Answer:
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
Step-by-step explanation:
We derive an expression for the rate of change for the height of the cone by differentiating the volume formula given on statement:
[tex]\dot V = \frac{\pi}{3}\cdot (2\cdot r\cdot h \cdot \dot r + r^{2}\cdot \dot h)[/tex] (1)
Where:
[tex]\dot V[/tex] - Rate of change for the volume of the cone, measured in cubic centimeters per minute.
[tex]r[/tex] - Radius of the cone, measured in centimeters.
[tex]h[/tex] - Height of the cone, measured in centimeters.
[tex]\dot r[/tex] - Rate of change for the radius of the cone, measured in centimeters per minute.
[tex]\dot h[/tex] - Rate of change for the height of the cone, measured in centimeters per minute.
If we know that [tex]\dot V = -148\,\frac{cm^{2}}{min}[/tex], [tex]r = 222\,cm[/tex], [tex]V = 21\,cm^{3}[/tex], [tex]\dot r = -5\,\frac{cm}{min}[/tex], then the rate of change for the height is:
[tex]h = \frac{3\cdot V}{\pi\cdot r^{2}}[/tex] (2)
Where [tex]V[/tex] is the volume of the cone, measured in cubic centimeters.
[tex]h = \frac{3\cdot (21\,cm^{3})}{\pi\cdot (222\,cm)^{2}}[/tex]
[tex]h \approx 4.069\times 10^{-4}\,cm[/tex]
From (1):
[tex]\frac{3\cdot \dot V}{\pi} = 2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h[/tex]
[tex]r^{2}\cdot \dot h = \frac{3\cdot \dot V}{\pi}-2\cdot r\cdot h\cdot \dot r[/tex]
[tex]\dot h = \frac{3\cdot \dot V}{\pi\cdot r^{2}}-\frac{2\cdot h\cdot \dot r}{r}[/tex]
[tex]\dot h = \frac{3\cdot \left(-148\,\frac{cm^{3}}{min} \right)}{\pi\cdot (222\,cm)^{2}} -\frac{2\cdot (4.069\times 10^{-4}\,cm)\cdot \left(-5\,\frac{cm}{min} \right)}{222\,cm}[/tex]
[tex]\dot h = -2.849\times 10^{-3}\,\frac{cm}{min}[/tex]
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
Find a unit rate: Joel ran 1500 meters in 6 minutes, 15 seconds.
Answer:
240 metres per minute
Step-by-step explanation:
1500 / 6.25 = 240
Jacob and Kerrie are trying to figure out how long they can live off their $84,670 savings if they spend $370 each month. They have each created an equation. Jacob's Equation Kerrie's Equation y = 84,670 + (370x) y = 84,670 − (370x) Which person has the correct equation to model this linear relationship?
A.Kerrie's equation is incorrect, because their spending will increase the amount of their savings. B.Kerrie's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings. C.Jacob's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings. D.Jacob's equation is incorrect, because their spending should be a fixed amount and should not be multiplied.
Answer:
B.)Kerrie's equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings
Step-by-step explanation:
Given : Jacob and kerrie are trying to figure out how long they can live off their 84,670 savings if they spend 370 each month.
To Find: Which person has the correct equation to model this linear relationship?
Jacob's equation : y = 84,670+(370x).
Kerrie's equation : y=84,670-(370x).
Since they have 84670 in savings
They spend each month = 370
They spend in x months = 370x
So, spending this amount from saving they left with amount = 84,670-(370x)
Thus Kerrie's equation is correct .
Hence Option B is correct
B.)Kerrie's equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings
hi remember me this is your answer :0
Answer:
the answer is B
Step-by-step explanation:
how many fluid ounces are in 3 quarts?
Answer: 96 fluid ounces
Step-by-step explanation:
1 quart = 32 fluid ounces
32 x 3 = 96
1 x 3 = 3
There are 96 fluid ounces in 3 quarts.
Hope this helps!
(y – 5) = 2/3 (x + 2)
Answer:
Use the slope-intercept form
m=[tex]\frac{2}{3\\}[/tex]
Step-by-step explanation:
I need help pls go to my page and answer the finance question it a lot of points.
DON'T ANSWER SOMETHING IGNORANT
Which graph represents a linear function?
A coordinate plane is shown with a line passing through the y-axis at 7.5 and the x-axis at 12
A coordinate plane is shown with a line that starts to the left of the y-axis, passing through -1 comma 10, then curving right to pass through the y-axis 7, then curving down to pass through the x-axis at 2
A coordinate plane is shown with a parabola opening downward in an upside-down U shape. The base of the parabola sits at the origin and continues downward on both sides of the y-axis
A coordinate plane is shown. A wavy line begins along the x-axis and moves in intervals downward and back up, dipping down to y equals negative 1 and up to y equals 1.
Answer:
First Graph Description
Step-by-step explanation:
A linear function shows as a straight line.
The first graph description describes a straight line.
The second, third, and fourth graph description says that either the line is curved, or that it is a parabola. A parabola is not linear.
A coordinate plane is shown with a line that starts to the left of the y-axis, passing through -1 comma 10, then curving right to pass through the y-axis 7, then curving down to pass through the x-axis at 2
A coordinate plane is shown with a parabola opening downward in an upside-down U shape. The base of the parabola sits at the origin and continues downward on both sides of the y-axis
A coordinate plane is shown. A wavy line begins along the x-axis and moves in intervals downward and back up, dipping down to y equals negative 1 and up to y equals 1.
Hope this helps.
3(2x) + 3(-1) = -21
6x - 3 = -21
What property is being used ?
A surveyor is studying a map of the community and is using vectors to determine the distance between two schools. On the map, the surveyor determined that school A is at (7, 12), and school B is at (–21, –13). The scale of the map is 1 unit = 100 meters.
Which vector represents the path from school A to school B, and what is the actual distance between them?
a) components: LeftAngleBracket 28, 25 RightAngleBracket, actual distance: about 37.54 meters
b) components: LeftAngleBracket 28, 25 RightAngleBracket, actual distance: about 3,754 meters
c) components:LeftAngleBracket negative 28, negative 25 RightAngleBracket, actual distance: about 37.54 meters
d) components:LeftAngleBracket negative 28, negative 25 RightAngleBracket, actual distance: about 3,754 meters
Answer:
C: <-28,-25>, etc.
Step-by-step explanation:
The vector from A to B is (-28, -25) and the distance between A to B is 3754 meters.
What is Coordinate Geometry?One of the most intriguing ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related. They can answer geometrical problems because it gives them geometrical aspects of algebra. In this area of geometry, a pair of ordered numbers is used to describe the location of points on a plane.
As per the given data:
Coordinates of school A = (7, 12)
Coordinates of school B = (-21, -13)
Scale of the map is 1 unit = 100 m
For vector representing the path A to B:
Final - Initial coordinates
= (-21 - 7, -13 - 12)
= (-28, -25)
Distance between A and B:
Distance formula = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
= [tex]\sqrt{(-21 - 7)^2 + (-13 - 12)^2}[/tex]
= 37.54 units {1 unit = 100 m}
= 3754 meters
Hence, the vector from A to B is (-28, -25) and the distance between A to B is 3754 meters.
To learn more about Coordinate Geometry, click:
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can someone find the equation plz and solve it.
i will give brainliest i need u guys to save my math grade lol :(
Answer:
$2 per Chicken and $9 per Duck
Step-by-step explanation:
the equations for the problem are as follows (x = the value of chickens and y = the value of ducks):
5x + 3y = 55
4x + 3y = 53
if you subtract the equations you would get x = 2, which means the chickens are worth $2 each
If we re-input the x that we now know as 2 and solve one of the equations for y, we will get y = 9
Answer:
If you need the cost of each duck and chicken it would be around 6 dollars per duck or chicken.
I'm not completely sure tho sorry.
Whose puppy weighed the most when the person got it? How much did it weigh? Part c
Answer:
Olivia's puppy, it weighed 5 pounds.
Step-by-step explanation:
In ΔNOP, the measure of ∠P=90°, NP = 60, ON = 61, and PO = 11. What ratio represents the cosine of ∠N?
Answer:
60/61
Step-by-step explanation:
Write the ratio as a fraction in simplest form 24 nickels to 48 nickels
Answer:
2/3
Step-by-step explanation:
just divide the numbers by 6 the first time and get 4/6 and then divide one more time and get 2/3
May someone please help me?
Answer:
x=8°
y=29°
Step-by-step explanation:
vertically opposite angles are equal
so 5x+9°=y+20°
therefore 5x-y=11°
Alternate angles are equal
so 4x+17°=y+20°
therefore 4x-y=3°
equation 1....... 5x-y=11°
equation 2......4x-y=3°
using elimination method x=8°
y=29°
Liz travels at a constant velocity of 65 miles per hour toward Tucson. Tucson is 275 miles away. How long will it take her to get there?
Answer:
4.23076923077
Step-by-step explanation:
if you need a remainer please comment hope this helps also if you do put this in if you need a shorder anwser put 4.2307
On mountainous terrain, a semi-truck travels 2 2__3miles on 1__2gallon of fuel . How many miles can the truck travel per gallon of fuel? Use drawings or equations to show your work .
What is the constant of proportionality for the relationship represented by this graph?
Answer: (5,11)
Step-by-step explanation:
Answer:
k = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The equation of proportionality is
y = kx ← k is the constant of proportionality
To find k use any coordinate point lying on the graph
Using (12, 6 ), then
6 = 12k ( divide both sides by 12 )
k = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
select the correct answer
John played 8 games of basketball this season. In his first 2 games, he averaged 5 more points scored than he did in the next 6 games. If he scored 90 points during the 8 game stretch, then how many points did he score in the first two games of the season, added together?
HELP FASTTTT I need the work for this problem
Answer:
30Step-by-step explanation:
Let the average score in the last 6 games be x, then average score in first 2 games is x + 5
Considering the total score of 90 solve for x the equation:
2(x + 5) + 6x = 902x + 10 + 6x = 908x = 80x = 10In the first 2 games John's score was:
2(10 + 5) = 30Identify each value of x that makes 11 + 2x < 13
Answer:
x < 1
Step-by-step explanation:
This is the answer because:
1) 11 + 2 = 13 and 13 is not less than 13, it is equal to 13. Therefore, x has to equal anything less than 1 because then only inequality statement will be true.
Therefore, the answer is x < 1.
Hope this helps! :D
The value of x that makes 11 + 2x < 13 is x < 1
Given:
11 + 2x < 13
< means less than
11 + 2x < 13
Subtract 11 from both sides11 + 2x - 11 < 13 - 11
2x < 2
divide both sides by 2x < 2/2
x < 1
x less than 1
Therefore, the value of x that makes 11 + 2x < 13 is x < 1
Learn more about inequality:
https://brainly.com/question/18881247
Slope of line a is ½. What is the equation of a line that is parallel to line a? Y+½x=2 -2x+y+2=0 2x-2=y -½x+y-2=0
Answer:
The equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0
Step-by-step explanation:
A line is a polynomial function of the first degree that has the following form:
y = m * x + b
where m is the slope of the line and b is the intercept with the Y axis. The slope is the inclination of the line with respect to the abscissa axis.
In this case you know that the slope of line a is ½.
Parallel lines are two or more lines in a plane that never intersect. Two lines are parallel if they have the same slope and different y-intercepts.
You have:
y+½x=2 → y= -½x +2-2x+y+2=0 → y=2x -22x-2=y -½x+y-2=0 → y=½x + 2The line that has the same slope as line a is the last one, so the equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0
Which of these is NOT part of a plot?
a
beginning
b
transition
C
middle
d
end
find x and m of angle wyl
Answer:
Step-by-step explanation:
x is clearly 42° because WU is an angle bisector of YWZ (which is 84, and bisecting means half of 84, that is 42)
now, for m of WYL
notice, YLW = 90°
also, UWL = 42°
name the intersection point of YL and WU as O in your mind
Apply angle sum property of a triangle for triangle WOL
angle WOL + angle UWL + angle YLW = 180
angle WOL + 90 + 42 = 180
angle WOL = 180 - 132
angle WOL = 48
now focus on line LOY
since LOY is a line, the angles a line intersecting it forms a linear pair, i.e
angle WOL + angle YOW = 180
48 + YOW = 180
angle YOW = 132
Now, apply angle sum property for triangle YOW
angle YOW + angle YWO (x) + angle WYO (or WYL) = 180
132 + 42 + WYO (or WYL) = 180
WYO (or WYL) = 6°
ask me in the comments if you have any doubts in this
Write an equation in slope-intercept form that represents the data. Show ALL work.
1.)
0
1
2
Sales per
day(x)
Daily pay ($), y
100
105
110
115
11212
I
Equation
Answer:
y = 5x + 100
Step-by-step explanation:
Using the x and corresponding y values from the given table.
Let's use the coordinate (0, 100) and (1, 105)
The equation in slope intercept form is expressed as y = mx+c
m is the slope
c is the y-intercept
Slope m = y2-y1/x2-x1
m = 105-100/1-0
m = 5/1
m =5
Get the y intercept
Substitute the slope m = 5 and any point say (0, 100) into the equation
y = mx+c
100 = 5(0) + c
100 = c
c = 100
Get the required equation;
y = mx+c
y = 5x + 100
Hence the equation in slope-intercept form that represents the data is expressed as y = 5x + 100
The wolf population of a park was 200 in the year 2000. It increased by 20% from 2000 to 2005. It then increased by 15% from 2005 to 2010. What was the wolf population in the park in 2010?
Answer:
Population 2010= 276
Step-by-step explanation:
Giving the following information:
Population 2000= 200
It increased by 20% from 2000 to 2005.
It then increased by 15% from 2005 to 2010.
First, we need to calculate the population in 2005:
Population 2005= 200*1.2
Population 2005= 240
Now, for 2010:
Population 2010= 240*1.15
Population 2010= 276
Dino's Dinosaur rental has two packages for renting a dinosaur costume.
Package #1: $50 initially to reserve the costume and $10 per hour to use the costume
Package #2: $35 initially to reserve the costume and $15 per hour to use the costume
Answer:
90$ all together
Step-by-step explanation:
Which equation is a linear function?
Answer:
I WOULD SAY B sorry caps
Step-by-step explanation:
Answer: I did um the one with 7 and it works
Step-by-step explanation:
Write the simplest polynomial function for each set of zeros
Zeros=4, 7 ,1
PLEASE HELP
Answer:
x^3-12x^2+39x-28
Step-by-step explanation:
(x-4)(x-7)(x-1)
(x^2-4x-7x+28)(x-1)
(x^2-11x+28)(x-1)
x^3-11x^2+28x-x^2+11x-28
x^3-11x^2-x^2+28x+11x-28
x^3-12x^2+39x-28
ab(a²-b²)
can somebody solve this for me.
Answer:
a³b - ab³
Step-by-step explanation:
Given
ab(a² - b²) ← distribute parenthesis by ab
= a³b - ab³
Which table shows values representing a cubic function? Table A Table B Table C Table D
Answer: C
Step-by-step explanation:
On edge
Describe the error?
38 + 7k = 8k + 12
-8k -8k
38 - 1k = 12
-38 -38
-1k = -26
/-1 /-1
K = 26
Answer:
Step-by-step explanation:
K=26