I assume the base of S is the disk centered at the origin, or x² + y² ≤ r². Solving for y gives two solutions corresponding to the upper and lower halves of the circular boundary,
[tex]x^2+y^2 = r^2 \implies y = \pm \sqrt{r^2-x^2}[/tex]
and the vertical distance between them - i.e. the side length of each cross section - is
[tex]\sqrt{r^2-x^2} - \left(-\sqrt{r^2-x^2}\right) = 2\sqrt{r^2-x^2}[/tex]
Then the volume of each square cross section 4 (r² - x²) ∆x, and the volume of S is
[tex]\displaystyle \int_{-r}^r 4(r^2-x^2) \, dx[/tex]
By symmetry, this is the same as
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx[/tex]
which gives a volume of
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx = 8 \left(r^3 - \frac{r^3}3\right) = \boxed{\frac{16r^3}3}[/tex]
Find the mean, median, and mode of the data set. Round to the hundredths, if necessary. 29,300 24,350 32,400 15,100 14,200 21,950 27,450 29,400 15,200 35,050 16,050 11,500 13,050 11,500 11,600 11,100 21,450
The mean of the data is 20038.24, the median is 16050 while the number with the highest frequency is 11500
Mean, median, and mode of a datasetMean are known as averages, median is the middle value after rearrangement while the mode is the value with the highest frequency
Calculate the mean
Mean = sum of data/sample size
Given the data
29300, 24350, 32400, 15100, 14200, 21950, 27450, 29400, 15200, 35050, 16050, 11500, 13050, 11500, 11600, 11100, 21450
The mean of the data is 20038.24
For the median being the value at the middle, the median is 16050 while the number with the highest frequency is 11500
Learn more on mean, median and mode here: https://brainly.com/question/14532771
7<2x+3<=13 write solution in interval notation
Answer:
2<x<_5
Step-by-step explanation:
if you will solve this math 50 point + brainlists=
5+6+6+83+15×53____84
Answer:
5+6+6+83+15×53=895
I hope it helps ty if yes pls make me brainliest take care
6 + 6 = 12
5+15 = 20
53x83= 4399
4399+32=4431
4431- 84 =4,347
please make me brainalist and keep smiling dude I hope you will be satisfied with my answer is updated
and you have asked me to help please tell me
17 divided into 3,536
Answer: 208
Step-by-step explanation:
The number 3536 is called the numerator or dividend, and the number 17 is called the denominator or divisor.
The quotient of 3536 and 17, the ratio of 3536 and 17, as well as the fraction of 3536 and 17 all mean (almost) the same:
3536 divided by 17, often written as 3536/17 = 208
9.9 ft 7.2 ft The figure above shows a movie screen with dimensions shown in feet. What is the length of the diagonal of the screen, in feet? Give the exact solution or round your answer to the nearest tenth of a foot.
Answer:
12.2
Step-by-step explanation:
use the Pythagorean theorem to determine the diagonal
9.9^2 + 7.2^2 = d^2
d = 12.2
-3 1/2 - (-4 1/4) on
3 ¾
Step-by-step explanation:
-3½+4¼=-²/⁴ +17/4=15/4
3¾
Answer:
5/4 or 1 1/4
Step-by-step explanation:
-3 1/2 - (-4 1/4) multiply the number by the denominator and add the numerator: -3*2 = -6 + 1 = -5 same for the other...
-5/2 - (-15/4) now you need the same least common denominator...
-10/4 + 15/4
= 5/4 or 1 1/4
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Find the slope of
the line
Gve your answer as
a fraction in simplest
form.
Answer:
slope = 1/2
Step-by-step explanation:
we rise 1 and run 2 which gives us y=1/2x
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 in, find its area.
Step-by-step explanation:
Length = 6x
width = let x be width
Perimeter = 84 in
Now
Perimeter = 2 ( l + b )
84 = 2 ( 6x + x )
84 = 2 × 7x
84 / 2 = 7x
42 = 7x
x = 42 / 7
x = 6
now
width = 6 yards
length = 6x = 6 × 6 = 36 yards
now
area = l × b
= 6 × 36 yd
= 216 yd²
explain in depth how 12 x √3/2 = 6√3 (GCSE MATHS)
Step-by-step explanation:
I hope this helps, you can ask any question for clarification
What is the difference between the
fastest sprint and the slowest sprint?
Fastest sprint - 12 2/4
Slowest sprint - 10 1/4
Answer:
2 1/4
Step-by-step explanation:
To find the difference, we must subtract the smaller number from the bigger one. In this case, the equation is 12 2/4 - 10 1/4.
Let us set aside the fraction and subtract 10 from 12 first.
12 - 10 = 2
Therefore, the whole number of the difference will be 2.
Let's solve for the fraction now.
2/4 - 1/4 = 1/4
Therefore, the fraction in the answer will be 1/4.
Add 2 and 1/4 to get 2 1/4, which is the answer.
I hope this helps and please mark me as brainliest!
can somebody help me please
________________________________________________
Calculate[tex]Substitute\ x=4\ into\\ f(x)=7x^2+4x-6[/tex]
_________________________________________________
Substitute[tex]f(4)=7\times 4^2+4\times 4-6[/tex]
___________________________________________________
Calculate the power[tex]f(4)=7\times 16+4\times 4-6[/tex]
___________________________________________________
Calculate the product or quotient[tex]f(4)=112+4\times 4-6\\ f(4)=112+16-6[/tex]
___________________________________________________
Calculate the sum or difference[tex]f(4)=128-6\\ f(4)=122[/tex]
I hope this helps you
:)
Rewrite each of the following expressions without using absolute value bars. |x-4| if x>4
we're given that x is greater than 4 (the symbol ">" indicates "greater than)
5 is greater than 4. Let's plug it in :
|5-4|
|1|
1 (remember, absolute value is always positive).
Now let's try 6 :
|6-4|
|2|
2
hope helpful ~
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = - 1/2 x + 1
Step-by-step explanation:
Answer:
y = -1/2x + 1
Step-by-step explanation:
m, rise/run = (2 - 4)/(-2 + 6) = -2/4 = -1/2
b, y-intercept = (0, 1)
y = mx + b
y = -1/2x + 1
Write the equation of the parabola in vertex form.
vertex (2,4), point (3,2)
Answer:
y=-3(x-2)^2+4
Step-by-step explanation:
The general equation for the data given is y = a(x-2)^2 + 4 based on the vertex information.
To find a, we use (3,1) to substitute. 1 = a(3-2)^2 + 4 or a = -3
So the full equation is y = -3(x-2)^2 + 4
John's water bill this month was $19.67 . Looking at the water bill, it says he used exactly 10,000 gallons of water. How much does he pay per gallon of water used?
Answer:
0.001967 per gallon
Step-by-step explanation:
19.67/10000 = 0.001967
Debbie receives 25% commission on all sales. Her sales totalled $400. How much commission does she earn?
Answer:
$100
Step-by-step explanation:
Debbie's earnings are found by multiplying her commission rate by her sales:
0.25 × $400 = $100
Debbie earns $100 commission on her sales.
simplify 24.4 / 0.002
Answer:
12,200
Step-by-step explanation:
Financial Planning: Purchasing a House
Part One:
1. Download the app Zillow
2. Make an account
3. Make a list of required features
4. Find a house that serves your current and future needs
Part Two:
1. Decide how much money you have for the down payment
2. Calculate how much you need to finance
3. Calculate your monthly payment to mortgage
4. Calculate how long you will be paying off and make a plan
Part Three:
1. Repeat parts one and two more times for a total of 3 potential houses
2. Put them into a graphic organizer and decide which one works best for you.
Given the matrices A and B, solve for X. Express the numbers using integers or simplified fractions.
Please!
Answer:
x=5
Step-by-step explanation:
A= 1+4+4+(-4)=5
B= 8+5+4+(-5)=15
15-5=10
10/2=5
x=5
I don't understand someone please help
Approximately how many
years would it take for an
investment of $1,000 to grow
to $1,500 with a simple
interest rate of 8%?
9. The area of a rectangle is 12x + 15. The
length of the rectangle is 6. What is the
width of the rectangle?
Answer:
oh that's hard lol just go to the lowest number and times it on a piece of paper
.......................................................
Name the characteristics a shape has to have to be defined as the following:
Quadrilateral
Triangle
Square
For a shape to be defined as a quadrilateral it has to have 4 sides.
For a shape to be defined as a triangle it has to have 3 sides, with the angles adding up to 180°
For a shape to be defined as a square it has to have 4 sides and angles. The angles must add up to 360° with equal side and angle length.
Answer:
Shapes are the outlines formed from a given area of figure. The characteristics of shapes vary and depend on what the given shape is. Here are the characteristics of a quadrilateral, triangle, and square.
1. Quadrilateral- Quadrilaterals should have four sides and four corners. As long as these two are present, you can call any shape a quadrilateral regardless of how it is formed.
2. Square- A square is a quadrilateral, so it must contain four sides and four corners. However, a square has its sides and corners equally made.
3. Triangle- A triangle should have three sides or vertices and three corners.
Step-by-step explanation:
Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.
Neighbor A:
Neighbor B:
Neighbor C:
Neighbor A can put up three 8 foot sections of wood fencing in two hours.
Neighbor B can put up 15 feet of chain link fencing each hour.
Neighbor C can put up 1 yard of vinyl fencing in half an hour.
Which neighbor's fencing project will take the least amount of time to complete?
Which neighbor's fencing project will take the most amount of time to complete?
Answer:
i think c
Step-by-step explanation:
Answer:
Neighbor C will take the least amount of time and Neighbor B will take the most amount of time. Let me know if i'm right!
Step-by-step explanation:
I hope this helps! Have a good weekend!! :)
IM CONFUSED CAN SOMEBODY HELP ME SOLVE THE EQUATION
Answer:
y = - ½(x - 2)² + 3
Step-by-step explanation:
HELP ASAP
In the diagram, m ZAFB = 78°
Which angle is supplementary to ZAFB and what is its measure?
Answer:
Angle AFE = 102(degree symbol)
Step-by-step explanation:
supplementary means two angles that add up to 180
hope this helps! :)
Answer:
The angle supplementary to ∠AFB is ∠EFA.
The reason why this is, is because a supplementary angle consists of two angles that have a sum of 180°.
Supplementary angles combine to form a straight line.
In this case, ∠EFA is the supplement of ∠AFB because, ∠EFA is the other part of the angle, AFB, that creates a full straight line(180°).
And to find the value of m∠EFA you would need to arrange an equation.
Since we know that the given angle measure of AFB is 78°, ∠EFA would have to equal a different measure so that both measures will have a sum of 180°.
We will consider the value of m∠EFA to be 'x' in our equation, so;
x + 78 = 180°
Solve for x:-
-78 -78
x = 102°, therefore m∠EFA = 102°.
A circle has a donated of 4.5cm a larger circle has a diameter of 24cm what is the aporximent diffrent in the circumference of the two circles
Answer:
difference ≈ 61.3 cm
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( d is the diameter ) , then
difference = 24π - 4.5π = 19.5π ≈ 61.3 cm ( to 1 dec. place )
Find the sum of the interior angle measures of a 14-gon.
The sum is___ degrees.
Step-by-step explanation:
the sum of interior angles in a triangle is 180°.
the sum of interior angles of a polygon, is the product of the number of triangles in the polygon (that can be created from a single vertex or corner via lines to all other corners) and 180°.
so, in reality, the number of triangles in each polygon is two less than the number of sides (because the lines to the 2 neighboring corners are sides and do not create triangles).
so the formula for the sum of all interior angles is
(n - 2) × 180
with n being the number of sides of the polygon.
in our case
(14 - 2) × 180 = 12×180 = 2160°
Naoya read a book cover to cover in a single session, at a rate of
55
5555 pages per hour. After reading for
4
44 hours, he had
330
330330 pages left to read.
How long is the book?
Answer:
550pages and 10 hours
Step-by-step explanation: