Answers
Given:
Radius of the cone = 6
Slant height of the cone = 10
To find:
The lateral area, surface area and volume of the cone.
Solution:
Let h be the height of the cone. By Pythagoras theorem, we get
[tex]10^2=(6)^2+h^2[/tex]
[tex]100=36+h^2[/tex]
[tex]100-36=h^2[/tex]
[tex]64=h^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{64}=h[/tex]
[tex]8=h[/tex]
The lateral area of a cone is:
[tex]A_L=\pi rl[/tex]
[tex]A_L=\pi (6)(8)[/tex]
[tex]A_L=48\pi[/tex]
The surface area of a cone is:
[tex]A_S=\pi rl+\pi r^2[/tex]
[tex]A_S=\pi (6)(8)+\pi (6)^2[/tex]
[tex]A_S=48\pi +36\pi[/tex]
[tex]A_S=84\pi[/tex]
Volume of cone is:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
[tex]V=\dfrac{1}{3}\pi (6)^2(8)[/tex]
[tex]V=\dfrac{288}{3}\pi [/tex]
[tex]V=96\pi [/tex]
Therefore, the lateral area of a cone is [tex]48\pi[/tex] sq. units, the surface area of a cone is [tex]84\pi[/tex] sq. units and the volume of the cone is [tex]96\pi[/tex] cubic units.
Related Questions
-6(2p + 1) = -7p - 31
Answers
Answer:
P=5
Step-by-step explanation:
-6(2p + 1) = -7p - 31
Expand -6(2p+1)
Apply distributive law;
a=-6, b=2p, c=1
=-6*2p+(-6)*1
=-6*2p-6*1
Simplify; -6*2p-6*1
=-12p-6
-12p-6=-7p-31
Add 6 to both sides;
-12p-6+6=-7p-31+6
simplify;
-12p=-7p-25
Add 7p to both sides;
-12p+7p=-7p-25+7p
Simplify;
-5p=-25
Divide both sides by -5
-5p/-5=-25/-5
Simplify:
p=5
Answered by the One and Only #DrippQueenMo
Answer:
p=5
Step-by-step explanation:
first you want to get rid of the parentheses in -6(2p+1) so take -6 and times it by 2p and 1 to get -12p-6. You can do this because of the distributive property. Now you have the equation -12p - 6 = -7p - 31. So now you want to get the p values on one side. Adding 7p to both sides of the equations get rid of the -7p. -12p + 7p equals -5p so now you have the equation -5p - 6 = -31. so now you need to get the whole numbers on one side. So add 6 to both sides so you can get rid of the -6. this leaves you with the equation -5p= -25. Now to find the value of p you divide both sides by -5. This gives you p = 5.
Explain the different ways you can name an angle. What are the different names for this angle?
Answers
Step-by-step explanation:
Hi,
This is an acute angle.
RST, STR, and TRS are the three different ways to represent/name this angle.
I hope this helps :)
In 1980 more than 35% of cars purchased had a manual transmission (i.e. stick shift). By 2007 the proportion had decreased to 7.7%. A random sample of college students who owned cars revealed the following: out of 133 cars, 31 had stick shifts. Estimate the proportion of college students who drive sticks with 90% confidence. Use a graphing calculator and round the answers to at least three decimal places. <
Answers
Answer:
The 90% confidence interval for the proportion of college students who drive sticks is (0.173, 0.293).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of college students who owned cars revealed the following: out of 133 cars, 31 had stick shifts.
This means that [tex]n = 133, \pi = \frac{31}{133} = 0.233[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.233 - 1.645\sqrt{\frac{0.233*0.767}{133}} = 0.173[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.233 + 1.645\sqrt{\frac{0.233*0.767}{133}} = 0.293[/tex]
The 90% confidence interval for the proportion of college students who drive sticks is (0.173, 0.293).
What is the volume of the rectangular pyramid ?
14 ft
9.5 ft
15 ft
Answers
9.5 ft
Step-by-step explanation:
trust in me pls I am serious this is the right answer
Which one is the correct answer..pls HELP a answer accurately..
Answers
Answer:
c
Step-by-step explanation:
$0.70 is the answer........
Look at the pattern shown below.
2, 4, 16, 256 ...
What is f(n+ 1) in terms of f(n), where n represents the position of a term in this pattern?
A. (F(n))^2
B. 2(f(n))
C. (F(n)-1)^2
D. 2(f(n)-1)
Answers
Answer: (a)
Step-by-step explanation:
Given
The pattern is 2, 4, 16, 256...
From the pattern, we can see that the next term is square of the previous i.e.
[tex]\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2[/tex][tex]\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2[/tex]
So, for the [tex]n^{th}[/tex] term, the function is [tex]f(n)[/tex]
For the next term, it is [tex]f(n+1)[/tex]
So,
[tex]\Rightarrow f(n+1)=[f(n)]^2[/tex]
Answer choices are
A.) x= 2 and x = -3
B.) x = 3 and x = 4
C.) -2 and x = -1
D.) -2 and x = 1
Answers
TIME REMAINING
58:47
The height of a cylinder is twice the radius of its base.
What expression represents the volume of the cylinder,
in cubic units?
2x
O4x?
О2лх
O x2 + 2x
O 2 + x
Answers
Answer:
I believe it should be C...............
NO LINKS
Mark wants to put a circular pool in his backyard. The pool has an area of 379.94 square feet. If his backyard is 10 x 15 feet, will the pool fit? Use 3.14 for pi
Answers
Answer:
no, the backyard is only 150 square ft. so a pool with an area of 379.94 square ft will not fit
Step-by-step explanation:
10×15=150
Please help ! Please help! I will heart you !
Answers
Answer:
x = 65
Step-by-step explanation:
x + 115 = 180
x = 65
Answer:
65 degrees
Step-by-step explanation:
180-115=65 degrees
The line that 115 degrees is on is equal to 180.
find equation of the line that contains the point (4,-2) and is perpendicular to the line y= _2x+8
Answers
Answer:
y = 1/2x - 4
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = -2x + 8. Its slope is -2. A line perpendicular to this one will have a slope of 1/2.
Plug this value (1/2) into your standard point-slope equation of y = mx + b.
y = 1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (4, -2). Plug in the x and y values into the x and y of the standard equation.
-2 = 1/2(4) + b
To find b, multiply the slope and the input of x (4)
-2 = 2 + b
Now, subtract 2 from both sides to isolate b.
-4 = b
Plug this into your standard equation.
y = 1/2x - 4
This equation is perpendicular to your given equation (y = -2x + 8) and contains point (4, -2)
Hope this helps!
9514 1404 393
Answer:
y = 1/2x -4
Step-by-step explanation:
We presume the given line is ...
y = -2x +8
This is in slope-intercept form, which allows us to determine easily that the slope of this line is -2.
A perpendicular line will have a slope that is the opposite reciprocal of -2:
m = -1/(-2) = 1/2
The y-intercept of the desired line can be found from the point (x, y) = (4, -2) using the equation ...
b = y - mx
b = -2 -(1/2)(4) = -4
Now, we know the slope and y-intercept of the desired perpendicular line through (4, -2), so we can write its equation as ...
y = 1/2x -4
__
Additional comment
"Slope-intercept form" is ...
y = mx + b . . . . . . where m is the slope and b is the y-intercept
Find the missing number if the following
subtraction is in base six
4 5 2
* * *
254
Answers
Question
The value of y varies directly as the cube of u and y = 54 when I = 3. Find the equation that represents this relationship.
Answers
Answer:
2x^3
Step-by-step explanation:
The equation that represents this relationship will be y = 2u³.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The value of y varies directly as the cube of u. y = 54 when u = 3.
y ∝ u³
Removed the proportionality constant and place the equal sign with constant k.
y = ku³
Put y = 54 when u = 3, then the value of k will be
54 = k (3)³
54 = 27k
k = 2
Then the equation that represents this relationship will be
y = 2u³
The equation that represents this relationship will be y = 2u³.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
please help me.......................
Answers
Answer:
do away withTrue[tex] \infty \infty [/tex]
True
B. 12th of April
a certain colony of bacteria begin with one cell and the population doubles every 20 minutes. What was the population of The Colony after 2 hours?
a. 6
b. 12
c. 32
d. 64
Answers
The population of The Colony after 2 hours is d. 64
How to determine the population?The given parameters are:
Initial, a = 1
Rate, b = 2 every 20 minutes
An exponential function is represented as:
y = ab^x
So, we have:
y = 1 * 2^x
y = 2^x
There are six 20 minutes in 2 hours.
This means that:
x = 6
So, we have:
y = 2^6
Evaluate
y = 64
Hence, the population of The Colony after 2 hours is d. 64
Read more about exponential functions at
https://brainly.com/question/2456547
#SPJ1
Identify the sets that contain 2 as an element. (Check all that apply.)Check All That Apply{2, 3, 4, 5, ...}{2, 3, 4, 5, ...}{0, 1, 4, 9, ...}{0, 1, 4, 9, ...}{ 2, {2} }{ 2, {2} }{ {2}, { {2} } }{ {2}, { {2} } }{ {2}, { 2, {2} } }{ {2}, { 2, {2} } }{ { {2} } }{ { {2} } }
Answers
Question:
Identify the sets that contain 2 as an element. (Check all that apply.)
[tex]A.\ \{2, 3, 4, 5, ...\}[/tex]
[tex]B.\ \{0, 1, 4, 9, ...\}[/tex]
[tex]C.\ \{2, \{2\} \}[/tex]
[tex]D.\ \{\{2\}, \{\{2\}\}\}[/tex]
[tex]E.\ \{\{2\}, \{2, \{2\}\}\}[/tex]
[tex]F.\ \{\{\{2\}\}\}[/tex]
Answer:
[tex]A.\ \{2, 3, 4, 5, ...\}[/tex]
[tex]C.\ \{2, \{2\} \}[/tex]
Step-by-step explanation:
Required
For which of the options is 2 an element
[tex]A.\ \{2, 3, 4, 5, ...\}[/tex]
The elements of this set starts from 2, then 3 and continues as thus.
Hence: 2 is an element
[tex]B.\ \{0, 1, 4, 9, ...\}[/tex]
From the given elements in the above set, 2 is not listed.
Hence: 2 is not an element of this set
[tex]C.\ \{2, \{2\} \}[/tex]
Here, 2 is listed as an element, 2 is also listed as a subset.
Since 2 is listed as an element, then 2 is an element of the set.
[tex]D.\ \{\{2\}, \{\{2\}\}\}[/tex]
Here, 2 is listed as a subset of {2} and also as a subset of subset of {{2}}.
Since 2 is not listed as an element itself, then 2 is not an element of the set.
[tex]E.\ \{\{2\}, \{2, \{2\}\}\}[/tex]
Here, 2 is listed as a subset of {2} and also as a subset of subset of {2,{2}}. This set only contains subsets, i.e. 2 is not listed as a direct element of the set.
Hence: 2 is not an element of the set
[tex]F.\ \{\{\{2\}\}\}[/tex]
Here, 2 is listed as a subset of subset of {{2}}. This set only contains subsets, i.e. 2 is not listed as a direct element of the set.
Hence: 2 is not an element of the set
Answer:
how
Step-by-step explanation:
how many squre deet of outdoor carpet will we need 11ft 3ft 2ft 3 ft
Answers
Answer:
39 sq feet
Step-by-step explanation:
Happy Paws charges $19.00 plus $4.50 per hour to keep a dog during the day. Woof Watchers charges $10.00 plus $5.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
Answers
Answer:
Hours are equal: 7.2
Cost of service are equal: 51.4
Step-by-step explanation:
Happy Paws:
y = 4.5h + 19
Woof Watchers:
y = 5.75h + 10
To solve for the hours are equal:
y = 4.5h + 19
y = 5.75h + 10 (Multiply by -1)
y = 4.5h + 19
-y = -5.75h - 10
0 = -1.25h + 9
-9 = -1.25h
h = 7.2
To solve for when the services are equal:
y = 4.5h + 19
y = 4.5(7.2) + 19
y = 32.4 + 19
y = 51.4
yuri completed a race in 0.88 fewer seconds than Josie. Josie's time was 23.95 seconds. How l9ng did it takes Yuri to complete the race?
Answers
Reason:
23.95-0.88= 23.07
HELPPPPPPPP NOWWWWWWW
Zack has 13 chains at 5 links each. He wants to combine them into a long chain by cutting and welding the fewest number of links. How many different links must be cut a welded.
Answers
Answer:
3
Step-by-step explanation:
There a 5 chains (each with 3 links). We take one chain and cut all three links. Now we are left with only four chains. This requires only 3 joints. Exactly the number of links I have. Therefore, the lowest number of cuts is three.
The number of different links must be cut a welded should be considered as the 3.
Calculation of the number of different links:Since
Zack has 13 chains at 5 links each. He wants to combine them
So here we considered only one chain and then cut off all 3 links
So the remaining should be four chains and it needs only 3 joints.
hence, The number of different links must be cut a welded should be considered as the 3.
Learn more about number here: https://brainly.com/question/24585170
Can somebody please help me with this whoever answers first gets a thanks and can you be quick please ❤️
Answers
A (-12, 14)
B (8, 8)
C (-12, -4)
D (0, -14)
E (14, 0)
F (0, 0)
Answer:
A (-12,14)
B ( 8,8)
C (-12,-4)
D (0,-14)
E (14,0)
F (0,0)
Step-by-step explanation:
(X,Y)
X coordinates go before Y coordinates in a given coordinate pair hope this helps!
Workout the probability that spinner A lands on 2 and spinner b does not land on b
Answers
Spinner diagram isn't attached. A related spinner diagram has been attached below to provide an hypothetical solution to the problem
Answer:
4 / 15
Step-by-step explanation:
For the numbered spinner :
P(landing on 2) = required outcome / Total possible outcomes
Total possible outcomes = (1, 2, 3) = 3
Required outcome = (1) = 1
P(landing on 2) = 1 /3
Lettered spinner :
P(does not land on b)
Total possible outcomes = (A, B, C, D, E)
Required outcome = (a, c, d, e)
P(does not land on b) = 4 / 5
Hence,
P(lands on 2, does not land on b) in this scenario is :
1/3 * 4/5 = 4 / 15
Tinley is training to run a half-marathon. She sets a pace so that every mile takes
7 minutes.
Write an equation for the amount of time,
t, it takes Tinley to run
m miles.
Answers
Answer:
t=7m
Step-by-step explanation:
In this equation, "t" represents time, and "m" represents miles. Each mile is 7 minutes. To find how much time this run will take her, multiple the amount of miles she will run by 7.
For example:
If Tinley runs 13 miles you should do-
7(13)= 91
13 miles would take Tinley 91 minutes
Paula runs a stable. 20 horses currently board at the stable, and 8 of them are bay.
What is the probability that a randomly chosen horse will be bay?
Write your answer as a fraction or whole number.
p ( bay ) = ?
Answers
Answer:
40% chance
Step-by-step explanation:
Take the number of horses total and divide the number of bay horses.
If the domain of f(n) = -4n - 3 is (-1, 1/4, 4), what is the range?
{-1, 2, -19)
{-7.-4.-13)
{1, -4, -19)
Answers
4. Dominick sent the following number of text messages each day over the last week:
SUN
MON
TUES
WED
THURS
FRI
SAT
64
58
63
51
60
61
70
What is the mean absolute deviation?
Explain what the mean absolute deviation represents in the situation:
Answers
plz help will give crown
Answers
Answer:
C
Step-by-step explanation:
Can I have crown
What is the value of w?
Answers
Answer:
180 - 35 - 74 = 71 degrees is the angle value that is right next to 35 degree angle.
35 + 71 = 106
180 - 106 = 74.
So w = 74 degrees.
x = 5 what is 6x equal
Answers
Answer:
6 x 5= 30
Step-by-step explanation:
6(5)=30
Help will award branliest
