Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Differentiate the equation with respect to time t, such that
[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]
To differentiate the product,
Let r² = u, so that
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]
Then, using product rule
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]
Since [tex]u = r^{2}[/tex]
Then, [tex]\frac{du}{dr} = 2r[/tex]
Using the Chain's rule
[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]
∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]
Then,
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
Now,
From the question
[tex]\frac{dr}{dt} = 7 m/min[/tex]
[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]
At the instant when [tex]r = 99 m[/tex]
and [tex]V = 180 m^{3}[/tex]
We will determine the value of h, using
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]
[tex]180 \times 3 = 9801\pi h[/tex]
[tex]h =\frac{540}{9801\pi }[/tex]
[tex]h =\frac{20}{363\pi }[/tex]
Now, Putting the parameters into the equation
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]
[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]
[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]
[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]
[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]
[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]
[tex]\frac{dh}{dt} = 0.021 m/min[/tex]
Hence, the rate of change of the height is 0.021 meters per minute.
how do you find the interior angle in a heptagon
Answer:
A heptagon has 7 sides, so we take the hexagon's sum of the interior angles and add 180 to it getting us, 720+180= 900 degrees
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is: (n-2) x 180 degrees. N is the number of sides
solve x3 = 8. A. x = 2.8. B. x = 2. C. x = 4. D. x = 8/3
Answer:
Option B x=2
Step-by-step explanation:
Assuming that the problem is X^3=8 you can find the cubed root of 8 which is 2
Point T is at (-3, 8). What are the coordinates of T' after R(y-axis) o R(x-axis)?
Given:
Point is T(-3,8).
To find:
The coordinates of T' after [tex]R(y-axis)\circ R(x-axis)[/tex].
Solution:
We know that, [tex]R(y-axis)\circ R(x-axis)[/tex] means the figure reflected across the x-axis then reflected across y-axis.
If a figure reflected across x-axis, then
[tex](x,y)\to (x,-y)[/tex]
[tex]T(-3,8)\to T_1(-3,-8)[/tex]
If a figure reflected across y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]T_1(-3,-8)\to T'(-(-3),-8)[/tex]
[tex]T_1(-3,-8)\to T'(3,-8)[/tex]
Therefore, the required point is T'(3,-8).
i will give many points and brainlest if you find the area of the polygon
Answer:
28
Step-by-step explanation:
You can split the figure up
3*4/2 = 6
3*4/2 = 6
8*2 = 16
6+6+16 = 28
If I can read 54 pages in 3 days, how many can I read in 1 day?
Answer:
18
Step-by-step explanation:
Step 1)
54 ÷ 3 = 18
Answer:
54/3
Step-by-step explanation:
we can use crisscross multiplePlease help me! I'm struggling!
Answer:
so one thing you can do is to put the standard form into slope-intercept form
so 6x+y= -4 into y=-6x -4
now, you put a point on (0,-4)
(x,y)
now the slope is -6/1 so you rise (go down) -6 points and run (sideways) 1
wHaT is 3+3x+45??????????
Answer:
3x+48
add 3+45=48
Step-by-step explanation:
Hope this helps! Please consider marking brainliest! I hope you have an amazing day. Always remember, your smart and you got this! -Alycia :)
Answer:
3(x+16)
Step-by-step explanation:
45+3=48
3x/3=x
48/3=16
3(x+16)
The sum of two numbers is 2490 and if 6.5 percent of one no. is equal to 8.5 percent of the other, then numbers are ?? Make sure it’s correct answer pls! 20 points for brainliest (also can u tell me how to mark someone brainliest?)
Answer:
The two number are :
x = 1411
y = 1079
Step-by-step explanation:
Let the two numbers = x and y
The sum of two numbers is 2490
x + y = 2490..... Equation 1
If 6.5 percent of one no. is equal to 8.5 percent of the other,
Hence:
6.5% of x = 8.5% of y
0.065x = 0.085y
Make x the subject of the Formula
x = 0.085y/0.065
x = 1.308y
We substitute 1.308y for x Equation 1
x + y = 2490..... Equation 1
1.308y + y = 2490
2.308y = 2490
y = 2490/2.308
y = 1078.8561525
y = 1079
x + y = 2490..... Equation 1
x = 2490 - y
x = 2490 - 1079
x = 1411
Hi whats
u = x - k solve for x
Answer:
x=u+k
Step-by-step explanation:
Answer:
x = k+u
Step-by-step explanation:
u = x - k
+k +k
u + k = x
Hope this helps!
Please help as well:
Solve for X
Answer:
If equal to 90 x is 4
Step-by-step explanation:
Mrs. Brown uses 1/4 package of graph paper for each class. She needs 1 1/2 packages to serve all of her classes. How
many classes does Mrs. Brown teach?
Answer:
I think the answer is 6 sorry if i'm wrong
Step-by-step explanation:
All students in the 6th grade either purchased their
lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the 6th grade?
Answer:250
Step-by-step explanation:
Write the equation in slope-intercept form for a line which points go through (-2,3), parallel to x=o
Answer:
x = -2Step-by-step explanation:
Line x = 0 is parallel to y-axis
Line parallel to given line is also parallel to y-axis. It passes through point (-2, 3), so its equation is:
x = -2Solve the system of equations by graphing:
y= 2x +8
-x+y=0
Answer:
Slope = 4.000/2.000 = 2.000
Slope = 2.000/2.000 = 1.000
Step-by-step explanation:
the first answer is for the first problem and the second answer is for the second problem. Hoped it helped i tried my best.
What is 3 /49 as a decimal?
Answer: 3/49 as a decimal is 0.06122
5 divided by 9/10 :))
plz, answer the question in the photo.
Answer:
H
Step-by-step explanation:
Step 1 of 2: Subtract, sub-step b: Convert mixed number to improper fraction.
Convert mixed number to improper fraction
2 and 1 over 32
1
3
= ( 2 × 3 ) over 3
2 × 3
3
+ 1 over 3
1
3
= ( 6 + 1 ) over 3
6 + 1
3
= 7 over 3
7
3
Step 1 of 2: Subtract, sub-step c: Find common denominator.
Find common denominator
32 over 9
32
9
− 7 over 3
7
3
= ( 32 × 1 ) over ( 9 × 1 )
32 × 1
9 × 1
− ( 7 × 3 ) over ( 3 × 3 )
7 × 3
3 × 3
= 32 over 9
32
9
− 21 over 9
21
9
9 is the least common multiple of denominators 9 and 3. Use it to convert to equivalent fractions with this common denominator.
Step 1 of 2: Subtract, sub-step d: Subtract.
Subtract
32 over 9
32
9
− 21 over 9
21
9
= ( 32 − 21 ) over 9
32 − 21
9
= 11 over 9
11
9
Step 1 of 2: Subtract.
Step 2 of 2: Simplify.
Simplify
11 over 9
11
9
= 1 and 2 over 91
2
9
HELPPPPPPPPP MEEEEE STARVINGGGGG
Actually help me with the screenshot though LOL
Answer: i think A, but might not be sry
Step-by-step explanation:
help for brainliest plsssssssssssssssssssssssssssssssssss
Answer:
32 canned goods per tub. There was one can left over.
Step-by-step explanation:
Answer:
32 in each tub with 1 left over I'm pretty sure
Step-by-step explanation:
think about how many times 5 can 161, then see what the number left over is. In this case, 5 can go into 161, 32 times with 1 left over
A small business has 15 full-time employees. How many people does the small business employ if the full-time workers make up 30% of the employees the company has?
Answer:
50 employees
Step-by-step explanation:
The total number of employees the business has will have to be made up the full-time employees and part-time employees.
The number of full-time employees = 15
Let the total number of employees = x
[tex]15 = 30 percent of x[/tex]
[tex]15 = 30/100 \times x\\x=1500/30 = 50[/tex]
The company has a total of 50 employees
15 points!
Can someone help me find the range of this question please.
Answer:
80, 95, 110, 125, 140
Step-by-step explanation:
How many gallons of water will a rectangular tank hold if the base is a square that is 8 feet 10 inches on one side and the tank is 10 feet 3 inches high? Round to the nearest tenth.
Answer:
reeeeee
Step-by-step explanation:
eeeeeeeeeeee
HELP PLS I JUST HAVE 10 MIN ILL PICK BRIALIAST
Answer:
0.6
Step-by-step explanation:
Brainliest please
pls help me with this question.
Answer:
Option B
Step-by-step explanation:
Slope = Change in y / Change in x
Slope = (8 - 2) / {6 - (-4)}
Slope = 6 / (6 + 4)
Slope = 6 / 10
Slope = 3 / 5
So option B is your answer
An item is regularly priced at $75. It is now priced at a discount of 35% off the regular price. Find the price now.
Answer:
48.75
Step-by-step explanation:
Find the area of the parallelogram. pick one of these
30 sq cm
40 sq cm
12 sq cm
17 sq cm
Answer:
The area of the parallelogram is 40.
Step-by-step explanation:
You multiply the base by the height:
4*10= 40
The “war council” is a meeting that Dally has with the leaders of the Socs. What is the plan/agreement that results from Dally’s meeting with “the war council”?
Answer:
yes
Step-by-step explanation:
yes
The expression x + 0.25x can be used to determine a 25% increase in the number of blog views from last month to this month. What expression shows this another way?
Answer:
1.25x
Step-by-step explanation:
Given that :
25% Increase in number of blog views can be expressed as (x + 0.25x)
Another way to make this representation is :
Total number of blog views + 25% of total
Total should add up to 100%
Let number of views = x
Hence,
(100% + 25%) of x
125% of x
125%x
= 1.25x
math question trignometry
Answer:
the answer is none of these
Step-by-step explanation:
What is the answer?
Answer:
clockwise
Q= (5,-2)
R= (-1,-3)
S= (0,0)
T= (3,-2)
counterclockwise
Q= (-5,2)
R= (1,3)
S= (0,0)
T= (-3,-2)
Step-by-step explanation:
this might not be right im a little rusty on my transformations but here goes nothing.
i dont know if this is a clockwise or a counter clockwise rotation so ill do both options.
clockwise (x,y) - (y,-x)
q=(2,5) - (5,-2)
r=(3,-1) - (-1,-3)
s=(0,0) - (0,0)
t=(-2,3) - (3,2)
counterclockwise (x,y) - (-y,x)
q=(2,5) - (-5,2)
r=(3,-1) - (1,3)
s=(0,0) - (0,0)
t=(-2,3) - (-3,-2)