Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the tunnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 3 inches and the altitude of the cone to be 4 inches.
Answers
so, bearing in mind that, the radius and height are two sides in a right-triangle, thus both are at a ratio of each other, thus the radius is at 3:4 ratio in relation to the height.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=3\\ h=4 \end{cases}\implies \stackrel{full}{V}=\cfrac{\pi \cdot 3^2\cdot 4}{3}\implies \stackrel{full}{V}=12\pi \\\\\\ \stackrel{\frac{2}{3}~full}{V}=12\pi \cdot \cfrac{2}{3}\implies \stackrel{\frac{2}{3}~full}{V}=8\pi ~in^3 \\\\\\ \textit{is draining water at a rate of }12~\frac{in^3}{min}\qquad \cfrac{8\pi ~in^3}{12~\frac{in^3}{min}}\implies \cfrac{2\pi }{3}~min[/tex]
[tex]\bf \textit{it takes }\frac{2\pi }{3}\textit{ minutes to drain }\frac{2}{3}\textit{ of it, leaving only }\frac{1}{3}\textit{ in it}\\\\ -------------------------------\\\\ \stackrel{\frac{1}{3}~full}{V}=12\pi \cdot \cfrac{1}{3}\implies \stackrel{\frac{1}{3}~full}{V}=4\pi\impliedby \textit{what's \underline{h} at this time?} \\\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=\frac{3h}{4}\\ V=4\pi \end{cases} \implies 4\pi =\cfrac{\pi \left( \frac{3h}{4} \right)^2 h}{3}[/tex]
[tex]\bf 12\pi =\cfrac{\pi \cdot 3^2h^2 h}{4^2}\implies 12\pi =\cfrac{9\pi h^3}{16}\implies \cfrac{192\pi }{9\pi }=h^3 \\\\\\ \sqrt[3]{\cfrac{192\pi }{9\pi }}=h\implies \sqrt[3]{\cfrac{64}{3}}=h\implies \cfrac{4}{\sqrt[3]{3}}=h \\\\\\ \cfrac{4}{\sqrt[3]{3}}\cdot \cfrac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}=h\implies \cfrac{4\sqrt[3]{9}}{\sqrt[3]{3^3}}=h\implies \cfrac{4\sqrt[3]{9}}{3}=h[/tex]
Related Questions
anybody can help I need it by today at 4 pm please please please please please please help
Answers
The speeds have to be converted to km/min as well:
88 km/h = 88/60 km/min
76 km/h = 76/60 km/min
Let's define the location dimension x as x=0 at Town A, then x=976 in Town B.
With this we can set up two location equations:
Andy: x(t) = 88/60 t
Bernard: x(t) = 976 - 76/60 t
When they meet, the equations are equal, so we solve t for:
88/60 t = 976 - 76/60 t => t=510
Convert this number back to a clock time by adding 510 minutes to 9 AM, and you get 5:30 PM.
if five notebooks cost $5.25, how much would three notebooks cost?
Answers
$1.05*3 notebooks= $3.15 for 3 notebooks
Tony rounded each of the numbers 1,210 and 1,148 to the nearest hundred. Which choice correctly compares the rounded numbers?
Answers
The process of rounding numbers 1,210 and 1,148 to the nearest hundred results in 1,200 and 1,100, respectively. Therefore, 1,200 is greater than 1,100.
Explanation:In Mathematics, rounding numbers is common practice for simplifying calculations. We are given the numbers 1,210 and 1,148, and we need to round them to the nearest hundred.
Let's round them:
1,210 rounded to the nearest hundred is 1,200.1,148 rounded to the nearest hundred is 1,100.So, when comparing the rounded numbers, 1,200 is greater than 1,100.
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Jon bought 1 2⁄3 pounds of green peppers and 3⁄5 pound of yellow peppers. How much more did the green peppers weigh than the yellow peppers?
Answers
Re-write the problem as "subtract 3/5 from 5/3."
5 3
--- - -----
3 5
Note that the LCD here is (3)(5) = 15.
Multiply 5/3 by (15/15) and also multiply 3/5 by (15/15). Your result should be
25 9
------- - -----
15 15
Subtracting, we get 16/15. This is the answer. The green peppers weighed 16/15 lb, or 1 1/15 lb, more than did the other peppers.
Jonah is playing a video racing game called Checkpoint. The speed of Jonah’s car is recorded four times during one lap. At the first checkpoint, his speed is 80 miles per hour. At the second checkpoint, his speed has reduced by 5%. At the third checkpoint, Jonah’s speed has increased by the speed from the previous checkpoint. At the fourth checkpoint, his speed decreased by 20% compared with the third checkpoint. What is Jonah’s net change in speed between the first and fourth checkpoints?
Answers
Answer:
negative 15 is your answer
Step-by-step explanation:
the last number was negative so it would be negative 15
Answer:
-15
Step-by-step explanation:
yes
if the perimeter of a rectangle is 318 inches, find the width and length. what's the answer?
Answers
let's consider that Length is n
Then width will be n+1
Perimeter of rectangle is equal to 2*(L+W) in this case
P = 2*(n + [n+ 1]) = 2*(n + n + 1) = 2(2n + 1)
P = 318
318 = 2(2n+1)
159 = 2n+1
159 - 1 = 2n
158 = 2n
79 = n
So this means that Length is 79 and Width is 80
or vice versa, Length is 80 and Width is 79
Round 6,482 to the nearest ten hundred
Answers
What are the factors of 27
Answers
Note that two negative factors such as -3 and -9 can also multiply to equal 27.
A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 32 square feet. Find the lengths of the sides of the poster and the sign?
Answers
Area of square two = [tex]x^2[/tex]
The difference of the area of two squares = 32
[tex]x^2-(x^2-4x+4)=32[/tex]
[tex]x^2-x^2+4x-4=32[/tex]
[tex]4x-4=32[/tex]
[tex]4x=32+4[/tex]
[tex]4x=36[/tex]
[tex]x=36/4[/tex]
[tex]x=9[/tex]
The side length of the poster = [tex]x-2 = 9-2 = 7 feet[/tex]
The side length of the sign = [tex]x=9[/tex]
For a Circle of radius is 5 feet, find the arc length s subtended by a central angle of 42 degrees
Answers
The arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The formula for arc length is given by:
s = rθ
where s is the arc length, r is the radius of the circle, and θ is the central angle subtended by the arc in radians.
To use this formula, we first need to convert the central angle from degrees to radians:
θ = (π/180) × 42 = 0.733 radians
Now we can plug in the values of r and θ into the formula to get:
s = 5 × 0.733
= 3.665 feet
Therefore, the arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.
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Ms. Smith has 28 sixth graders and 35 seventh graders for math. If she wants to break the two grades into identical groups without any students left over, how many students will be in each group? Is it lcm or gcf?
Answers
Which expression represents the number of possible combinations of n items taken r at a time?
Answers
Answer:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Step-by-step explanation:
Given :Total items = n
Items taken at a time = r
To Find: Which expression represents the number of possible combinations of n items taken r at a time?
Solution:
We will use combination over here.
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Now Total items = n
Items taken at a time = r
Thus expression represents the number of possible combinations of n items taken r at a time is [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Graph the image of the given triangle after the transformation with the rule (x, y)→(x−1, y+2) . Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created. PolygonMove UndoRedoReset
Answers
Answer:
Hope this helps
Step-by-step explanation:
What is the quotient of 0.8449 ÷ 0.71?
Answers
Sorry, but hope this helps!
Create a process that will calculate the series 1 + x + x2 + x3 + x4 .......... + xn where x is a floating point number and n is a positive number. you process should be designed so exponentiation (or the pow function in c++) is not needed.
Answers
1. n is an integer.
2. Language is c++
double expr(double x, int n)
{
double sum = 0.0;
double power = 1.0; // Will have the value x^y where y ranges from 0 to n
int i;
for(i=0; i <= n; ++i) {
sum += power;
power *= x;
}
return sum;
}
Where did the Maya's lived?
Thanks,
-Laura B
Answers
The Mayans lived, hmm, where is now know as Southern Mexico and northen Central America, including lots of countrys in their. etc, Guatemala, Belize, El Salvador
I hope this helps! :>
A jar of natural peanut butter normally cost four dollars today it's on sale for $3.60 what is the percentage of the discount
Answers
Which equation represents a line that passes through (5, 1) and has a slope of ?
A. y – 5 = (x –1)
B. y – = 5(x –1)
C. y – 1 = (x –5)
D. y – 1 = 5
Answers
when you y -1 = ( x - 5)
1- 1 = 5 -5
0 = 0
where A y - 5 = ( x - 1)
1 - 5 = ( 5 - 1 )
-4 dosenot equal 4
Samah has made 20kg of chilli. There are 100g of chilli in a portion. how many portions of chilli has Samah made?
Answers
20kg of chilli is equal to 20,000g of Chilli
20,000g divided by 100g equals 200 100g servings of chilli
Koen works at the Middletown Cafe. This week he served a table a meal costing $53.69 and received a 15% tip. He received a tip of ____.
Answers
The cost of two mopeds is the same as the cost of seven bicycles. The cost of one bicycle is $152. Therefore, the cost of one moped is
Answers
1 bike = 152
7 bikes = 152*7 = 1064
1 moped = 1064/2 = $532
Suzanne can read 1 page in 3 minutes. How many pages can she read in 5 hours?
Answers
1h= 60 min
5x60= 300 min
1 page read in 3 min.
300 min /3 min = 100.
In 5 h, 100 pages can be read.
The campsite is square in shape and has a length of 65 metres.
What is the area of the campsite?
Answers
Area of square = length*length
Applying this:
65*65
4225 square metres
Hope this helped!
The sales tax on the purchase of a futon is $34.1634.16. If the tax rate is 77%, find the purchase price of the futon.
Answers
so, "x" is the 100%, and we know that 34.16 is the 77%, what's "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 34.16&77 \end{array}\implies \cfrac{x}{34.16}=\cfrac{100}{77}\implies x=\cfrac{34.16\cdot 100}{77}[/tex]
To find the purchase price of the futon, divide the sales tax by the tax rate. The purchase price is approximately $44.48.
Explanation:To find the purchase price of the futon, we need to divide the sales tax by the tax rate. Let's call the purchase price P. We can set up the equation as: 0.77P = 34.16. To solve for P, we divide both sides of the equation by 0.77. P = 34.16 ÷ 0.77. Using a calculator, the purchase price of the futon is approximately $44.48.
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Compare the values of the two 8s in the number 467882
Answers
The two 8s in the number 467882 have different values based on their positions. The first 8 is worth 80 while the second 8 is worth 8.
Explanation:The number 467882 has two 8s. The first 8 is in the tens place and the second 8 is in the ones place. The value of the first 8 is 8 times the value of the place it is in (or 8 x 10 = 80). The value of the second 8 is 8 times the value of the place it is in (or 8 x 1 = 8).
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Steps to divide 125.00 by 7.75
Answers
7.75 | 125
we want to get rid of that decimal....so we move it 2 spaces to the right....by doing that, we also have to move the decimal under the division sign by 2 spaces to the right....turning ur problem into :
16.1 R 225 <== ur answer
______
775 |12500.0
775
------- subtract
4750
4650
---------subtract
1000
775
-----------subtract
225
A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle.
Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.
Answers
Using the 45°-45°-90° triangle theorem in a right triangle, where 'a' represents the triangle's leg that is also the trapezoid's height, 'h' equals 'a' and the hypotenuse is 'a' times √2. Additional information would be needed to solve for a numerical value of 'h'.
Explanation:In this problem, the wall's shape is a trapezoid, and we are using the 45°-45°-90° triangle theorem to find 'h', the height of the wall. We know in a 45°-45°-90° triangle, the two legs are congruent (same length), and the length of the hypotenuse is √2 times the length of a leg (based on Pythagorean theorem). In this case, if 'a' is the length of the triangle's leg connected to the rectangle, then 'h' would be equal to 'a' (since they are the legs in a 45-45-90 triangle), and the hypotenuse would be a√2.
Given an additional variable or measurement in this problem such as the length of the wall or the hypotenuse of the triangle, we could plug it in to solve for 'h'. Without additional information, the exact numerical height cannot be determined.
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what is 11.4 rounded to the nearest tenth
Answers
Rounded to the nearest tenth, 11.4 becomes 11.4.
When rounding a number to the nearest tenth, you look at the digit in the hundredths place.
If it's 5 or greater, you round up; if it's less than 5, you round down. In 11.4, the digit in the tenths place is 4, which is less than 5.
Therefore, 11.4 remains unchanged when rounded to the nearest tenth, resulting in 11.4.
This means the number stays the same, as it's already accurately represented to the nearest tenth without needing any adjustments.
Miguel score 35 fewer points in second bowling game than his first game his total score for the two games was 395 how many points did he score in each game? (plz show step by step)
Answers
his second game's score "b", and it was 35 fewer points, so is b=a - 35.
we also know that the total score for both games was 395, thus
[tex]\bf \begin{cases} a+\boxed{b}=395\\ a+\boxed{a-35}=395 \end{cases} \\\\\\ 2a-35=395\implies 2a=395+35\implies 2a=430\implies a=\cfrac{430}{2} \\\\\\ a=215[/tex]
how many did he score in the second game? well, b = a - 35.
What is the lateral area of the pyramid?
Answers
9*12.3 = 110.7
11*11.9 = 130.90
130.90 + 110.70 = 241.6 ft^2
Answer:
Step-by-step explanation:
Alright, lets get started.
The lateral area will be the area of all 4 sides.
The two sides have base length 11 feet and height of 11.9 feet.
The area of this side is : [tex]\frac{1}{2}*base*height[/tex]
The area of this side is : [tex]\frac{1}{2}*11*11.9=65.45[/tex]
The two sides have base length 9 feet and height 12.3 feet.
The area of this side is : [tex]\frac{1}{2}*9*12.3=55.35[/tex]
All 4 sides area will be : [tex]2(65.45+55.35)[/tex]
All 4 sides area = 241.6 square feet
Hence the lateral area will be 241.6 square feet : Answer B
Hope it will help :)