants to get 59 balloons, how many yards of string will he need?
1 foot =
1
3
yard
If R, S, and T are collinear and RS + ST = RT, which of the following is true?
T is between R and S.
RS = RT
S is between R and T.
S is the midpoint of ./rt
Answer:
[tex]S \: is \: between \: R \: and \: T.[/tex]
Answer:
S is between R and T.
Step-by-step explanation:
Describe how you would find the value of an "a" coefficient.
Answer:
A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Variables with no number have a coefficient of 1.
Step-by-step explanation:
The circumference of the earth is approx. 40,000 km.
a) What is the diameter of the earth?
b) Calculate the volume of the soil
number of
Joshua has ad Jarr of apple Jam and
36 gars of mango Jam. He want to place
the pamiam into the greatest possible
boxes so that cach box
the same number of Jars of each
kind of sam. How many boxes does
he need?
lwoeofpxs kfi wn ee's osoakem
Step-by-step explanation:
owlekdx9zinqrnxiz n.v w w d f ds no wkw
While walking in the country, you count 35 heads and 96 feet in a field of pigs and chickens. How many of each animal are there?
Answer
Answer:
13 pigs and 22 chickens
Step-by-step explanation:
What is a correct way to rewrite abac?
a(b + c)
a2bc
2a(b + c)
abc
Answer: A(b+c)
Step-by-step explanation: Since you're multiplying A and A you would add the B+C
Answer:
a(b + c)
Step-by-step explanation:
Please help find the measurement of exterior angle MBI
Answer:
The measure of an exterior angle is found by the following formula: Aˆ0B=^AB-^CD2. An interior angle has its vertex at the intersection of two lines that intersect inside a circle. The sides of the angle lie on the intersecting lines. You can find a measure of an exterior angle of a regular polygon with
N sides. It is equal to 360 o N .
Step-by-step explanation:
Angles of a general polygon (exterior and interior) with more than 3 sides are not defined by the lengths of its sides.
However, we can calculate the sum of all interior or exterior angles of any convex polygon. It equals to 360 o .
It can be proven geometrically since each exterior angle describes a rotation by some angle and a sum of all exterior angles describes a rotation by full angle of
360 o . So, if all exterior angles are equal, like in a regular polygon, each one equals to 360 o N .
It can also be defined with some algebraic calculations based on the fact that a sum of all interior angles is ( N − 2 ) ⋅ 180 o .
Dividing the above by N
we will obtain a value of an interior angle: ( N − 2 ) ⋅ 180o N .
Therefore, exterior angle of a regular polygon is 180 o − ( N − 2 ) ⋅ 180 o N = 360 o N
How is the derivative of a function related to the slop of the function?
Hi there!
The derivative of the function is the slope of the function at a specific x-value, or its instantaneous rate of change.
For example, take the equation y = x².
Using the power rule, we get:
y' = 2x
If we plug in any x-value into this equation, we can find the slope of the function at any point.
Ex:
x = 0; 2(0) = slope of 0
x = 2; 2(2) = slope of 4
Ava is going to the county fair. The cost of admission is $5.50 and it is $1.50 for each ride. If Ava has $19.00, Write and solve an equation to determine how many rides Ava can ride.
Answer:
5.50 + 1.50x = 19
x = 9
Ava can ride 9 rides.
Step-by-step explanation:
5.50 + 1.50x = 19
-5.50 -5.50
1.50x = 13.50 (divide both sides by 1.50)
x = 9
A salesman makes both a base salary and also a commission, which is a percentage of
what he sells. Each month, if his sales total s dollars, he makes a total of 5000+ 0.2s. What
does the 5000 represent?
Answer:
a salesman make 5000+0.2
total 5000+5000.2=10000.2
Raj recorded the scores of six of his classmates in the table.
Math Scores
98
76
100
88
82
70
What is the range of their test scores?
28
30
85
86
Answer:
30
Step-by-step explanation:
range is highest number subtracted by lowest
Answer: The answer is B aka 30
Step-by-step explanation:
PLEASEEE HURRY
What is the rate of change?
Equation that describes function?
Linear or non linear?
Answer:
can you tell me the grade so I can help you please
Please help me ASAP! on these two questions please and thank you have a great and blessed day!
Answer:
1: 1.268, 1.265, 1.256
2: $16.42
Step-by-step explanation:
I did the math.
help pls i'll give brainliest
Answer:
no they aren't inverses bc they arent the same numbers
Step-by-step explanation:
Answer:
They aren't inverse as they intersect with each other more than once.
Please help i need answers am bad at math
Answer:
1) 2 5/9
2) 4 5/6
3) 4 3/8
4) 5 3/5
5) 7 1/3
6) 6 1/9
7) 7 1/8
8) 2 2/9
9) 5 3/4
Step-by-step explanation:
Hope this helps