Answer:
The volume of the cone with the same radius and height as the given cylinder is approximately [tex]\(459.325 \, \text{cm}^3\)[/tex].
Explanation:
To find the volume of a cone with the same radius and height as the given cylinder, we'll use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Given that the cylinder has a volume of 1884 cm³, and the radius [tex](\(r\))[/tex] and height [tex](\(h\))[/tex] of the cone are the same as the cylinder, we can first find the radius and height of the cylinder.
The volume of the cylinder is given by:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
Given [tex]\(V_{\text{cylinder}} = 1884 \, \text{cm}^3\)[/tex], we can solve for [tex]\(r^2 h\)[/tex], the product of the square of the radius and the height:
[tex]\[ r^2 h = \frac{1884}{\pi} \][/tex]
Now, we need to find the radius and height of the cylinder. Since we're told that the cone has the same radius and height as the cylinder, we can use these values for the cone as well.
[tex]\[ r^2 h = \frac{1884}{\pi} \][/tex]
Given that [tex]\( r = h \)[/tex], we can substitute [tex]\(r\)[/tex] for [tex]\(h\)[/tex] to get:
[tex]\[ r^3 = \frac{1884}{\pi} \][/tex]
[tex]\[ r = \sqrt[3]{\frac{1884}{\pi}} \][/tex]
Now that we have the value of [tex]\(r\)[/tex], we can find the volume of the cone using the formula for the volume of a cone:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \left( \sqrt[3]{\frac{1884}{\pi}} \right)^2 \left( \sqrt[3]{\frac{1884}{\pi}} \right) \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \left( \frac{1884}{\pi} \right)^{2/3} \left( \frac{1884}{\pi} \right)^{1/3} \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \left( \frac{1884^2 \cdot 1884}{\pi^2} \right)^{1/3} \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \left( \frac{1884^3}{\pi^2} \right)^{1/3} \][/tex]
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi \left( \frac{671161856}{9.869604401} \right)^{1/3} \][/tex]
[tex]\[ V_{\text{cone}} \approx \frac{1}{3} \pi \left( 67968372.82 \right)^{1/3} \][/tex]
[tex]\[ V_{\text{cone}} \approx \frac{1}{3} \pi \cdot 438.327 \][/tex]
[tex]\[ V_{\text{cone}} \approx 459.325 \, \text{cm}^3 \][/tex]
What is the surface area of the figure below? Use 3.14 for Pi.
Answer:
132.52 [tex]cm^{2}[/tex]
Step-by-step explanation:
radius=3
Area of circle= 3.14x3 squared
=28.26
28.26x2=56.52
area of rectangle=76
The surface area of the composite figure will be 136.52 square cm.
What is the area?The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The area is a combination of the area of the rectangle and the area of the circle. Then we have
A = L x W + 2 x πr²
The radius, length, and width will be 3 cm, 20 cm, and 4 cm, respectively.
The area is calculated as,
A = 20 x 4 + 2 x 3.14 x 3 x 3
A = 80 + 56.52
A = 136.52 square cm
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Solve the following inequality: 6x - 9 ≥ 11x - 17.
1. x<=5/8
2.x>=8/5
3.x>=5/8
4.x<=8/5
Answer:
x ≤8/5
Step-by-step explanation:
6x - 9 ≥ 11x - 17
Subtract 6x from each side
6x -6x-9 ≥ 11x - 17-6x
-9 ≥ 5x- 17
Add 17 to each side
-9+17≥ 5x - 17+17
8≥ 5x
Divide each side by 5
8/5≥ 5x /5
8/5≥ x
whats 4×5/8 please help
Answer:
5/2 = 2 1/2 = 2.5
Step-by-step explanation:
4 * 5/8 = 4/1 * 5/8 = (5 * 4)/(1 * 8) = 20/8 = 5/2 = 2 1/2 = 2.5
Answer is 2.5 because 4 times 5 is 20 and 20 divided by 8 is 2.5
Find the distance between the points (4, 2) and (-5, 3).
Hope this will help u....
Given the sequence.
125, 25, 5, ...
Write the rule an using the geometric sequence formula:
The given sequence follows a geometric pattern, and the common ratio is 0.2. Using the geometric sequence formula, we can find any term in the sequence by substituting the values into the formula.
Explanation:The given sequence 125, 25, 5, ... follows a geometric pattern where each term is obtained by multiplying the previous term by a common ratio. To find the common ratio (r), we divide any term by its previous term. Let's divide 25 by 125 to find the common ratio: r = 25/125 = 1/5 = 0.2.
Now that we have the common ratio, we can use the formula for a geometric sequence:
aₙ = a₁ × r(n-1)
Here, aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the term number. Since the first term (a₁) is 125 and the common ratio (r) is 0.2, we can substitute these values into the formula to find the nth term.
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The rule for the given geometric sequence 125, 25, 5, ... is an = 125 × 5(n-1).
Explanation:The given sequence is 125, 25, 5, ...
To find the rule using the geometric sequence formula, we need to determine the common ratio. The common ratio is found by dividing any term by its previous term. Let's take the first two terms: 125/25 = 5. So, the common ratio is 5.
The formula for a geometric sequence is given by: an = a¹ × r⁽ⁿ⁻¹⁾, where an is the nth term, a¹ is the first term, r is the common ratio, and n is the position of the term.
Using this formula with the first term (a¹ = 125) and the common ratio (r = 5), we can find the rule for the sequence. Let's find the rule for the third term: a³ = 125 × 5⁽³⁻¹⁾ = 125 × 5² = 125 × 25 = 3125.
Therefore, the rule for the sequence is: aⁿ = 125 × 5⁽ⁿ⁻¹⁾.
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What is the mode of 50,60,80,60,70,55,85,70,90,50
Answer:
50, 60, 70
Step-by-step explanation:
The mode is the value that appears the most:
2 50s
2 60s
1 80s
2 70s
1 55s
1 85s
1 90s
The modes are 50, 60, and 70
Answer:
The mode is 50,60,70
Step-by-step explanation:
They are the numbers that repeat themselves multiple times but they all repeat the same amount so all 3 are correct
The distance between the points (-3,4) and ( 5,4)
Application of the Pythagorean theorem
so the answer is 8 units.
Hope this will help u...
In circle N, KL ≅ ML. Circle N is shown. Line segments N J, N M, N L, and N K are radii. Lines are drawn to connect each point on the circle to create secants J M, M L, L K, and K J. M L and K L are congruent. The measure of arc J K is (5 x + 24) degrees, the measure of arc J M is (13 x + 2) degrees, the measure of arc M L is (8 x minus 3) degrees, and the measure of arc K L is (7 x + 7) degrees. What is the measure of Arc J M? 77° 90° 132° 154°
Answer:
[tex]arc\ JM=132^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
we know that
[tex]arc\ JM+arc\ ML+arc\ LK+arc\ KJ=360^o[/tex] ----> by complete circle
substitute the given values
[tex](13x+2)^o+(8x-3)^o+(7x+7)^o+(5x+24)^o=360^o[/tex]
solve for x
[tex](33x+30)^o=360^o\\33x=360-30\\33x=330\\x=10[/tex]
step 2
Find the measure of arc JM
[tex]arc\ JM=(13x+2)^o[/tex]
substitute the value of x
[tex]arc\ JM=(13(10)+2)^o=132^o[/tex]
Answer:
132 maybe
Step-by-step explanation:
Solve for x: d 28−x 7+x +8=14
Can someone pls answer this thanks
Answer:
64 pi
Step-by-step explanation:
divide 50.24 by 3.14 to find diameter
16 = diameter
8 = radius
Area = 8^2 pi = 64 pi
Answer:
A=200.96
Step-by-step explanation:
How will the graph of line y = -3x+8 be affected if the 8 is changed to -3?
A. The y-intercept will be moved 3 units downward.
B. The y-intercept will be moved 5 units downward.
C. The y-intercept will be moved 11 units downward.
D. The x-intercept will be moved 3 units to the left.
E. The x-intercept will be moved 11 units to the left.
Answer:
C
Step-by-step explanation:
A y intercept lies on the y axis.
This means that the movement will happen with the y intercept, on the y axis.
8 is the original y intercept.
It is now changed to -3.
-3 is lower than 8 on the y axis so we are moving downward.
Now, to find the number of squares it moves, we can find the difference between 8 and -3.
8-(-3)=11
Therefore, The y-intercept will be moved 11 units downward.
Answer:
C.
Step-by-step explanation:
The -3x tells you the slope (rise/run). In this case, it will go downward because it is negative. It will have a slope of 3/1. The +8 or -3 is the y intercept and tells which direction the original line will go from its' starting point. So you would add those together to know which way the line moves.
which binomials below is a factor of this trinomial, x^2 - 6x - 16
I WILL MARK BRAINLIEST
Answer:
(x - 8) and (x + 2) are both factors
Step-by-step explanation:
Given
x² - 6x - 16
Consider the factors of the constant term (- 16) which sum to give the coefficient of the x- term (- 6)
The factors are - 8 and + 2, since
- 8 × 2 = - 16 and - 8 + 2 = - 6, thus
x² - 6x - 16 = (x - 8)(x + 2)
Answer:
x + 2
Step-by-step explanation:
Just took the quiz
A coordinator will select 4 songs from a list of 11 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
The number of different possible line ups are; 4,233,600
What is permutation and combination?
We are told that;
List of songs = 11 songs
Number of songs to be selected = 4 songs
Thus, the number of different possible line ups is gotten from permutation formula as;
¹¹P₇ = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 = 4,233,600
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Answer:
answer is 7920
somehow you miscalculated
One month Donna rented 5 movies and 6 video games for a total of $48. The next month she rented 3 movies and 2 video games for a total of $18. Find the
rental cost for each movie and each video game.
Rental cost for each movie: s]
x
5
?
Rental cost for each video game: S
Answer:
Cost for each movie: $1.50 Cost for each video game: $6.75
Step-by-step explanation:
Let x be the cost (in dollars) of renting a movie.
Let y be the cost (in dollars) of renting a video game.
The total cost of renting 3 movies and 2 video games is +3x2y dollars.
We're given that this total cost is $18, so we have =+3x2y18.
The total cost of renting 5 movies and 6 video games is +5x6y dollars.
We're given that this total cost is $48, so we have =+5x6y48.
Therefore, we get the following system of equations.
=+3x2y18
=+5x6y48
Multiplying the first equation by −3 and adding gives us the following.
−9 x− 6 y = −54 5 x+ 6 y = 48 −4 x+ 0 y = −6
So we get the equation =−4x−6.
Solving for x, we get the following.
=x1.5
To find y, we can substitute 1.5 for x in =+3x2y18, the first equation in the system.
Then we solve for y.
+31.52y =18
+4.52y =18
2y =13.5
y =6.75
So, we have found that =x1.5 and =y6.75.
This means that the rental cost for each movie is $1.50 and the rental cost for each video game is $6.75.
D(1) =3
D(n) = d(n-1)-14
Answer:
D(1)=3
Step-by-step explanation:
Answer:
The 3rd term is -25
Step-by-step explanation:
This is a recursive formula. It tells us that the first term is 3 and that the common difference is -14.
d(1)=3
d(2) = d(1) -14 = -11
d(3) = d(2) - 14 = -25
The 3rd term is -25
Which number line plots the integers –12, -3, and 7?
Answer:
A
Step-by-step explanation:
It’s just a rough estimate, but using reasoning that -12 is between-10 and -15, -3 is found between 0 and -5, and 7 being between 5 and 10
Which of the following are alternate interior angles? Select all that apply.
A.
∠5 and ∠4
B.
∠6 and ∠5
C.
∠2 and ∠8
D.
∠8 and ∠1
E.
∠3 and ∠5
Answer:
C & E
Step-by-step explanation:
∠3 and ∠5 are alternate interior angles
∠2 and ∠8 are alternate interior angles
What is the area of the sector that is NOT shaded?
a. 80 pi units2
b. 16 pi units2
c. 20 pi units2
d. 8 pi units2
PLEASE HURRY!! I HAVE LIMITED TIME!! :)
Answer:
area of the shaded sector
= 72°/360°π(10)²
= 0.2×100π. sq. units
=20π sq. units
area of the not shaded region=π(10)²-20π
= (100-20)π = 80π sq. units
A market sels 6 cans of food for every 7 boxes of food. The market sold a total of 26 cars and bones today. How many of
each kind did the market sel?
O 6 cars and 20 boxes
O 12 cans and 14 boxes
14 cans and 12 boxes
20 cans and 6 boures
Answer:
12 Cans and 14 boxes
1. How are sine functions connected to the unit circle?
2. How are cosine functions connected to the unit circle?
Answer:
1) The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle.
2) The secant function is the reciprocal of the cosine function (secx=1cosx) x = 1 cos .The co-secant function is the reciprocal of the sine function (cscx=1sinx) x = 1 sin . It can be found for an angle t by using the y -coordinate of the associated point on the unit circle: csct=1y t = 1 y .
Step-by-step explanation:
Final answer:
Sine and cosine functions are related to the unit circle with their values representing the y and x coordinates of a point on the circle, respectively. They oscillate between +1 and -1, repeating every 2π radians and are used to model simple harmonic motion, differing by a phase shift of π/2 radians.
Explanation:
The sine and cosine functions are directly related to the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate system. When an angle θ is drawn from the positive x-axis, the coordinates of the point where the terminal side of the angle intersects the unit circle are (cos θ, sin θ).
For the sine function, think of it as projecting the point on the unit circle onto the y-axis. This projection gives the y-coordinate, which is the sine of the angle θ. Therefore, the sine function oscillates between +1 and -1 as the angle θ increases, repeating every 2π radians because this is the circumference of the unit circle.
Similarly, the cosine function is obtained by projecting the point onto the x-axis, providing the x-coordinate or the cosine of the angle θ. It also oscillates between +1 and -1 and repeats every 2π radians. Both sine and cosine functions describe simple harmonic motion when modeling periodic phenomena, and they differ by a phase shift of π/2 radians.
The initial conditions of a sine function with zero phase shift are that the function starts at 0, indicating that, for simple harmonic motion, the initial position is at equilibrium. With a cosine function, the initial value is 1 when the phase shift is zero, indicating that the motion starts at its maximum displacement. This concept can also be used to model wave functions and determine scalar components using triangles.
Line B is 55 cm long. It is an enlargement of Line A which is 5 cm long. What is the scale factor of the enlargement?
Answer:
11
Step-by-step explanation:
Line B is an enlargement of Line A, which is 5 cm long. Let's say that the scale factor is "k". Then, when we multiply k by the length of Line A, we should get the length of Line B:
(Line A length) * k = (Line B length)
5 * k = 55
k = 55/5 = 11
Thus, the scale factor is 11.
Hope this helps!
Answer:
11
Step-by-step explanation:
Length of enlarged line is: 55 cm
Length of the original line: 5 cm
Let the scale factor be t
Then,
5t = 55
t = 55/5
t = 11
simplify without the absolute value |x+3| ; if x>2
Answer:
[tex]x+3[/tex] if [tex]x>2[/tex]
Step-by-step explanation:
Recall some following basic ideas about absolute value:
[tex]|0|=0[/tex] or I guess [tex]-(0)=0[/tex]
[tex]|3|=3[/tex]
[tex]|-3|=-(-3)[/tex] or just [tex]3[/tex] but there is a reason why I wrote it the way I did.
You see that the absolute value returned the same value if the value was positive.
You see that the absolute value returned the opposite value if the value was negative.
You can include 0 in either.
Let's look at [tex]|x+3|[/tex] alone for a second.
*[tex]|x+3|=x+3[/tex] if [tex]x+3[/tex] is positive or zero.
When is [tex]x+3[/tex] positive or zero? [greater than or equal to 0]
[tex]x+3\ge 0[/tex]
Subtract 3 on both sides
[tex]x\ge -3[/tex]
*[tex]|x+3|=-(x+3)[/tex] if [tex]x+3[/tex] is negative or zero.
When is [tex]x+3[/tex] negative or zero? [less or equal to 0]
[tex]x+3\le 0[/tex]
Subtract 3 on both sides
[tex]x\le -3[/tex]
So looking at the bullet points (the *), [tex]x>2[/tex] fits into the first inequality.
Therefore, [tex]|x+3|=x+3[/tex].
The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus.
How many passengers got on after stop 4?
A:27
B:14
C:22
D:13
Answer gets brainliest
Answer:
b.14
Step-by-step explanation:
xoxoxoxoxoxoxoxoxo you're welcome
A lomy owner has his own fuel supply and needs to refill his storage tank. He has just completely
filled the fuel tank of the lorry with 170 litres from empty. He now has 100 litres of fuel left in his
storage tank. With the price of fuel expected to fall soon he only wants to buy enough for the next
fortnight. Normally his regular short daily trips total 300 km and this leaves just 20 litres in the
lorry's fuel tank. He expects to complete three regular days of 300 km journeys each week, but
this could rise to five. Sometimes the total journeys are longer but his daily trips never total more
than 400 km in a day. He never works more than five days in a week. His storage container holds
4000 litres
How much fuel should he order to be certain that he has enough for the next two weeks?
Answer: He should order for 1046.67 litres fuel to be certain that he has enough for the next two weeks
Step-by-step explanation:
Note that he has just completely
filled the fuel tank of the lorry with 170 litres from empty. He now has 100 litres of fuel left in his storage tank
If his regular short daily trips total 300 km and this leaves just 20 litres in the lorry's fuel tank.
That is 100 litres -20 litres = 80 litres
On 300km, he consumed 80 litres
He plans to complete three regular days of 300 km journeys each week, but this could rise to five. Sometimes the total journeys are longer but his daily trips never total more than 400 km in a day. He never works more than five days in a week. His storage container holds
4000 litres
From all these analysis, we can deduce that the maximum km of journey he should prepare for is
400km × 5 = 2000km for one week
Since he consumed 80 litres of fuel for any 300km
Then,
80/300 = L/2000
L = 1600/3
L = 533.33 litres
The journey for two weeks will be
533.33 × 2 = 1066.67 litres
Recall that he left 20 litres in the tank. Take this away from 1066.67 litres.
1066.67 - 20 = 1046.67 litres
He should therefore order for 1046.67 litres fuel to be certain that he has enough for the next two weeks
What are these values?
Answer:
what is the values of what?
Which expression is the same as 2 hundreds, 6 tens, and 804 thousandths?
Choose 1 answer:
©
(2 x 100) + (6 x 10) + (8 x 100) + (4 x
1000)
© (2 x 100) + (6 x 10) + (8 x 7) + (4 x 1000)
© (2 x 100) + (6 x 10) + (8 x HD) + (a < too)
Answer:
(2 x 100) + (6 x 10) + (804 x 10^-3)
Step-by-step explanation:
The figure located at the hundred must be multiplied by 100
The figure located at the tens must be multiplied by 10
The figure located at the ones must be multiplied by 1
The figure located at the tenth must be multiplied by 10^-1
The figure located at the hundredth must be multiplied by 10^-2
The figure located at the thousandths must be multiplied by 10^-3
All the previous expression must be added. Then, 2 hundreds, 6 tens, and 804 thousandths is the same as:
(2 x 100) + (6 x 10) + (804 x 10^-3) = 260.804
Answer:
I think its the 1st one
which choices are equivalent to the expression? √(5) x √(20)
Answer:
10 is the answer
Step-by-step explanation:
You have to multiply with whats inside the roots. you would have [tex]\sqrt{5} times \sqrt{20} will give you \sqrt{100} which is 10[/tex]
What is the degree of t-4t^2+2t^3
Answer:
3
Step-by-step explanation:
t-4t^2+2t^3
Rewriting this in order from largest to smallest exponent
2t^3 -4t^2 +t
The highest power is 3
So this is degree 3
Q18) Find the percent change from 70 to 56.
Answer:
20%
Step-by-step explanation:
Jus do the math for it and that be your answer right there.
A sports franchise would like to increase their Instagram followers by 25%. This means they would need 300,000
more followers. How many followers do they currently have?
a) 75,000
b) 300,000
c) 525,000
d) 1,200,000
Answer:
D. 1,200,000
Step-by-step explanation:
25%=0.25 which if multiplied by 4 = 1 which is the current followers. 300,000 multiplied by 4 = 1,200,000
Using percentages we know that the current followers of the sports franchise are (D) 1,200,000.
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the current followers are:
Let the correct followers be x.Now calculate as follows:
x/100 × 25 = 300,00025x = 30,000,000x = 30,000,000/25x = 1,200,000Therefore, using percentages we know that the current followers of the sports franchise are (D) 1,200,000.
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