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nata0808 [166]
3 years ago
9

Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in.

The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?
Mathematics
1 answer:
DIA [1.3K]3 years ago
6 0
The volume of the pyramid for a square base can be written as: 

V = \frac{ s^{2}H }{3}

First, get the volume of the first pyramid
V = ?
s = 20 in.
H = 21 in.

V = \frac{ 20^{2}(21)}{3}
V = 2800 in³

Since, the volume of two pyramids are the same, we will equate it to equation 2 

V = 2800 in³
s = ?
H = 84 in.

Applying it to the formula:
2800 = \frac{ s^{2}(84)}{3}
\frac{(2800)(3)}{84} = s²    ⇒ combine like terms 
100 = s²        ⇒ get the square root of both sides to get the value of s
10 in = s       ⇒<span>side length of the base of the second pyramid</span>
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Answer:

14,130 cm³

Step-by-step explanation:

V = 4/3πr³

   = 4/3 x 3.14 x 15 x 15 x 15

   = 20 x 225 x 3.14

   = 706.5 x 20

   = 14,130 cm³

7 0
3 years ago
Find the second derivative at the point (2,2), given the function below. 2x^4=4y^3
Bogdan [553]

The second derivative at the point (2,2) is 34/9

<u>Explanation:</u>

<u></u>

2x⁴ = 4y³

2x⁴ - 4y³ = 0

We first need to find dy/dx and then d²y/dx²

On differentiating the equation in terms of x

dy/dx = d(2x⁴ - 4y³) / dx

We get,

dy/dx = 2x³/3y²

On differentiating dy/dx we get,

d²y/dx² = 2x²/y² + 8x⁶/9y⁵

\frac{d^2y}{dx^2} = \frac{2 X 2^2}{2^2} + \frac{8 X 2^6}{9 X 2^5}\\  \\\frac{d^2y}{dx^2} = 2 + \frac{16}{9}\\  \\

d²y/dx² = 34/9

Therefore, the second derivative at the point (2,2) is 34/9

7 0
3 years ago
Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery C
deff fn [24]

Answer:

$68.24

Step-by-step explanation:

Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery County tax rate is 9.5%.

Given data

The total bill was $76.25

tip

=20/100*76.25

=0.2*76.25

=15.25

Tax

=9.5/100*76.25

= 0.095*76.25

=$7.24375

In all the bills is 76.25-15.25+7.24375

=61+7.24375

=$68.24

7 0
3 years ago
Which of these equations could represent the blue line?
belka [17]

Hello from MrBillDoesMath!


The first choice (y = 2x) is NOT the blue line because it has twice of the slope of the line y=x. That is,  for a given positive x value the graph of y= 2x  appears above the black line which is not the case for the blue line shown.

The second choice (y =.001x) is a possibility but the multiplier .001 is so small I think the graph of that line would be "close" to the x-axis. I don't think it's the blue line.

y = -x. Now here we can say NO!  That line goes through the origin all right but has a slope of -1 so is heading "downward" from left to right. That is not the blue line either.

Well, then, it seems that the last equation ( y = 1/2x) is the only remaining reasonable answer.


Regards,  MrB.


5 0
3 years ago
Solve the inequality. 4m – 3(m + 1) – 4 &lt; 0 A) m &lt; 7 B) m &gt; 7 C) m &lt; -1 D) m &lt; -7
agasfer [191]

Answer:

A) m < 7

Step-by-step explanation:

4m – 3(m + 1) – 4 < 0

Distribute the 3

4m -3m -3-4<0

m-7 <0

Add 7 to each side

m-7+7 <0+7

m<7

3 0
3 years ago
Read 2 more answers
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