Cones a and b are similar.
the surface area of cone a is 36cm2.
the surface area of cone b is 100cm2.
the volume of cone a is 162cm3.
work out the height,
h
, of cone a and the volume of cone b:
Answers
The height of cone A is 12 and the volume of cone B is 750
How to determine the height and the volume?The given parameters are:
Surface area of cone a is 36cm²Surface area of cone b is 100cm²Volume of cone a is 162cm³Both cones are similar.
The similarity ratio is represented as:
[tex](\frac{V_A}{V_B})^\frac 13 = (\frac{A_A}{A_B})^\frac 12 = \frac{h_A}{h_B}[/tex]
Where:
V represents volumeA represents surface areah represents heightRemove the height expression in the equation [tex](\frac{V_A}{V_B})^\frac 13 = (\frac{A_A}{A_B})^\frac 12 = \frac{h_A}{h_B}[/tex]
So, we have:
[tex](\frac{V_A}{V_B})^\frac 13 = (\frac{A_A}{A_B})^\frac 12[/tex]
This gives
[tex](\frac{162}{V_B})^\frac 13 = (\frac{36}{100})^\frac 12[/tex]
Evaluate the exponent of 1/2
[tex](\frac{162}{V_B})^\frac 13 = \frac{6}{10}[/tex]
Take the cube of both sides
[tex]\frac{162}{V_B} = \frac{216}{1000}[/tex]
Make VB the subject
[tex]V_B = \frac{162 * 1000}{216}[/tex]
Evaluate
[tex]V_B = 750[/tex]
Remove the area expression in the equation [tex](\frac{V_A}{V_B})^\frac 13 = (\frac{A_A}{A_B})^\frac 12 = \frac{h_A}{h_B}[/tex]
[tex](\frac{V_A}{V_B})^\frac 13 = \frac{h_A}{h_B}[/tex]
Substitute known values
[tex](\frac{162}{750})^\frac 13 = \frac{h_A}{20}[/tex]
Multiply both sides by 20
[tex]h_A = 20 *(\frac{162}{750})^\frac 13[/tex]
Evaluate
[tex]h_A= 12[/tex]
Hence, the height of cone A is 12 and the volume of cone B is 750
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Related Questions
How does the slope of g(x) compare to the slope of f(x)? the slope of g(x) is the opposite of the slope of f(x). the slope of g(x) is less than the slope of f(x). the slope of g(x) is greater than the slope of f(x). the slope of g(x) is equal to the slope of f(x).
Answers
The statement that correctly compares the slopes of the linear functions is: the slope of g(x) is less than the slope of f(x).
How to Find Slope of a Linear Function?Slope of a linear function = change in y / change in x = rise/run
Given the linear functions, g(x) and f(x) as shown in the image attached:
Slope of g(x) = 1/2 = 0.5
Slope of f(x) = 2/1 = 2
Therefore, we can conclude that: the slope of g(x) is less than the slope of f(x).
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How can I solve (-2x-6x^2-4)+(5x^2-2x).
[tex] ( - 2x - 6x ^2 - 4) + (5 x^{2} - 2x)[/tex]
Answers
Step-by-step explanation:
we can only solve an equation.
but here we only have an expression, which we can simplify :
(-2x - 6x² - 4) + (5x² - 2x)
-2x - 2x - 6x² + 5x² - 4
-4x - x² - 4
Needing a bit of help
Answers
Answer:
x=2, y=-4
Step-by-step explanation:
If you put a vertical or horizontal line straight through the shape and it looks the same, then it is symmetrical. You can put a symmetrical line both vertically AND horizontally. To do this, you just need a line going through the points at the tips and the points at the sides of the quadrilateral. A line that is vertical will be an x=, because it only covers one x-value. So, the line for x will be x=2, because it goes through both tips of the quadrilateral. A horizontal line will be y= because it only covers one y-value. So, the line for the horizontal line will by y=-4, because this goes through both sides of the quadrilateral.
Hope this helps!
I really need help with this. Please.
A chef has two dozen meatballs to add to a pot of sauce. Each meatball has a two-inch diameter. Before the meatballs are added, the sauce is 2 inches from the top of the 14-inch diameter pot. Will the sauce spill over when the chef adds the meatballs to the pot? Show all of your work to justify your answer.
Answers
Given the volume of the space in the pot and the volume of the meatballs, the sauce will not spill over.
Will the sauce spill over?
The first step is to determine the volume of the remaining space that the sauce is yet to fill. A pot usually has the shape of a cylinder, so the formula for the volume of a cylinder would be used.
Volume of a cylinder = πr²h
π x (14/2)³ x 2 = 98 in³
The second step is to determine the volume of the two dozen meatballs.
Volume of a sphere = 4/3πr³
24 x (4/3 x π x (2/2)³) = 32π in³
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The sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.
Volume of the sauce in the potThe volume of sauce in the pot is calculated as follows;
V = πr²h
V = π x (7)² x (2)
V = 98π in³
Volume of the two dozen meatballsArea of 1 meatball = πr² = π x (1)² = π in²
Area of the 2 dozen = (2 x 12) x A
= 24 x π in² = 24π in²
the height of each meatball = 2 in,
Volume of the 2 dozens = 2 in x 24π in² = 48π in³
Total volume of the meatball and sauce in the pot = 98π + 48π = 146π in³
Thus, the sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.
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Find the 5th term in the sequence an=3n - 5
Answers
Answer:
aₙ = 3n - 5
5th term = a₅ = 3.5 - 5 = 15 - 5 = 10
Answer:
a₅ = 10Step-by-step explanation:
aₙ = 3n - 5
Put n = 5:
a₅ = 3 · 5 - 5
a₅ = 15 - 5
a₅ = 10
PLEASE HELP DUE IN 10 MINS!!!
Use the space below to show your work check your work very carefully because you will need to use your answers to complete part 2 HELP ME WITH THE ONE ON THE BOTTOM BUT IF I HAVE A MISTAKE PLS TELL ME
Answers
Answer:
yes, all answers are correct
Step-by-step explanation:
= 2. Given the quadratic equation 3x2 – 8x + k = 0 has no real roots. Find the range of values of k.
Diberi persamaan kuadratik 3x2 – 8x + k = 0 tidak mempunyai punca nyata. Cari julat nilai k.
Answers
[tex]\text{If there are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)[/tex]
what is 103 + 343 + 252
Answers
Answer:
its 698...............................
Simplify: 6(x-2y) - 3(2x+y)
Answers
Answer: -15y
Step-by-step explanation:
6(x-2y) - 3(2x+y)
6x-12y -6x-3y
0x -15y
-15y
Answer:
-15y
Step-by-step explanation:
6(x-2y) - 3(2x+y)
6x-12y -6x-3y
0x -15y
-15y
In rhombus ABCD, AB=12 and AC=22. Find the area of the rhombus to the nearest 10.
a) 195
b) 221.3
c) 105.5
d) 100.8
Answers
Answer:
c) 105.5 square units
Step-by-step explanation:
The area of a rhombus can be computed as half the product of the diagonal lengths.
__
Half the diagonal BD will be one leg of the right triangle formed by the diagonals and the sides of the rhombus. The length of that leg is found using the Pythagorean theorem:
a² +b² = c²
11² +b² = 12²
b² = 144 -121 = 23
b = √23 ≈ 4.796
This value is half the length of diagonal BD, so multiplying it by the length of diagonal AC will give the area of the rhombus.
Area = 1/2(AC)(BD) = (22)(4.796) ≈ 105.5 . . . . square units
What is the approximate length of arc s on the circle below? use 3.14 for pi. round your answer to the nearest tenth. a circle is shown. 2 rays form an angle of 45 degrees. the length of the rays is 8 inches. arc s contains the angle measuring 45 degrees. 5.6 in. 6.3 in. 14.3 in. 25.1 in.
Answers
The length of an arc with central angle of 45 degrees and radius of 8 inches is 6.3 inches.
How to find length of an arc?length of an arc = ∅ / 360 × 2πr
where
∅ = central angler = radiusHence,
r = 8 inches
∅ = 45 degrees
Therefore,
length of an arc = 45 / 360 × 2 × 3.14 × 8
length of an arc = 2260.8 / 360
length of an arc = 6.28 inches
length of an arc = 6.3 inches
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Answer:
b
Step-by-step explanation:
A fair spinner has 12 equal sections: 4 red, 5 blue and 3 green.
It is spun twice.
What is the probability of getting 2 different colours?
Answers
Answer: 2/3 i beleive
Step-by-step explanation:
What is TS? Need some help on this
Answers
Answer:
8
Step-by-step explanation:
I hope this helps! If it does, please click "Thanks" to help me out!
Answer:
TS = 8 units
Step-by-step explanation:
see image.
Write a proportion. Crossmultiply and solve.
Anyone know the answer to this
Answers
Answer:
The answer is A
Step-by-step explanation:
because the angle in the circle is a central angle the angle is the same value as the arc.
Hope this helps!!
The splasher pool holds what percent of the water the paddler pool holds?
Answers
Answer:
the splasher pool holds 133%.
Step-by-step explanation:
sponsored / paddler equals 144 pi over 108 pi equals 1.3 * 100 = 133%
Determine the equation of the graph.
Answers
Answer: A
Step-by-step explanation:
Answer:
well its slop interform
Step-by-step explanation:
PLSSSS HELP IVE TRIED EVERYTHING AHHHHHHH
For each graphically defined functions below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.
Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?
Answers
Answer:
Domain: input values (x-values)
Range: output values (y-values)
Increasing function: the average rate of change is positive
Decreasing function: the average rate of change is negative
Constant function: y-values do not vary, regardless of x-values
Graph 1From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-2, 2]
Increasing function: (-2, 0)
Decreasing function: (0, 3)
Graph 2From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-2.5, 2]
Increasing function: (-2, -1) ∪ (1.5, 3)
Decreasing function: (-1, 1.5)
Graph 3From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-1, 2]
Increasing function: (-2, -1)
Constant: (-1, 1)
Decreasing function: (1, 3)
Which is the value of this expression when p = -2 and q = -1?
-4
-1/16
1/16
4
Answers
Answer:
Here is the ans...hope it helps:)
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 Function 2 f(x) = −x2 + 2x − 15 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (−14, 1). Function 2 has the larger maximum at (1, −14). Question 10(Multiple Choice Worth 1 points) (08.03 MC) The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 Provide the next step to derive the quadratic formula. a times the quantity x squared plus b over a times x end quantity equals negative c x(ax + b) = −c x squared over a plus b over a times x equals negative c over a x squared over a plus b over a equals negative c over a Question 11(Multiple Choice Worth 1 points) (08.01 MC) A food packet is dropped from a helicopter and is modeled by the function f(x) = −12x2 + 19200. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds: graph of function f of x equals 19200 minus 12 multiplied by x squared Use the graph to determine the domain of f(x) for all viable x values, based on the context. All real numbers x ≤ 19200 −40 ≤ x ≤ 40 0 ≤ x ≤ 40 Question 12(Multiple Choice Worth 1 points) (08.06 LC) The graphs of f(x) and g(x) are shown below: Graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals negative 2.5 times x minus 2 What are the solutions to the equation f(x) = g(x)? x = −3, 4 x = −4, 2.5 x = −0.8, 2.5 x = 8, −8 Question 13(Multiple Choice Worth 1 points) (08.02 MC) The function f(x) = −x2 − 9x + 10 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does
Answers
The function 2 represented by the equation f(x) = -(x - 2)² + 5 has the larger maximum.
How to complete the function?The functions are given as:
Function 1
f(x) = -(x - 4)² + 1
Function 2:
f(x) = -(x - 2)² + 5
A quadratic function is represented as a (x - h)² + k, when a is negative then, the vertex of the function is a maximum. In both functions, the value of a is -1. This means that both functions are at a maximum
The values of k in both functions are k = 1 and k = 5. By comparison, 5 is greater than 1. Therefore, function 2 has larger maximum.
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10. Select the three lengths that could
form a right triangle.
A. 5
B. 6
C. 8
D. 12
E. 13
F. 15
Answers
Answer:
5, 8, 12
Step-by-step explanation:
l ]
l ] 8
l. ]
5 l
l________________]
12
Wanja bought fruits which were being sold at 3 fruits for sh 2.00. She then sold them at 3 fruits for sh 3.50. What profit did she make after selling 450 fruits? [1990 No. 25) sh 300.
Answers
Answer:
The answer is sh50......
how do you find the perfect square (x+1)^2=0
Answers
Answer:
By multiplying the term by itself (x+1)(x+1)
Some people like to use the box technique, which formats like this:
x + 1
x x^2 1x
+
1 1x 1
The terms multiply in columns, and then add all together
So
x^2 + 1x + 1x + 1 can be simplified to x^2+2x+1 = 0, which is the perfect square of (x+1)^2 = 0
Step-by-step explanation:
Please help me on this!
Answers
Answer: Choice B
The initial amount in the account.
==================================================
Reason:
x is the number of years
x = 0 is the starting point. Let's plug that in to find...
[tex]y = 982(1.07)^x\\\\y = 982(1.07)^0\\\\y = 982(1)\\\\y = 982\\\\[/tex]
At the start, Sammy has $982 in the bank.
Side note: The 1.07 means the account is growing by 7% each year.
You deposit $200 in a savings account that earns
5% annual interest compounded continuously.
How much money will you have after 5 years?
A. $255.26
B. $1518.75
C. $2436.50
D. $256.81
Answers
The answer is B which is 1518.75
What’s the volume of the figure below
Answers
Answer:
41.89 cm3
Step-by-step explanation:
Given : Height = 10 cm
Given: Radius = 2 cm
Find the volume,
The formula for volume is,
V = π([tex]r^2[/tex])[tex]\frac{h}{3}[/tex]
Fill in the formula with the given values,
π · [tex]2^2[/tex] · [tex]\frac{10}{3}[/tex]
= 41.8879.....
Round answer to the nearest hundredth,
(The Rule For Rounding: the last digit is less than 5, keep the previous digit the same. If it's 5 or more then you should round the previous digit up.)
41.8879
7 is more than 5 so bring the 8 up to a 9,
41.89
Therefore the answer is 41.89 cm3.
Answer:
41.9 cm³ (nearest tenth)
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 2 cmh = 10 cm[tex]\begin{aligned}\implies \textsf{Volume} &=\sf \dfrac{1}{3} \pi \cdot 2^2 \cdot 10\\\\ & = \sf \dfrac{1}{3}\pi \cdot 40\\\\& = \sf \dfrac{40}{3}\pi\\\\ & = \sf 41.88790205\:cm^3\end{aligned}[/tex]
Therefore, the volume is 41.9 cm³ (nearest tenth)
Leo is buying candies for his friends. Each pound of chocolate candies costs $5.28 and each pound of hard candies costs $2.09. How much will Leo spend if he buys nine pounds of each type of candy? $
Answers
Answer: $66.33
Step-by-step explanation: Since Leo buys 9 pounds of each candy, multiply $5.28 x 9 and $2.09 x 9.
$5.28 x 9 is $47.52.
$2.09 x 9 is $18.81.
Add $47.52 and $18.81.
Total is $66.33
What is TU in circle D?
5.1
3.4
ا
O 3.4
O 3.8
O 7.6
O 5.1
Answers
Answer:
answer-3.4
Step-by-step explanation:
2022 edge
Marina he spends one-third of his money on food and three-fifths of the rest on drinks If he had $120 left over,¿how much money did he have to start with?
Answers
Answer: $184
Step-by-step explanation:
Step (1)- 1/3 of 120= $40
Step (2)= 3/5 of 40= $24
Step (3)- 40+24+120= $184 (ToTaL)
Hope this helpss!
What is the length of the missing leg?
Answers
Answer:
[tex]a=12[/tex]
Step-by-step explanation:
Pythagorean Theorem: [tex]a^{2}+b^{2}=c^{2}[/tex]
In this case, a = 9, b = a, and c = 15.
[tex]9^{2}+a^{2}=15^{2}[/tex]
[tex]81+a^{2}=225[/tex]
The, we subtract 81 from both sides getting:
[tex]a^{2}=144[/tex],
Then, [tex]a=12[/tex]
carrie is building a wooden birdhouse for her mom. She finds a plank in the garage to use for the base. When she realizes its too long, Carrie cuts 3 inches off the plank. Now its the correct length of 8.25 inches. what does she subtract the 3 with to get 8.25?