The volume of the right circular cylinder is changing at a rate of approximately 50.265 cubic inches per second.
Given that a right circular cylinder is changing shape.
The radius is decreasing at the rate of 2 inches/sec
dr/dt = -2 inches
The radius is increasing at the rate of 2 inches/sec
dh/dt=5 inches
We have to find dv/dt when r is 4 inches and h is 6 inches.
Volume=πr²h
Differentiate with respect to 't' to find the change of volume:
[tex]\frac{dV}{dt}=\pi(2rh\frac{dr}{dt}+r^2\frac{dh}{dt})[/tex]
Plug in the values:
[tex]\frac{dV}{dt}=3.14(2(4)(-2)(6) + 16(5))[/tex]
[tex]=3.14(-96+80)[/tex]
[tex]=3.14(-16)[/tex]
[tex]=-50.265[/tex] inch³/sec.
Hence, the volume change is -50.265 inch³/sec.
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SOMEONE PLEASE HELP ME ASAP
Answer:
its 2
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
9 + -13= -4
add nine on both sides
then subtract -13 from 9
and you will get -4
What is the sum of the exterior angles, one at each vertex, of any polygon?
Answer:
Polygon Exterior Angle Sum Theorem. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .
Y=-2x+9 answer to this question
Answer:
5.5
Step-by-step explanation:
Divide 6 divided by 3/5
Answer only if u know please:)
Answer:
The answer is 10 or 10/1
A model car is built to a scale of 1 in. : 2.5 ft. If the model is 5.8 in. Long how long is the car in real life?
Answer:
14.5 ft
Step-by-step explanation:
We are told that the model car is built to a scale of 1 in. : 2.5 ft.
That means 1 inches represents 2.5 ft in actual measurement.
Thus, for a 5.8 inch long model, the real life measurement is;
(5.8 inch × 2.5 ft)/1 inch = 14.5 ft
PLEASE HELP ME ASAP!!!! My entire grade depends on these questions and I need to show the work that go me there
I know it is a long one, but I am giving away all of my points!!! I know most of the answers, but for all exept the graphing questions the work needs to be shown!
Consider the quadratic function.
f(x)=-(x+4) (x-1)
(a) What are the x-intercepts and y-intercept?
(b) What is the equation of the axis of symmetry?
(c) What are the coordinates of the vertex?
(d) Graph the function on the coordinate plane. Include the axis of symmetry.
Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the
development of a recreational park on the west side of town. A community action group interested in
preserving the environment claims that 45% of the town’s residents favor the development of a recreational
park.
To determine whether the sample supports the population proportion, a simulation of 100 trials is run, each
with a sample of 200, using the point estimate of the population. The minimum sample proportion from the
simulation is 0.46 and the maximum sample proportion is 0.76.
(a) What is the point estimate of the population?
(b) The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
(c) The margin of error of the population proportion is found using the half the range.
What is the interval estimate of the true population proportion?
(d) Is the community action group’s claim likely based on either interval estimate of the true population
proportion? Explain.
Solve the system of equations. Show your work.
y=x^2-3x+4
x+y=4
Answer:
Answers are in bold
Step-by-step explanation:
Part 1A
Use the Zero Product Property to find the x-intercepts:
0=-(x+4)(x-1)
0=(x+4)(x-1)
0=(x+4)
-4=x
x=-4
0=(x-1)
1=x
x=1
So the x-intercepts are x=-4 and x=1 which is also (-4,0) and (1,0)
For the y-intercepts, plug in x=0:
f(x)=-(0+4)(0-1)
f(x)=(-4)(-1)
f(x)=4
So the y-intercept is y=4 which is also (0,4)
Part 1B
In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k
For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:
f(x)=-(x+4)(x-1)
f(x)=-(x^2+3x-4)
f(x)=-x^2-3x+4
So now we know a=-1 and b=-3, therefore we can plug them in:
x=-b/2a
x=-(-3)/2(-1)
x=3/-2
x=-3/2
x=-1.5
So the equation of the axis of symmetry is x=-1.5
Part 1C
We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:
f(x)=-(-1.5+4)(-1.5+1)
f(x)=-(2.5)(-0.5)
f(x)=-(-1.25)
f(x)=1.25 <-- y-coordinate
So the coordinates of the vertex are (-1.5,1.25)
Part 1D
See the image below
I'll let someone else do the last 4 questions as I am unable to answer them.
1/3+ 1/8 show your work a with equation
please hurry
Answer: 11/21
Step-by-step explanation:
Answer:
11/24 or 0.453
Step-by-step explanation:
1/3 + 1/8
1/3 × 8/8 = 8/24
1/8 × 3/3 = 3/24
8/24 + 3/24 = 11/24
zora recently got an afterschool job to save money to buy a car. She opened a savings account and deposits a fixed amount each week so that she can quickly meet her savings goal. The table below shows the relationship.
Answer:
40
Step-by-step explanation:
The initial value of the function is 40, which represents the amount of money she deposits each week
Simplify the following equation (2^3)^-2
A password is 4 characters long, consisting of 2 letters and 2 numbers. The password must begin and end with a
letter. If numbers can be repeated but letters cannot, how many possibilities are there?
a. 65,000
b. 60,840
c. 58,500
d. 52,650
Answer:
a.
65,000
Step-by-step explanation:
There are 65000 possibilities of 4 character-password
What is a password?A password is a security code that is used for verifying identities
The password has 4 characters.
The password must begin and end with a letter.
So the selections are:
First = 26
Last = 25
The other selections are:
Second = 10 digits
Third = 10 digits
So, the number of password is:
Password = 26 * 10 * 10 * 25
Evaluate
Password = 65000
Hence, there are 65000 possibilities of 4 character-password
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30 cents in each dollar is a paid tax. what fraction is paid in tax? what percentage is not paid in tax?please i need an answer within 10 minutes I'm In an exam
Answer:
30 cents of a dollar is 30% tax paid and 70% not paid.
A dollar is 100 cents.
Step-by-step explanation:
The height of a firework shot upward from the ground with the initial velocity of 10meters per second is represented by the function h(t) = - 16t2 + 4t How long did it take the firework to reach the ground
Answer:
0.375 seconds
Step-by-step explanation:
In simple terms, to find the time it took to reach the ground, we need to find t from the equation.
If we differentiate h with respect to t we will get the velocity with which the fireworks is moving at.
[tex]h(t) = - 16t^2 + 4t.\\dh/dt =-32t +4[/tex]
We can now equate this to its velocity and solve for t
10 = -32t +4
t = 0.1875 ( time cannot be negative in value, so we ignore the negative sign)
Therefore, the time it took the fireworks to reach the ground is = 2 x 0.1875= 0.375 seconds.
(We need to account for the fact that the fireworks went up and came down)
does 3,34 satisfy the equation y= 8x + 10
Answer:
Let y=34 and x=3
Step-by-step explanation:
y = 8x + 10
34 = 8 (3) + 10
34 = 24 + 10
34 = 34
Hence,3 and 34 satisfies this equation.
Prove that (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)=0
Answer:
x=0 x=y=z. with these presumed variable amounts, one can conclude that the equation you asked is equivalent to 0
Answer:
Step-by-step explanation:
(x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)
=x²-y²+y²-z²+z²-x²
=0
are you smarter than a 7th grader get your answers by answering this question please please please please please
Answer:
F
Step-by-step explanation:
8 - (2-3) -1 = 8
6 - (-2) = 8
8-(2-3)-1=6-(-2)
I need help please
Answer: SAS
Explanation: There are two sides that are congruent and there is one vertical angle between them which are always congruent.
Is this a function? Yes or No?!
{(1, 14), (2, 28), (3, 42), (4, 52), 5, 52)}
Answer:
Yes
Step-by-step explanation:
This is a function because each x value is given one y value. More simply, no x value was repeated.
What is the initial value in this question y=8x+6 8 or 6?
Answer:
it should be an 8
Step-by-step explanation:
The initial value in this question y = 8x+6 will be 8 .
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The equation is given as;
y = 8x+6
We can see that the equation contains two terms that are 8x and 6.
The initial value is the first number of the first term in the equation.
Here, the first term is 8x.
Hence, the initial value in this question y = 8x+6 will be 8 .
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help plzzzzzzzzzzzzzz
Answer:
i am not sure try 56
Step-by-step explanation:
Hope this helps!:)
A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot
Answer:
20.62 feet
Step-by-step explanation:
The ladder propped against a building forms a right angle triangle
Height of the ladder (hypotenuse) = 21 feet
Base of the ladder from the building (adjacent) = 4 feet
Height of the building (opposite) = x feet
Hypotenuse ² = opposite ² + adjacent ²
21² = x² + 4²
21² - 4² = x²
441 - 16 = x²
425 = x²
x = √425
= 20.62 feet
Answer: 20.62 ft or rounding it to 20.6 ft
Step-by-step explanation:
It is Friday and you and your friends are going to hit up
the local amusement park. The park costs $30 dollars
to enter and then the tickets for the rides each cost
$3.50. Write an equation when y is total price of
amusement park and x is the number of tickets bought.
Interpret the slope and y-intercept when asked to
explain your answer
Helpp plss
Answer:
y= 30 + 3.50
Step-by-step explanation:
lol I think you're Giselle for my school but that's what the answer it im pretty sure.
What is the x- intercept of y+ 12 =3 (x-9)?
Answer:
13,0
Step-by-step explanation:
12=3(x-9)
divide both sides by three
4=x-9
add 9 to both sides
x=13
so, the x intercept is (13,0)
Answer:
x-intercept: (13,0)
y-intercept: (0,-39)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x .
To find the y-intercept, substitute in 0 for x and solve for y .
Plssssss help ASAP
And thx it u do :)
360 students in the 6th grade voted for class president. The loser received 108 votes. What percentage of the vote did the winner receive?
A) 20%
B) 30%
C) 60%
D) 70%
can someone please answer this
Answer:
y = -0.6x + 24.6
Step-by-step explanation:
Dinner at your grandfather's favorite restaurant now costs $25.25 and has been increasing steadily at 4% per year. How much did it cost 35 years ago when he was courti
your grandmother?
At one gas station, gas costs $2.75 per gallon. Complete the equation that relates the total cost, C, to the number of gallons of gas purchased, g.
C = __
Answer:
C = 2.75
Step-by-step explanation:
it does not tell how much there for it is 1 gallon
Find the perimeter of the shaded region of this composite figure.
Answer:
perimeter of shaded region:
area of rectangle- area of semicircle
l×b‐(pie r²) diameter of circle‐6m; Radius‐3
8×6‐(3.14×3×3)
42— 28.26=13.74m
HOPE IT WILL HELP YOU
Can an isoceles triangle be an obtuse triangle? Explain.
Answer:
it can and cant at the same time.
9y - 1 = -10y + 227
Answer: y=12
Step-by-step explanation:
What is the slope of the line that passes through the points M (4,-5) and N (0, -8)?
A.) -3/4
B.) 13/4
C.) -4/3
D.) 3/4
Answer:
D. 3/4
Step-by-step explanation:
using the y2-y1/x2-x1 to find the slop: -8--5/0-4 = 3/4
Answer:D
yee
Step-by-step explanation: