How many 1/4 inch lengths of rod can be cut from 3 1/2 inch rod

1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is

solong [7]

Answer:

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

$V = \frac{1}{3}h\pi r^{2}$

Where:

r: is the radius

h: is the height

The rate of change of the volume can be calculated by using the chain rule:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]$

Since h = 4/3 r we have:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]$ (1)

With:

$\frac{dr}{dt}$ = 3 in/min

$r = 3 ft*\frac{12 in}{1 ft} = 36 in$

And by entering the above values into equation (1) we have:

$\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]$

$\frac{dV}{dt} = 16286 in^{3}/min$

Therefore, the volume is increasing at a rate of 16286 in³/min.

I hope it helps you!

3 0

3 years ago

Which fraction is equal to 1/4

Morgarella [4.7K]

A fraction that can be equaled to the same as 1/4 is 2/8. Now 2/8 is the larger fraction that can be shortened to 1/4.

5 0

3 years ago

Han and Priya were making a kite. Han cut out a piece of fabric so

Lemur [1.5K]

A kite is a quadrilateral which has two equal adjacent sides. Therefore measuring the lengths accurately would make the pieces of wood perpendicular. Since the diagonals of a kite are at right angle to each other.

Quadrilaterals are shapes which has four straight sides. Examples are; square, trapezium, kite, rectangle etc.

A kite is a shape which has adjacent sides to have equal lengths. It has two diagonals, and one line of symmetry.

The lengths of the sides of the fabric being exact imply that the pieces of wood would be perpendicular as suggested by Priya when fixed appropriately to the piece of fabric. This is because the diagonals of a kite are always perpendicular. Thus measuring the angles as suggested by Han is not necessary.

Visit: brainly.com/question/21979359

8 0

1 year ago

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The cloth top of the gazebo in Mr. Chang’s backyard has ripped from weathering. He needs to know the area of the cloth so he can

antoniya [11.8K]

Answer:

The correct answer is A. 60 square feet.

Step-by-step explanation:

1. Let's review the data provided to us for solving the question:

The gazebo in Mr. Chang's backyard, according to the figure, is a square pyramid because its base is a square of 6 feet as length of its sides.

Length of the sides of the base = 6 feet

Slant length = 5 feet

Height = 4 feet

2. How much cloth, in square feet, will Mr. Chang need, assuming he does not need to replace the cloth at the bottom of the figure?

Area of a square pyramid = Base area + 1/2 Perimeter * Slant length

Replacing with the real values, we have:

Area of a square pyramid = 6 * 6 + 1/2 (6 + 6 + 6 + 6) * 5

Area of a square pyramid = 36 + 1/2 (24) * 5

Area of a square pyramid = 36 + 12 * 5

Area of a square pyramid = 36 + 60

Area of a square pyramid = 96 feet ²

3. But remember than Mr. Chang doesn't need to replace the cloth at the bottom of the gazebo.

So we need to subtract the area of the base to the area of the square pyramid:

Area of the square pyramid - area of the base

Area of the base = 6 * 6 = 36 feet ²

96 feet ² - 36 feet ² = 60 feet ²

The correct answer is A. 60 square feet.

7 0

3 years ago

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Maggie’s brother is three years younger than twice her age. The sum of their ages is 24. How old is maggie?

JulsSmile [24]

To solve this problem, we must set up a system of equations. In this case, let's let Maggie's age be represented by the variable m and her brother's age be represented by the variable b. We are told that the sum of their ages is 24, which gives us our first equation: m + b = 24. We can construct our next equation from the first sentence of given information: b = 2m - 3. This makes our system of equations:

m + b = 24

b = 2m - 3

To solve, we are going to substitute the value for b in terms of m given by the second equation into the first equation for the variable b.

m + b = 24

m + 2m - 3 = 24

To simplify, we must first combine the variable terms on the left side of the equation using addition.

3m - 3 = 24

Next, we should add 3 to both sides of the equation to get the variable term alone on the left side of the equation.

3m = 27

Finally, we should divide both sides by 3 in order to get the variable m alone.

m = 9

Therefore, Maggie is 9 years old (using the first equation and substituting in this value you can find that her brother is 15 years old).

Hope this helps!

8 0

2 years ago

Read 2 more answers