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den301095 [7]
3 years ago
12

Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass

is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? (4 points)
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

The solution would be like this for this specific problem:

Volume of a cylinder = pi * r^2 * h 

Volume of a cone = 1/3 * pi * r^2 * h 

Total Height = 47

Height of the cone = 12

Height of the cylinder = 35

If the top half is filled with sand, then:

volume (sand) = pi * 4^2 * 36

volume (cone) =  1/3 * pi * 4^2 * 12

Total volume = 1960.353816 cubic millimeters

353816 / (10 * pi) = 62.4 seconds.

It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.

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Two times a number x minus six times another number y is negative six.
Pie

Answer:

2x-6y=6, 2x+5y=18

Step-by-step explanation:

Translating the phrase into an equation, we get:

2x-6y=6

And:

-2x+5y=18

So the system of equations would be:

2x-6y=6, 2x+5y=18

If you want to put it into slope-intercept form, you can simplify both equations:

2x-6y=6\\6y=2x-6\\y=\frac{1}{3}x-3

2x+5y=18\\5y=-2x+18\\y=-\frac{2}{5}x+\frac{18}{5}

7 0
2 years ago
If s(x) = 2x2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =
Paladinen [302]

Answer:

\large\boxed{s(x)\cdot t(x)=2x^3+11x^2+8x-16}

Step-by-step explanation:

s(x)=2x^2+3x-4,\ t(x)=x+4\\\\s(x)\cdot t(x)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\s(x)\cdot t(x)=(2x^2+3x-4)(x+4)\\\\=(2x^2+3x-4)(x)+(2x^2+3x-4)(4)\\\\=(2x^2)(x)+(3x)(x)+(-4)(x)+(2x^2)(4)+(3x)(4)+(-4)(4)\\\\=2x^3+3x^2-4x+8x^2+12x-16\\\\\text{combine like terms}\\\\=2x^3+(3x^2+8x^2)+(-4x+12x)-16\\\\=2x^3+11x^2+8x-16

7 0
3 years ago
What is (f−g)(x)<br> (f−g)(x)=
quester [9]

Answer:

3x^5 -2x^4 -x^2 +x -21

Step-by-step explanation:

We need to subtract g(x) from f(x)

f(x) = 3x^5 +6x^2 -5

g(x) = 2x^4 +7x^2 -x+16

f(x) -g(x) = 3x^5 +6x^2 -5 - (2x^4 +7x^2 -x+16)

Distribute the minus sign

3x^5 +6x^2 -5 - 2x^4 -7x^2 +x-16

I like to line them up vertically

3x^5             +6x^2      -5

        - 2x^4 -7x^2    +x-16

---------------------------------------

3x^5 -2x^4 -x^2 +x -21

6 0
3 years ago
How do u work out percentages
Ksju [112]
Turn the percentage into a decimal by sliding the decimal twice from the right to the left and multiply it to the number
add/subtract it depending on if it's increasing or decreasing
8 0
3 years ago
Two equations are given below:
Klio2033 [76]
First, you want all the variables to be on one side:
a - 3b = 4
a - b = -2

Now you want to eliminate one of the variables, in this case a is easiest.

Subtract the second equation from the first and you're left with:
-2b = 6
so b = -3

Sub the value of b back into either of the equations and solve for x:
a - (-3) = -2
a = -5

So your answer is (-5,-3)
7 0
4 years ago
Read 2 more answers
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