A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the circumference of the circular base of the cone and = 120°. Find:
a. the angle between [A F] and the base of the cone
Answers
Answer:
The angle between [A_F] and the base of the cone = 68.2°
The area of the base of the cone ≈ 12.57 m²
Step-by-step explanation:
The given parameters are;
The height of the cone = 5 m
The base radius of the cone = 2 m
The angle which the A[tex]\hat O[/tex]C = 120°
Therefore, we have;
The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone
The angle between [CF] and the base of the cone = tan⁻¹(5/2) = tan⁻¹(2.5) ≈ 68.2°
∴ The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone = 68.2°
The angle between [A_F] and the base of the cone = 68.2°
The area of the base of the cone = π × r² = π × 2² = 4·π ≈ 12.57
The area of the base of the cone ≈ 12.57 m².
Related Questions
Use the calculator to evaluate the function y = 1 *2 - 2 for the given values of x.
x= 4, y =
x=6, y=
Answers
Answer:
when x= -4, y= 2
when x= 6, y =7
Step-by-step explanation:
We have the x values, so we can plug them in and solve. for the first problem, it becomes y =1/4 (-4)^2 -2
first we do the exponent
y= 1/4 (16) - 2
Then the multiplication
y= 4-2
then subtraction
y=2
For the second problem, it becomes y= 1/4 (6)^2 -2 We follow the same steps
y = 1/4 (36) - 2
y= 9-2
y= 7
The function y = 1 *2 - 2 for the given values of x are
when x= -4, y= 2
when x= 6, y =7
We have the x values, so we can plug them in and solve. for the first problem, it becomes y =1/4 (-4)² -2
First we do the exponent
y= 1/4 (16) - 2
Then the multiplication
y= 4 - 2
then subtraction
y = 2
For the second problem, it becomes y= 1/4 (6)² -2 We follow the same steps
y = 1/4 (36) - 2
y = 9 - 2
y = 7
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Lillian works 7hours each day for 5 days a week she earn £420 each week how much does she earn per hour
Answers
Answer:
£12 per hour
Step-by-step explanation:
7 × 5 = 35 hours
35 h : 420
1 h : x
x = 420×1 / 35
= £12 per hour
4x+5=6x-7
How do I solve this?
Answers
Answer:
x=6
Step-by-step explanation:
4x+5=6x-7
4x-6x=-7-5
-2x=-12
x=-12/-2
x=6
Answer: x=6
Isolate the variable by dividing each side by the factors that don't contain variables
reciprical of 17 plz and thank u
Answers
Answer:
the answer is 1/17
Step-by-step explanation:
whats 1000000000000000000000000x10000000000000000000000000
Answers
Answer:
I think my calculator broke and it gave me 1e49
Do you have a recipe that requires 1/3 cup of sugar, but you only want to make a fourth of the recipe how much sugar do you need to make this fraction of the recipe? A) 1/12 cups. B) 7/12 cups. C) 3/4 cups. D) 4/3.
Answers
Answer:
1/12
Step-by-step explanation:
i did 3x4=12 so you only need 1/12
152
Find the x of the angle
Answers
Intro:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
So first we will do 180-152 to get the measure of the angle besides the angle. That'll give us 28, then we know that those base angles of this mini triangle are congruent so we will do 28+28 to get 56. Now we will do 180-56 to get the last angle of the triangle, which is 124. And this angle is the same as the angle with x because they are corresponding angles so x is 124°.
if f(x)=3^x+10x and g(x)=5x-3, find (f-g)(x)
Answers
-5.8 + -2.2= a positive number
Answers
Answer:
it would be negative (-8)
Step-by-step explanation:
-5.8 + -2.2 = -5.8 - 2.2
this would result in a negative number (-8)
Consider the diagram.
Lines AC and RS can best be described as
intersecting.
parallel.
perpendicular.
skew.
Answers
Answer:
Scew option D
Step-by-step explanation:
I have the same test
When lines are not parallel, and they do not intersect, such lines are said to be skewed.
Line AC and RS are skew.
From the diagram, we have two planes.
Plane x Plane yLine AC is on plane x, while line RS is on plane y.
This means that both lines are non-coplanar
Planes x and y are not parallel; so lines AC and RS are not parallel.
Using the condition of skewness stated above, we can conclude that line AC and RS are skew.
See attachment for plane x and plane y
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The prices for different lengths of ribbon sold at a fabric store are shown in the table.
Which statement BEST justifies whether or not the relationship between the length and price represents a function?
A.
This relationship does not represent a function because it relates inches and dollars.
B.
This relationship represents a function because no length of ribbon has more than one price.
C.
This relationship represents a function because the price per inch decreases as the length of ribbon increases.
D.
This relationship does not represent a function because the prices of different lengths of ribbon are all different.
Answers
Answer:
B. This relationship represents a function because no length of ribbon has more than one price.
Step-by-step explanation:
A relation is considered as a function when there is exactly just one possible range value that any of the domain value can give. In order words, each domain value of a function cannot have more than one range value.
In the given table of values representing the length and price of ribbon, the domain includes all the set of lengths of the ribbon while the range is the set of the corresponding prices the lengths can cost.
Thus, each length given has exactly just one price. No particular length has more than one price. Therefore, we can consider this as a function.
Plz help me
Last year, 75 new houses were built in a neighborhood. So far this year, 5/8 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
Answers
What is -6x+4x in standard form? This is due today and I never understand these
Answers
Answer:
-2x would be the answer
Step-by-step explanation:
You have to combine like terms.
Find the slope of the line passes through (1,4) and (9,1)
Answers
Answer:
-0.375
Step-by-step explanation:
Way one(the harder one):
Let the line which passes through (1,4) and (9,1) be f(x)=kx+b
Sub (1,4) and (9,1) in and we get [tex]\left \{ {{4=1k+b} \atop {1=9k+b}} \right.[/tex]
=> (9k+b)-(k+b)=1-4
8k=-3
k=-3/8 or -0.375
Therefore the slope of the line is -3/8 or -0.375
Way two(the easier one):
k= [tex]\frac{change in y}{change in x}[/tex] = [tex]\frac{1-4}{9-1}[/tex] = -[tex]\frac{3}{8}[/tex]
HELP ASAP!!!
Select all that apply.
Which of the following statements are true of the greatest common factor of two numbers?
O Each number must share the factor.
O The number must be large.
O The greatest common factor could be 1.
O The number must be the largest factor both numbers share.
Answers
Answer:
the second answer is wrong, and the rest is all correct
Step-by-step explanation:
The GCF has to be the largest factor they share, but it's not necessary for it to be large.
Answer:
each number must share the factor.
the greatest common factor could be one.
the number must be the largest factor both share.
Step-by-step explanation:
Six friends shared 79 trading cards and kept a record of how they did it. What does 13 represent? the answers are- The number of trading cards each friend ended up with The number of trading cards left after each friend got the same amount The number of trading cards left after each friend got 10 The number of friends sharing trading cards
Answers
Answer: The number of trading cards each friend ended up with
Step-by-step explanation:
Given that:
Total Number of trading cards = 79
Number of friends = 6
Number of trading cards each friend got of shared equally :
Total Number of trading cards / number of friends
= 79 / 6
= 13.166
Highest number of cards got by each = 13
Number left : 79 - (13 * 6) = 1
Hence, 13 represents the number of trading cards each friend ended up with
Hotel A charges $140 and an additional $10 per person. Hotel B charges $80 and an additional $20 per person. Write an equation that will help determine how many people must rent the room for the charges to be the same?
Answers
Answer:
2 people must rent the room in hotel B to make the charges the same
Step-by-step explanation:
A bookstore sells textbooks for $80 each and notebooks for $4 each. Th
bookstore would like to sell $800 in merchandise by the end of the week
write a linear equation that describes the problem
Answers
Answer:
the equation is 80×9=720 20×4=80 and if you add them together you get 800
Am I correct, if not please explain the correct answer.
Answers
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No buddy you are wrong .
Look ;
(( Left table )) :
[tex] \frac{y}{x} = 6 \\ [/tex]
[tex] \frac{48}{8} = 6 \\ [/tex]
[tex] \frac{60}{10} = 6 \\ [/tex]
[tex] \frac{72}{12} = 6 \\ [/tex]
Thus it is proportional .
_________________________________
(( Right table )) :
[tex] \frac{y}{x} = \: .... \\ [/tex]
[tex] \frac{12}{6} = 2 \\ [/tex]
[tex] \frac{28}{7} = 4 \\ [/tex]
[tex] \frac{68}{8} = 8 \\ [/tex]
_________________________________
Thus the left table is proportional and
y is 6 times x in it.
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I need help plz someone help me plz :(
Answers
Mr. Brooks has $14.20 in his checking account, he uses
his debit card to buy four Sonic meal deals for $4.25 each. His
bank charges him a $20 overdraft fee for insufficient funds.
What is the new balance in Mr. Brooks’ checking account?
Answers
Answer:
-$22.80.
Step-by-step explanation:
The 4 meals cost 4.25 * 4 = $17 which gives him a new balance of
14.20 - 17 -20
= -$22.80.
Which representations have the same rate of change of y with respect to x as the slope -0.5?
I really need help!
The last option is "All of the above"
Answers
Answer:
All of the above
Step-by-step explanation:
Hay 323232 delanteros y 808080 defensas en la liga de baloncesto de Leo. Leo debe incluir a todos los jugadores en un equipo y quiere que cada equipo tenga el mismo número de delanteros y el mismo número de defensas. Si Leo crea el mayor número de equipos posible, ¿cuántos defensas habrá en cada equipo?
Answers
Answer:
5 defensores
Step-by-step explanation:
La pregunta correcta es la siguiente;
Hay 32 delanteros y 80 defensas en la liga de baloncesto de Leo. Leo debe incluir a todos los jugadores en un equipo y quiere que cada equipo tenga el mismo número de delanteros y el mismo número de defensas. Si Leo crea el mayor número de equipos posible, ¿cuántos defensas habrá en cada equipo?
Responda como sigue;
Ahora queremos saber el número de defensas que deberíamos tener por equipo.
La respuesta a esta pregunta es simplemente encontrar la relación entre el número de delanteros y el número de defensores.
matemáticamente,
eso sería 32:80 = 2: 5 Entonces esto significa que por cada 2 delanteros en un equipo, debería haber 5 defensores
through: (0, 4) and (−2, −4)
Answers
Answer:m=4
Step-by-step explanation:Use the slope formula. The set up would be -4-4/-2-0. This gives us -8/-2 which you can simplify to 4.
Alecia placed the numbers 0, 2, 14, -8, and -11 on the number line. Which of the numbers is furthest from zero?
Answers
Answer:
14
Step-by-step explanation:
Which number below has a value between 6.6 and 6.7?
Answers
The correct answer for this question is .1.
A car wash washes 68 cars in 8 hours. At this rate, how many cars are washed in 1 hour?
Answers
Answer:
8.5 (If just pure cars then 8.)
Step-by-step explanation:
To find this, just divide 68/8 to find how many cars are washed in an hour. Plugging it into a calculator, we find out that it is 8.5. If you need elaboration, just comment.
Which of the following statements cannot be assumed from the diagram?
Answers
Answer:
Can you give me any more context?
which statement about the following system of inequalities is true? y-2x<2.5
Answers
Haha a good day
What is the slope of the function?
-6
-4
4
6
Answers
Answer:
-6
Step-by-step explanation:
TO find the slope pick two points and do y2 - y1 / x2 - x1
I picked the first two:
2 - 8/ -1 - -2 = -6/ 1 = -6
The slope of the given line is - 6 as per slope-intercept form.
What is the slope of a straight line?The linear equation y = mx + c represents the slope-intercept form of a line passing through the point (x, y).
Here, 'm' is the slope and 'c' is the y-intercept of the given line.
The slope of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:
m = (y₂ - y₁)/(x₂ - x₁)
Therefore, the slope of a line that passes through (-2, 8) and (-1, 2) is
= (2 - 8)/[- 1 - (- 2)]
= - 6/1
= - 6
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