I need help please!!
assume that the height of your cylinder is 8 inches. consider a as a function of r, so we can write that as a(r)=2πr2+16πr. what is the domain of a(r)? in other words, for which values of r is a(r) defined? part b: continue to assume that the height of your cylinder is 8 inches. write the radius r as a function of a. this is the inverse function to a(r), i.e to turn a as a function of r into. r as a function of a.
Answers
Step-by-step explanation:
The domain of A(r) is [tex]r \geq 0.[/tex] The expression for A(r) is
[tex]A(r) = 2\pi r^2 + 16\pi r[/tex]
Let's write A(r) as simply A and divide the equation by [tex]2\pi[/tex] to get
[tex]r^2 + 8r = \dfrac{A}{2\pi}[/tex]
We can complete the square on the left hand side by adding 16 to both sides:
[tex]r^2 + 8x + 16 = \dfrac{A}{2\pi} + 16[/tex]
[tex]\Rightarrow (r + 4)^2 = \dfrac{A}{2\pi} + 16[/tex]
Taking the square root of the equation above and then solving for r, we get
[tex]r = -4 \pm \sqrt{\dfrac{A}{2\pi} + 16}[/tex]
In this exercise we have to use our knowledge about cylinders to calculate the function that best represents its value:
[tex]r=-4+\sqrt{\frac{A}{2\pi} +16}[/tex]
The area domain of A can be written as:
[tex]A(r)=2\pi r^2+16\pi r[/tex]
Let's write A(r) as simply A and divide the equation by [tex]2 \pi[/tex]to get:
[tex]r^2+8r=\frac{A}{2\pi}[/tex]
Now we can sum on both sides like:
[tex]r^2+8X+16=\frac{A}{2\pi}+16\\(r+4)^2=\frac{A}{2\pi}+16[/tex]
Taking the square root of the equation above and then solving for r, we get:
[tex]r=-4+\sqrt{\frac{A}{2\pi} +16}[/tex]
See more about cylinders at brainly.com/question/3692256
Related Questions
The finishing times for a race happen to be normally distributed with a mean of 10.2 seconds and a standard deviation of 1.4 seconds. Find the cut off score for the top 10%. Interpret this result.
Answers
Using the normal distribution, it is found that the cut off score for the top 10% is of 8.4 seconds. It means that a person with a time of 8.4 seconds or lower is in the faster 10% of runners.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 10.2 seconds, hence [tex]\mu = 10.2[/tex]Standard deviation of 1.4 seconds, hence [tex]\sigma = 1.4[/tex].The lower the times, the faster the runners are, hence, the cut off score for the top 10% is the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 10.2}{1.4}[/tex]
[tex]X - 10.2 = -1.28(1.4)[/tex]
[tex]X = 8.4[/tex]
The cut off score for the top 10% is of 8.4 seconds. It means that a person with a time of 8.4 seconds or lower is in the faster 10% of runners.
A similar problem is given at https://brainly.com/question/24663213
Christopher bought 15 feet of fabric from Walmart. The fabric cost $1.75
per foot, including sales tax. If Christopher gave the cashier $30, how much
change should he receive?
O $2.40
$6.00
$8.55
O $3.75
Answers
Answer:
He should recieve 3.75 in change
Step-by-step explanation:
1.75x15=26.25
30-26.25=3.75
Need help fast plzzz
Answers
2) 1 because it shows (0,1) on the table And y intercepts are always (0,-)
3) y=-3x+1
What is the probability of choosing a red ace of clubs from a standard deck of cards????
Answers
Answer:
0
Step-by-step explanation:
The ace of clubs is black.
There is no red ace of clubs.
p(red ace of clubs) = 0
Answer:
Step-by-step explanation:
There is no Red ace of club. All the clubs are black in colour. So the probability is 0
Multiply 7x43 True or false .Using partial products the products are 21 and 28
Answers
Answer:
thats false
Step-by-step explanation:
you need to use 21 and 280 because if you split the 43 you do 40x7
and 7x3
Solve the system of equations using the substitution method.
-5x + 21 = 18
y= 2x+8
Answers
Answer:
(-3;2)
Step-by-step explanation:
if the first equation is -5x+21=18y, then:
[tex]\left \{ {{y=2x+8} \atop {-5x+21=18*(2x+8)}} \right. \ => \ \left \{ {{y=2x+8} \atop {-5x+21=36x+144}} \right. \ => \ \left \{ {{y=2x+8} \atop {41x=-123}} \right. \ => \ \left \{ {{y=2} \atop {x=-3}} \right.[/tex]
help me with math and ill mark brainliest
Answers
Answer:
226
Step-by-step explanation:
In the given picture,
Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.
Segment TU joins the midpoints of the sides PS and RQ.
Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."
Therefore, m(TU) =
7x - 26 =
7x - 26 = 6x + 10
7x - 6x = 26 + 10
x = 36
m(TU) = 7x - 26
= 7(36) - 26
= 252 - 26
= 226
Therefore, Option (1) will be the answer.
game where speed
Train B
300
Distance (mi)
200
Distance 1000
100
2 4
Time (h)
Aega seed
Tanase greater speed
They bome the same speed
D
to be termine which tranhas the greater speed
Answers
Answer:
300 train b
Step-by-step explanation:
train b is the right answer
PLEAS ill mark brainliest
Answers
Answer:
pede PO ba na iba namn PO yng question Kasi medyo bobo ako ehg
Step-by-step explanation:
ako na sasabi
Answer:
Es la B creo sorry si está mal
Which statement represents the expression?
3×2+5
a.the product of 3 and the sum of 2 and 5
b.3 times the sum of 2 and 5
c.3 times 2 plus 5
d.the product of 3 and 2 combined with 5
Answers
Answer:
answer is D (the product of 3 and 2 combined with 5)
because, product of 3 and 2 = 3x2 = 6 and 6+5 = 11.
hope it helps u...
Answer:
c.3 times 2 plus 5
Step-by-step explanation:
pretty sure its right
whats the greatest common factor of 18 and 27 and 54
Answers
Answer: 9
Step-by-step explanation:
From doing the math I think it should be 9
Start with the smallest number, 18:
The factors of 18 are: 1, 2, 3, 6, 9, 18.
So the GCF for all three must be one of those.
Now consider the next smallest number. Of the factors of 18, only these are also factors of 27:
1, 3, 9
Now consider the last number, 54. Of the remaining factors, 9 is the greatest and 9 goes into 54.
The GCF is 9.
By starting with the smallest number, you usually limit how many factors you'll ever need to consider.
The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator?
Use 3.14 for .Round your answer to the nearest ten thousand.
Answers
Answer:
Length of equator = 40212.39 km
Step-by-step explanation:
Hope this helps! Please mark brainliest for you can! :)
Answer:
40,000 km
Step-by-step explanation:
The circumference is given by the formula ...
C = 2πr
For the given values of π and radius, the circumference is ...
C = 2·3.14·6400 km = 40,192 km
Rounded to the nearest 10,000, the length of the equator is 40,000 km.
_____
Additional comment
The original definition of the meter was 1/10,000,000 of the distance from the north pole to the equator, through Paris. Essentially, the polar circumference of the earth was defined as about 40,000 km. The polar distance in the southern hemisphere will differ from that in the northern hemisphere, and apparently, the chosen longitude also makes a difference. All of these are different from the equatorial circumference. That definition has long been superseded.
How is this problem to be solved?
Answers
Step-by-step explanation:
I hope this helps you!!!!!!
Felisa read the first 60 pages of a book in 3 days. She reads the last 90 pages in 6 days. Are these reading rates equivalent? Explain your reasoning.
Answers
60/3 = 20
90/6= 15
Both of the answers aren’t equivalent.
Evaluate the expression when x = 1/4 and y = 1/2
2 (1/16 + x2) + 5y
Answers
Answer:
2 3/4
Step-by-step explanation:
x = 1/4
y = 1/2
so we have to plug in these numbers wherever we see x and y
2 (1/16 + (1/4)^2) + 5(1/2)
using pemdas we solve what's in the parenthesis first
(1/16 + (1/4)^2) = (1/8)
next is multiplication so
2 (1/8) = 1/4 and 5(1/2) = 5/2
lastly we add so
1/4 + 5/2 = 11/4 or 2 3/4
A person bikes 2
1
2
miles at a constant rate in
1
8
of an hour.
What distance, in miles, does the person bike in an hour?
Answers
Answer:
The person bikes 20 miles in an hour
Step-by-step explanation:
A football coach filled a water cooler with 37.85 liters of water before a game. The players drank 25.9 liters during their game. How many liters of water were left in the cooler?
Answers
Answer:
37.85 subtract by 25.9 that's how I got 11.95 liters left
plz help need this done by tomorrow thank you [Photo]
Answers
Answer:
angle 5
Step-by-step explanation:
angle 5 is in the same position as angle 3.
Answer:
angle 5 corresponds angle 3.
Consider the function f ( x ) = cos ( 0.65 x ) f(x)=cos(0.65x). How much does x x have to vary for the argument of f f to vary by 2 π 2π?
Answers
We want to see how much must vary x so the argument of f(x) varies by 2 pi. We will see that x must vary (2π)/0.65.
So let's take the variation from 0 to 2π.
The argument is zero when x = 0
Argument = 0.65*x
if x = 0
Argument = 0.65*0 = 0
Now let's see which must be the value of x such that the argument is equal to 2π, so we must solve:
2π = 0.65*x
(2π)/0.65 = x
So we can see that x must vary from 0 to (2π)/0.65, or just a variation of (2π)/0.65.
If you want to learn more, you can read:
https://brainly.com/question/6904750
8×100+4×10+7×110+3×1100
Answers
Answer:
4910 - i think
Step-by-step explanation:
Answer:
4,910
Step-by-step explanation:
Mrs. Steele read 75% of her 80 books. How many books has she finished reading?
Answers
Answer:
first you have to find 75% of 80 books
so you multiply
75/100 multiply 80/1
then you cancel
..........
the answer is 60 btw
if you get it right ill bark brainliest
Answers
Answer:
diagonals does not intersect at right angles
Step-by-step explanation:
In parallelogram diagonals does not intersect at right angles.
HELPPP LAST ATTEMPT!!
Answers
Answer:
Step-by-step explanation:
I answered this same question but uhm it’s (-6,3) just click on my pfp to see where I answered it :3
Draw a diagram to represent 3 ÷ 2/5
Answers
Answer:
a diagram? or just how to solve it
Step-by-step explanation:
Prove that a line that divides two sides of a triangle proportionally is
parallel to the third side.
1.
1. Let ABC be a triangle. Segment
DE intersects sides AB and CA,
respectively and divides those
sides proportionally, As such,
ADIAB=AE/AC
2
2.
3. Triangles ADE and ABC are
3.
4.
4.
5. Segments DE and BC must be
to one
another
5. By the Converse of the
Theorem
Answers
Answer:
Step-by-step explanation:
If (from the image attached) DE is a line segment that divides the sides AB and AC proportionally in ΔABC then we can prove that line segment DE is parallel to BC using the parallel transversal theorem. Based the parallel transversal theorem, the triangles ABC and ADE are similar therefore angles are congruent and line DE must be parallel to line BC
The function f(x) = {' is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
=
0 1-3,375)
0 1-2
o (2.7
0 (3, -125
Answers
Answer:
0 1-3,375)
Step-by-step explanation:
Jada paints a circular table that has a diameter of 44 inches. What is the area of the table? Round to the nearest whole number!!!
Answers
22 inches = radius
Then multiply the radius by pi, let’s assume it 3.14
22 x 3.14 = 69
Then you multiply it by 2 bc the formula of an area of a circle is pi times the radius times 2
So, 69 x 2 = 138
So area of the table is 138 inches
600+600+200-200 Giving Brainliest
Answers
Answer:
600+600+200-200=1200
Find
h ′(2), given that f(2) = −3, g(2) = 4, f ′(2) = −2,and g ′(2) = 5.
I only need help with part d (picture attached)
Answers
Answer: [tex]-\frac{1}{2}[/tex]
=========================================================
Work Shown:
Apply the quotient rule
[tex]h(x) = \frac{g(x)}{1+f(x)}\\\\h(x) = \frac{A}{B}\\\\h'(x) = \frac{A'*B-A*B'}{B^2}\\\\h'(x) = \frac{g'(x)*(1+f(x))-g(x)*(1+f(x))'}{(1+f(x))^2}\\\\h'(x) = \frac{g'(x)*(1+f(x))-g(x)*f'(x)}{(1+f(x))^2}\\\\h'(2) = \frac{g'(2)*(1+f(2))-g(2)*f'(2)}{(1+f(2))^2}\\\\h'(2) = \frac{5*(1-3)-4*(-2)}{(1-3)^2}\\\\h'(2) = \frac{-2}{4}\\\\h'(2) = -\frac{1}{2}\\\\[/tex]
What are the solutions of this quadratic equation? x2 + 10 = 0 A. B. C. D.
Answers
Answer:
x2+10=0A.B.C.D.
it is A because 0 can't enter into a letter if it can enter then it will be the same letter
