It would be +2 so -3+2=-1, -1+2=1, 1+2=3
Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle with vertices ( 0 , 0 ) , ( 1 , 0 ) , and ( 0 , 8 ) around the y -axis.
The exact volume of a general Cone is [tex]\frac{8\pi}{3}[/tex]
To solve this problem, we will make use of the second theorem of Pappus. This theorem is concerned with finding the volume produced when a plane shape is rotated around an axis ( the volume of the solid of revolution ).
The theorem states:
The volume of a solid of revolution obtained by rotating a lamina F (the triangle) about a non-intersecting axis (the y-axis) lying in the same plane is equal to the product of the area A of the lamina F and the distance d traveled by the centroid of F.
That is
[tex]V=A\times d[/tex]
When the centroid travels, it forms a circumference d given by,
[tex]d=2\pi r[/tex]
Therefore
[tex]V=A\times 2\pi r[/tex]
From the diagram below,
The vertices (or, corners) of the triangle are A(0, 0), B(1, 0), and C(0,8).
G is the centroid of the triangle. The centroid of the triangle is the geometric center of the triangle. The centroid would be the balance point if a pin were to be used to balance the triangle.
r is the distance from the centroid to the axis of rotation ( the y-axis in this case). It is like saying the radius of rotation.
The things we need to find are A (the Area) and r.
Calculate A:
[tex]A=\frac{1}{2} \left| \Delta \right|[/tex]
[tex]\Delta = \left|\begin{array}{cc} x_{B}-x_{A} & y_{B}-y_{A} \\ x_{C}-x_{A} &y_{C}-y_{A}\end{array}\right|= \left|\begin{array}{cc} 1-0 & 0-0 \\ 0-0 & 8-0\end{array}\right|= \left|\begin{array}{cc} 1 & 0 \\ 0 & 8\end{array}\right|[/tex]
[tex]\Delta =8\times 1 -0\times 0=8[/tex]
[tex]A=\frac{1}{2} \left|8\right|=\frac{1}{2}\times 8=4[/tex]
Calculate r:
[tex]r=\overline{x}=\frac{x_A+x_B+x_C}{3}=\frac{0+1+0}{3}=\frac{1}{3}[/tex]
Finally, Calculate the volume, V:
[tex]V=A\times 2\pi r=4 \times2\pi\times\frac{1}{3}=\frac{8\pi}{3}[/tex]
Learn more about centroids: https://brainly.com/question/20305516
13. Amy will rent 10 different movies this month.
•A one-day rental fee is $1.50.
A monthly pass is $10.00. (Unlimited visits during the month)
How much money will Amy save by buying a monthly pass?
Please help I will give you brainless please
Answer:
35
Step-by-step explanation:
1.5x30=45 -
45-10= 35
month=30 days
Movie costs 1.5 for a day and it will cost 10 for a month so you have to do 1.5x30=45 then you have to subtract 10 becuses that's the monthly pay so your answer would be 35 please (give brainless)
Find sine, where is the angle shown.
Give an exact value, not a decimal approximation.
Answer:
[tex] \sin( \theta) = \frac{opp}{hyp} \\ {c}^{2} = {a}^{2} + {b}^{2} \\ {c}^{2} = {8}^{2} + {15}^{2} \\ = 64 + 225 = 289 \\ c = \sqrt{289} \\ c = 17 \\ \sin( \theta) = \frac{15}{17} = 0.882 \\ \theta = { \sin}^{ - 1} (0.882) \\ \theta = 66.88 \degree\approx 67\degree[/tex]
Last month, Donovan ran 48 miles. James ran m miles. Donovan ran 3 times as far as James. Which equation can be used to find m, the number of miles James ran?
Answer:
45
Step-by-step explanation:
78
Write the angles of DEF in order from smallest to largest
Answer:
F, D, E
Step-by-step explanation:
the smallest angle is opposite the smallest side, the largest angle is opposite the largest side, etc.
Natalie is a real estate agent and earns a 3% commission on all homes she sells. She estimates that she will earn $8,250 on the next house she sells. She actually earns $9,210. What was Natalie’s estimate for the selling price of the home? What was the actual selling price of the home?
Using the percentage principle, the estimated and actual sale price of the Home are $275, 000 and $307,000 respectively.
Commission on sale = 3%Estimated commison = $8250
Let Estimated sale price = P
3% × P = 8250
0.03p = 8250
p = 8250 / 3
p = $275000
Actual commission earned = $9210
Let Actual sale price = P
3% × P = 9210
0.03p = 9210
p = 9210 / 3
p = $307,000
Therefore, the estimated and actual sale price are $275,000 and $307,000 respectively.
Learn more : https://brainly.com/question/18112348
Sandra transforms a line segment such that the new image is longer than the original line segment. What type of transformation must the line segment have undergone?
A. dilation
B reflection
C rotation
E translation
The type of transformation must the line segment have undergone if Sandra transforms a line segment such that the new image is longer than the original line segment, is dilation, so option A is correct.
What is dilation?The process of dilation entails scaling or changing a thing. It is a transformation that uses the specified scale factor to make the objects smaller or larger.
Given:
Sandra transforms a line segment such that the new image is longer than the original line segment,
The above transformation is an example of dilation, as in dilation the image can be transformed into a large image or a small image,
Thus, the given transformation is an example of dilation.
To know more about dilation:
https://brainly.com/question/13176891
#SPJ6
The basketball team scored 49 points in thechampionship game. This is 12 points more than
half of their score in the first round game. How many points did the team score in their first round game?
pls help asap i rly need this
Answer:
THey are countin by 2 and 5 on the graph
Step-by-step explanation:
What is the total price of a $45.79 item when a 7% sales taxe is added
Answer:
The total price after tax is $48.99
Step-by-step explanation:
Answer:
you have to put the 45.79/ 7% That's the taxes and you have to check your work first if you get something else different than a higher number you divide it again in long division and then if that doesn't work try to multiply in decimals
Does the graph represent a function that has an inverse function
9514 1404 393
Answer:
No
Step-by-step explanation:
A horizontal line can be drawn that intersects the graph in more than one place. That means the graph fails the "horizontal line test" and does not have an inverse function.
(The horizontal line shown intersects in 3 places.)
Ana starts eating lunch at 12:15 pm she finishes eating lunch 49 mins later what lock shows the time that Ana finishes eating lunch
Answer:
What kind of problem? Multiplication? Division? What?
Step-by-step explanation:
2x=16−2 Value of x ?
Answer:
x = 7
Step-by-step explanation:
2x = 16 - 2
2x = 14
x = 14 / 2
x = 7
Answer:
[tex]\sf\longmapsto \: x = 7[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 2x = 16 - 2[/tex]
[tex]\sf\longmapsto \: 2x = 14[/tex]
[tex]\sf\longmapsto \: x = \frac{14}{2} [/tex]
[tex]\sf\longmapsto \: x = 7[/tex]
Hello, need help on this (:
The answer is attached below
Answer:
he anwersed so hello
Step-by-step explanation:
Which linear function represents the line given by the point-slope equation y-8 = 1/2(x – 4)?
O f(x) = 1/2x + 4
Of(x) = 1/2x + 6
O f(x) = 1/2x-10
Of(x) = 1/2x-12
Answer:
y = 1/2x + 6
Step-by-step explanation:
y - 8 = 1/2 (x - 4)
y - 8 = 1/2x - 2
y = 1/2x -2 + 6
Four students are training for their cross country team at school. They were told to run for as long as they could without stopping. The coach measured their total distances and their overall time. Calculate the average speed for each student and find the two students who tied for the same average speed.
A) Brev and Chris
B) Brev and leslie
C) Chris and Dylan
D) Dylan and Leslie
Answer:
C) Chris and Dylan
Step-by-step explanation:
Find the measure of angle B
tyler swims at constant speed, 5 meters every 4 seconds. how long does it take him to swim 114 meters?
28.5 seconds
cuz 114 ÷ 4 = 28.5 = 28.5 × 4 = 28.5
hope it will help u
Answer:
91.2 secondsStep-by-step explanation:
5 m = 4 second
1 m = 4/5 second
1 m = 0.8 second
∴ 114 m = 114 x 0.8
= 91.2 seconds.
Brainliest would be really appreciated if it helped :)
A. 23.7
B. 8.7
C. 13.8
D. 9.5
Answer:
a
Step-by-step explanation:
just cuzyfhyf
15. Enter the missing digit to complete the subtraction statement
2 5 4, 8 1 7
- 1 3 _, 1 2 5
__________
1 1 8, 6 9 2
8.618 divided by 0.695
Answer:
8.618 divided by 0.695= 12.4
hope this helps <3
I will mark brainlist please help!!
- dilation (lesson)
1) in a dilation of a figure, the distance between two consecutive vertices does not change
• true
• false
2) the coordinates of the vertices of a triangle JKL are J (4,8) K (8,8) L (4,2). Find the coordinates of the vertices of the image after a dilation by K = 0.25
• J (2,1) K (2,2) L (1,2)
• J (-2,1) K (4,2) L (1,0.5)
• J (1,2) K (2,2) L (1,0.5)
133.5 divided by 5 show work
Answer:
26.7
Step-by-step explanation:
Use a c a l c u l a t o r :P
What is the value of m?
42.78/m=93
Answer:
m=0.46
Step-by-step explanation:
Answer:
m=42.78÷93
m=0.46
Step-by-step explanation:
please mark me as brainlest
Thomas, a waiter at a local restaurant, is paid $ 4 an hour plus tips. His friend Marie works at a local bookstore for $12 an hour. Marie and Thomas worked the same number of hours. If Thomas made $120 in tips and both made the same amount of money, how many hours
1.please just give me the first step on how it’s written out
Answer:
15 hours
Step-by-step explanation:
Let h = numbers of hour worked, x = tips, t = Thomas' pay, and m = Marie's pay
We can set up an equation for this question:
t = 4h + x
Now plug in 120 for x
t = 4h + 120
Now we set up Marie's pay:
m = 12h
Since Thomas and Marie made the same amount of money over the same number of hours, we can say:
4h + 120 = 12h
120 = 8h
h = 15
This means they both worked for 15 hours.
A pet store has 7 cats. Here are their weights (in pounds).
8, 15, 11, 10, 11, 6, 7
Send data to calculator
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
add 8,15,11,10,11,6,7 then the answer you get divide by 7
Answer:
The answer that has been rounded by the tenths is 9.7
What is the difference of 18 - 10 2/8 ?
Answer:
7 3/4
Step-by-step explanation:
[tex]18 - 10\frac{2}{4}[/tex] [tex]18 - 10\frac{1}{4}[/tex] [tex]18 - \frac{41}{4}[/tex] [tex]\frac{72}{4} - \frac{41}{4}[/tex] [tex]\frac{31}{4}[/tex] [tex]7\frac{3}{4}[/tex]2. Carlie graphed a line with a negative slope.
What must be true about the graph?
a. The graph decreases from left to right.
b. The graph increases from left to right.
c. The graph must cross (0,0).
d. The graph must be contained in Quadrants
III and IV.
Answer:
A. The graph decreases from left to right
What is the equation of the line shown on the graph?
A y=x
B y=4x
C Y= -x
D Y =1/4 X
Find the distance between the points (6,3) and (-1,-6).
Answer:
All you need is the distance formula. The distance betwen two points
(x1,y1) and (x2,y2) is d= sqrt((x2-x1)2 + (y2-y1)2)
plugging in the values we get:
d= sqrt((6-(-6))2 + (6-1)2)
= sqrt((6+6)2+52)
= sqrt(144+25)
= sqrt(169)
= 13
Answer:
[tex]\sqrt{130}[/tex]
Step-by-step explanation:
6 - (-1) = 7
3 - (-6) = 9
7^2 + 9^2 = c^2
49 + 81 = c^2
c^2 = 130
