The rate of change of the area as a function of time is:
A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)
How to get the rate at which the area increases?
Remember that for a circle of radius R, the area is:
A = 3.14*R^2
Now, if the radius increases at a rate of 4 ft/min, then we can rewrite R as:
R(t) = R₀ + 4ft/min*t
Where t is the time in minutes, and R₀ is the initial radius.
So the area function is:
A(t) = 3.14*(R₀ + 4ft/min*t)^2
The rate of change is given by the differentiation with respect to t, it is:
A'(t) = 2*3.14*(R₀ + 4ft/min*t)*(4ft/min)
A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)
The rate at which the area increases, as a function of time, is given by:
A'(t) = 6.28*(R₀ + 4ft/min*t)*(4ft/min)
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whats the value of -15-9+(-7)?
A. -31
B. -17
C. -13
D. -1
Answer:
Step-by-step explanation:
-15-9+(-7)
answer: A, -31.
hope this helps! mark me brainliest as well please.
Answer:
-31
Step-by-step explanation:
you can subtract -15 and -9 which equals -24. After that, you can just subtract it by 7 . because +(-)= - so -15-9-7= -31
(3x+6)^2
Please show the work step-by-step, thank you! <3
Please help! The possible answers and the question are in the photo below.
Answer:
B
Step-by-step explanation:
The average is in the limits
Rounded to the nearest tenth of a centimeter, what is the length of arc lmn? 7.9 cm 10.2 cm 12.6 cm 14.2 cm
The length of arc LMN is the number of units on the arc
The length of arc LMN is 14.2 cm
How to calculate the length of the arc?The given parameters are:
Arc LM = 6.3 cmRadius, r = 6 cmAngle MON = 75 degreesStart by calculating the length of arc MN using:
[tex]MN = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]MN = \frac{75}{360} * 2 * 3.14 * 6[/tex]
Evaluate the product
MN = 7.85
The length of arc LMN is then calculated using:
LMN = LM + MN
This gives
LMN = 6.3 + 7.85
Evaluate the sum
LMN = 14.15
Approximate
LMN = 14.2
Hence, the length of arc LMN is 14.2 cm
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Answer:
D ( 14.2 )
Step-by-step explanation:
edg 2022
( Find the Mean Absolute Deviation and the Mean with an explanation )
How many siblings do the students in my math class have?
3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3
The mean of the data is 1.31, while the mean absolute deviation is 2.56.
What is the Mean Absolute Deviation?The mean is the average of a data set, while the mean absolute deviation is the average distance of the each data point from the mean.
Given the data:
3,2,2,5,4,1,3,4,1,0,3,2,1,1,6,3
Find the Mean:
Mean = (3 + 2 + 2 + 5 + 4 + 1 + 3 + 4 + 1 + 0 + 3 + 2 + 1 + 1 + 6 + 3)/16 = 41/16 Mean = 2.5625
Find the Mean Absolute Deviation:
Mean abosolute deviation = (3 - 2.5625) + (2 - 2.5625) + (2 - 2.5625) + (5 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (3 - 2.5625) + (4 - 2.5625) + (1 - 2.5625) + (0 - 2.5625) + (3 - 2.5625) + (2 - 2.5625) + (1 - 2.5625) + (1 - 2.5625) + (6 - 2.5625) + (3 - 2.5625) / 16
Mean abosolute deviation = 21/16 = 1.3125
Therefore, the mean of the data is 1.31, while the mean absolute deviation is 2.56.
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50 points!
Ahmed needs to take a close-up shot of an orange for his art class. He frames a shot of an orange as shown below, so that the lines of sight form tangents to the orange. If the measure of the cameras viewing angle is 34 degrees, what is angle ACB?
Answer:
either 34 or 214
Step-by-step explanation:
What is the true solution to the equation below? l n e superscript l n x baseline l n e superscript l n x squared baseline = 2 l n 8
The true solution of the logarithmic equation [tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex] will be 4.
What is a logarithm?Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic equation is given as
[tex]\ln e^{\ln x} + \ln e^{\ln x^2} = 2\ln 8[/tex]
We know that the formula
[tex]\ln e = 1\\\\\ln b^a = a \ln b\\\\\ln a + \ln b= \ln a +b[/tex]
Then we have
[tex]\begin{aligned} \ln x \times \ln e + \ln x^2 \times \ln e = \ln 8^2\\\\\ln x + \ln x^2 = \ln 64\\\\\ln x*x^2 = \ln 64 \end{aligned}[/tex]
Then take antilog, then we get
[tex]\rm x^3 = 64\\\\x^3 = 4^3 \\\\x \ =4[/tex]
More about the logarithm link is given below.
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Answer:
b, x=4
Step-by-step explanation:
edge 2022
State reasons why these two triangles are congruent
If a = −3, then a + a2 − a3 + a4 − a5 = _____
the diagram shows a right angled triangle.what is the value of h
Answer:
I got the answer as h=8.184cm
Is there any way for my to view my full highschool transcript online
sorry brain ly won't let me tell you I'm sorry
Brandon recorded which donut his nephew picked for breakfast the past few months.
cake donuts 2
chocolate frosted donuts 2
jelly-filled donuts 5
glazed donuts 3
Considering this data, how many of the next 20 donuts Brandon's nephew picks for breakfast would you expect to be glazed donuts?
Answer:
5
Step-by-step explanation:
2+2+3+5=12
12/3=4
4 divided by 20 =5 glazed donuts
Four friends went to the movies.
Each person bought a movie ticket, and the total the four friends spent on the tickets was $52.
Which equation can be used to find the cost of each ticket?
4+2 = 52
B 2 - 4 = 52
4.3 = 52
© = 52
Answer:
C. 4x = 52
Step-by-step explanation:
If each person spent $x,
then the total amount spent will be 4x
we already know that the total amount spent is 52
so, 4x = 52
Answer:
4x=52
Step-by-step explanation:
[tex]let \: the \: price \: for \: each \: ticket \: be = x \\ since \: four \: persons \: bought \: the \: ticket \: \\ 4x = 52 \\ the \: equation \: for \: each \: ticket \: will \: be \: \\ 4x = 52[/tex]
a 2014 mustang originally costs $25000.00 and depreciates at a rate of 8% per year. What is the cost of the car after 7 years?
In a right triangle, sin(β) = 0.292. If the hypotenuse of the triangle has a length of 17.5 cm, what is the length of the side adjacent to angle β. Note: You will also need to use the Pythagorean theorem to answer this question.
16.7 cm
5.1 cm
11.4 cm
4.1 cm
So, the length of the side adjacent to angle β is approximately 17.15 cm. triangle Therefore, the closest option is 16.7 cm.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
sin(β) = opposite/hypotenuse
[tex]hypotenuse^2 = adjacent^2 + opposite^2\\17.5^2 = adjacent^2 + opposite^2\\306.25 = adjacent^2 + opposite^2\\[/tex]
opposite = sin(β) x hypotenuse = 0.292 x 17.5 = 5.095 cm
[tex]306.25 = adjacent^2 + 5.095^2\\306.25 - 5.095^2 = adjacent^2\\294.81 = adjacent^2\\[/tex]
√294.81 = adjacent
So, the length of the side adjacent to angle β is approximately 17.15 cm. Therefore, the closest option is 16.7 cm.
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What do you think would be a good way to select a random sample of all the students at the 12 schools in the school district?
Step-by-step explanation:
At a birthday party, teams for a game are chosen by putting everyone's name into a jar, and then choosing the names at random for each team
Identify the quadrants in following coordinate plane
I NEED ANWSER FAST!!!!!
Answer:
Step-by-step explanation:
starting from the upper right corner and going counterclockwise.
upper right: I
upper left: II
bottom left: III
bottom right: IV
11] You buy a house for $175,000. The economy goes
down and your house is losing value at 4% semi-annually.
How much is your house worth in 5 years?
Answer:
4% of 175,000 is 7,000
7,000x 5=35,000
175,000-42,000 equals 140,000 the value of the house
Solve for the formula for r. C=2πr Question 2 options:
r=C2π
r=2Cπ
r=2πC
r=2πC
Answer:
r = [tex]\frac{C}{2\pi }[/tex]
Step-by-step explanation:
C = 2πr ( isolate r by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = r
=
5. If p(x) = 1/2(x–5)^2+ 14, what is the
value of p(3)?
Answer:
i think since p(x) = p(3)
Step-by-step explanation:
then p(3) = 3
where you see x add 3
so 1/2(x-5)^2 + 14
1/2(3-5)^2 + 14
1/2(-2)^2 + 14
1/2 x 4 + 14
cancel out 4 by 2 ( divide)
you get 2 + 14
16.
p(x) = 16.
Hope this helps .
SOLVE THIS!!!! CAUSE...WELL BRAINLY
please fill in the blanks
Time is an illusion~
that helps things make ____
so we're always living in the present tense
it is unforgiving when a good thing ____
Answer: sense happens
Step-by-step explanation:
Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Answer:BC AND AD is parellogram since it has sides.
Step-by-step explanation:
To estimate the number of students in your school who play a sport outside of school, you decide to survey the players on the boys' baseball team.
100 POINTS PLEASE ANSWER
What do you think? How do superheroes help teach us about the world we live in? What values should superheroes represent?
Respond in a cohesive paragraph that includes the following:
- provide 3 values and elaborate their importance
- address what your superhero would teach society
- provide a name and superpower
Answer:
Superheroes are meant to inspire. They represent someone we are not, or someone that can do things that we can't. They can provide an escape into a world where someone is there for us even when our protectors or our medical and social institutions have let us down.
While cleaning out the garage, Nelson discovers some containers of oil that need to be taken in for recycling. The containers hold 25 fluid ounces, 2 cups, and 7 quarts, respectively. Find the total amount of oil ready to be recycled (in fluid ounces)
Answer:265
Step-by-step explanation: 2 cups is 16fluid Ounce, 7quaryz is 224 fluid ounce
Total will 265 fluid ounce (225+16+224)
What percent of the time did she eat at most 8 cookies?
Answer:80%
Step-by-step explanation:8/10×100
Find the coordinates of the turning point for the equation of the graph below
y=x^2– 16x +39
=
Answer:
x = 8 - sqrt(y + 25)
Step-by-step explanation:
Step-by-step explanation:
comparing given equation with ax^2+bx+c;
a=1 b=-16 c=39
now,
x coordinate of vertex = -b/2a
= 16/2*1
= 8
again,
y coordinate of vertex = (8)^2-16(8)+39
=-25
Therefore, the turning point is (8,-25).
HELPEHEGEDHGDGXCCVCCXVV
Step-by-step explanation:
1) 7x+3y=19
2)2x-7y=12
3) x=5, y=0
4) x=15/2, y=(-63/4)
5) x=9, y=92
6) x=(-2) , y=(-9)
7) x=5, y=(-2)
8) x=2, y=2
The length of a rectangular garden is 2 m greater than the width. The area is 80 m^2. Find the dimensions of the garden.
The width of the garden is ___m.
The length of the garden is ___m.
Answer:
Length of rectangle = 10 mWidth of the Rectangle = 8 mStep-by-step explanation:
Given :-
Length of a Rectangular garden is 2m greater than the width .Area of garden = 80 m²To Find :-
Dimensions of the gardenSolution :-
Let's assume:
Width of the rectangle = xLength of the rectangle = x + 2We know that,
Area of rectangle = Length × Width↠ (x)(x + 2) = 80
↠ x² + 2x - 80 = 0
↠ x² + 2x - 80 = 0
↠ x² + 10x - 8x - 80 = 0
↠ x(x +10) -8 (x + 10) = 0
↠ (x-8) (x + 10) = 0
↠ x = 8 or -10
↠ x = 8
Hence,
Width of the rectangle = x = 8 mLength of the rectangle = x + 2 = 10 mAnswer:
Given:-
Length of rectangular garden is 2m longer than its widthArea of Rectangular garden is 80m²To Find :-
Dimensions of Rectangular gardenSolution:-
Let the width be x and length be x + 2According to the question ,
Area = 80m²
putting the known values ,
(X)(X+2) = 80m
x² +2x - 80= 0
x² +10x-8x -80m= 0
x(x + 10) - 8(x+10) = 0
(x-8) = 0 ; (x+10) = 0
X = 8 ; X = -10
As dimensions can not be negative so , X = 8Length = X + 2 ; 10 m
Width = X ; 8 m
A cone has a volume of 923.16 cubic meters and a height of 18 meters. What is its radius?