Answer:
[tex]7s^{2}[/tex] + 8k - 32
Water is filling a cylindrical water tank. As it is filled the radius of the tank expands at 0.2cm/s and the height decreases at the rate of 0.5cm/s. Find the rate at which the volume of the tank is changing at the instant the radius equals 1.8cm and height equals 65 cm. What is the volume of water at this point? Show all working. Volume, V, of the cylinder is given by V = ϖr2h.
Recall that V is a function of both r (radius of the cylinder) and h (the height of the cylinder). This is a partial differentiation problem. The volume is also changing with time.
Answer:
141.94 cm³/s
Step-by-step explanation:
Since the volume of the tank V = πr²h, and both the height and radius of the tank change with time, we find the rate of change of the volume with time, dV/dt from
dV/dt = dV//dr × dr/dt + dV/dh × dh/dt
where dV/dr = 2πrh, dr/dt = + 0.2 cm/s (since the radius of the tank expands), dV/dh = πr² and dh/dt = -0.5 cm/s (since the height of the tank decreases)
So,
dV/dt = dV/dr × dr/dt + dV/dh × dh/dt
dV/dt = 2πrh × + 0.2 cm/s + πr² × -0.5 cm/s
dV/dt = 0.4πrh cm/s - 0.5πr² cm/s
dV/dt = πr(0.4h - 0.5r) cm/s
We now find the rate at which the volume is changing when r = 1.8 cm and h = 65 cm.
So,
dV/dt = π(1.8 cm)(0.4 × 65 cm - 0.5 × 1.8 cm) cm/s
dV/dt = π(1.8 cm)(26 cm - 0.9 cm) cm/s
dV/dt = π(1.8 cm)(25.1 cm) cm/s
dV/dt = π(45.18 cm²) cm/s
dV/dt = 141.94 cm³/s
What is the difference between a trapezoid and a rhombus?
A) A trapezoid is a parallelogram and a rhombus is not.
B) A rhombus always has 4 equal sides and a trapezoid does not.
C) A rhombus always has 4 right angles and a trapezoid does not have to.
Eliminate
D) A rhombus never has 2 sets of parallel sides and a trapezoid always does.
twice the sum of a number and ten
Answer:
2(x+10)
Step-by-step explanation:
Well since sum is addition and the number and 10 are the sum, let’s make the “number“ (x) and add em up. 10+x.
Now we gotta double that sum which is basically
2(10+x)
WILL MARK BRAINLIEST IF GOTTEN RIGHT
Answer:
20 ft.
Step-by-step explanation:
Diameter is length across the circle/ across the middle
GO GO GO
<3
What is the positive square root of 16?
Answer:
4
Step-by-step explanation:
because The square root of 16 is 4, which is a rational number.
Answer:
4
Step-by-step explanation:
is 8/28 proportional to 2/7
Yes
Both of them reduced is 0.2857
What is the circumference of a circle with a radius of 3 3/4mm
Answer:
23.56mm
Step-by-step explanation:
Circumference = 2 * pi *r = 2*pi* (3.75mm)
Answer: 23.56mm
A watering can contained 5 ½ quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
7 cups
18 cups
40 cups
84 cups
Answer: 18 cups
Step-by-step explanation:
Answer:
the answer is 18 cups :))
(3x^2+7)+(2x^2-5x+10)
Answer:
5x² - 5x + 17
Step-by-step explanation:
(3x² + 7) + (2x² - 5x + 10)
Combine the like terms.
3x² + 2x² = 5x²
-5x does not have a like term, so there is no change.
7 + 10 = 17
Combine them, and the final equation is
5x² - 5x + 17.
Answer: 5x² - 5x + 17
Step-by-step explanation:
(3x^2+7)+(2x^2-5x+10)
3x^2 + 2x^2
-5x
7 + 10
5x^2 - 5x + 17
- If I've understood correctly
1
Factorise 2x2 + 11x + 12. You can use the grid to help.
2x
3x
8x
1
12
2x2 + 11x + 12 =
Answer:
(2x+3)(x+4)
Step-by-step explanation:
hope the picture helps.
Shawna is a member of the swim team. She can swim 3 laps in 3 minutes
and 21 seconds. If Shawna swims at the same pace, how long would it take
her to swim 8 laps?
Plzz show work
Answer:
8 mins 56 secs
Step-by-step explanation:
3 minutes and 21 seconds divided by 3 laps is 1.07 so it takes her 1 minute and 0.7 sec for each lap then u just multuply 1.07 by 8 and u get 8.56 meaning 8 mins and 56 secs. hope i helped :)
what is the inequality for more than 100,000
Answer:
>100,000
Step-by-step explanation:
Can someone plz help me with this Math problem and plz explain how you got your answers
A nickel has a mass of 5 grams. What is the mass of the nickel in milligrams?
Answer:
5,000 milligrams
Step-by-step explanation:
Know That One 1 gram equals = 1,000 milligrams
Hope this Helps!
please check answer!
Please help I will give you BRAINLIEST
Answer:
5x² - 10x + 4
Step-by-step explanation:
11x² - 10x + 4 = 6x²
Subtract 6x² from both sides of the equation.
5x² - 10x + 4
PLEASE HELP ASAPPP!!!
Step-by-step explanation:
hope it helps you......
What expression is equivalent to (5x6)x(3x2)
(5x6)x(3x2) = (30x6)= 180
simplify the algebraic expression!!
Answer:
[tex]\frac{y^{3}}{2z^{7}}[/tex]
Step-by-step explanation:
1. Move z^ − 3 to the denominator using the negative exponent rule b ^− n = 1/ b ^n
2. Multiply z ^4 by z ^3 by adding the exponents.
3. Cancel the common factor of 4 and 8
4. Cancel the common factor of x^2
Answer:
[tex]\frac{y^{3} }{2z^{7} }[/tex]
Step-by-step explanation:
Five years ago today, Artie was four times as old as his sister Carrie. In five years time, Artie will be twice as old as Carrie. Find their current ages using a system of linear equations.
Answer: 25 , 10 years
Step-by-step explanation:
Suppose the present age of Artie and Carrie is x and y
According to the question, 5 years ago
[tex]\Rightarrow x-5=4(y-5)\\\Rightarrow x-4y=-15\quad \ldots(i)\\[/tex]
In five year time
[tex]\Rightarrow x+5=2(y+5)\\\Rightarrow x-2y=5\quad \ldots(ii)[/tex]
Solving (i) and (ii) we get
[tex]x=25,y=10[/tex]
The current age of Artie and Carrie is 25 and 10 years
A spinner has 6 numbers on it, from 1-6, all with equally spaced area. Find the probability of spinning a
Prime number, P(Prime)
Select the correct response.
1
2
5
6
2
3
1
3.
Answer:
first option 1/2
Step-by-step explanation:
2,3,5 are the prime numbers from that set
each individual number has a 1 in 6 chance of landing on it and we have 3 so...
3 of 6 possibilities would be prime numbers. Simplify to...
1 in 2
a baseball team played 32 games and lost 8 . Katy was the catcher in 5/8 of the winning games and 1/4 of the losing games. what fraction of the games did the team win? and how many games did Katy play catcher
Answer:
17
Step-by-step explanation:
what you have to is simple, first do 32-8 which get you 24, thats how many they won. Then do 8x1/4 to get 2, she played 2 games as catcher and lost, then do the same thing with the winning games. 24x5/8 should get you 15. she played 15 games as catcher and won. then do 15+2 to get 17.
hope that helps!
Answer:
1/4 - won
7/8 - katy played catcher
hope this helps you :)
A diver found a school of fish 85 feet below the surface of the ocean. He found coral 95 feet deeper than the fish. How many feet deep from the surface was the coral?
Answer:
180 feet
Step-by-step explanation:
85+95=180 because depth + depth.
The total deep 180 feet from the surface was the coral.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that diver found the school of fish 85 feet below the surface of the ocean. Which he found coral 95 feet deeper than the fish.
The total deep from the surface was the coral.
Therefore, it could be;
depth + depth.
85 + 95 = 180
Hence, the total deep 180 feet from the surface was the coral.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Carol has 88cm of string and cuts it in the ratio 5 : 6. How much longer is the
longest piece compared to the shortest piece
Given:
Carol has 88cm of string and cuts it in the ratio 5 : 6.
To find:
How much longer is the longest piece compared to the shortest piece.
Solution:
Let the lengths of two pieces of string are 5x and 6x. Then,
[tex]5x+6x=88[/tex]
[tex]11x=88[/tex]
[tex]x=\dfrac{88}{11}[/tex]
[tex]x=8[/tex]
Now, the lengths of pieces are:
[tex]5x=5(8)[/tex]
[tex]5x=40[/tex]
And,
[tex]6x=6(8)[/tex]
[tex]6x=48[/tex]
The difference between the longer piece and shorter piece is:
[tex]48-40=8[/tex]
Therefore, the longer piece is 8 m longer than the shorter piece.
Order the numbers from least to greatest.
LEAST
1
8
= 0.13
= 0.12222...
12.7%
PLEASE HELP I WILL GIVE BRAINIEST. What is the range?
Answer:
range= 8
Step-by-step explanation:
to find range> subtract highest number to the lowest
so 10- 2= 8
one package of strawberries costs $4.50 how many will 3 packages cost?
if you can please show your work:)
I think you have to multiply them to get the answer $13.5
How much commission would a salesperson ear for selling a car that costs $29,389? He receives 16% commission on each sale.
Answer:
Commission on car = $4,702.24
Step-by-step explanation:
Given:
Sales price of car = $29,389
Commission on sale of car = 16% = 0.16
Find:
Commission on car
Computation:
Commission on car = Sales price of car x Commission on sale of car
Commission on car = 29,389 x 16%
Commission on car = 29,389 X 0.16
Commission on car = $4,702.24
Solve the following system of equations using Substitution, showing all work.
2x+y=9
3x−2y=17
Answer:
(x,y)=(5,-1)
Step-by-step explanation:
1. 2x+y=9 ---> y=9-2x
2. Substitute y=9-2x into 3x-2y=17 ---> 3x-2(9-2x)=17 ---> 3x-18+4x=17 --> 7x=35 ---> x=5.
3. Substitute x=5 into 2x+y=9 ---> 2*5+y=9 ---> y=9-10 ---> y= -1
WILL MAKR BRAINLIEST IF GOTTEN RIGHT
Answer:
20 feet
Step-by-step explanation:
20 feet
because the diagram said so....