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dybincka [34]
4 years ago
6

Tamara stacked two cubes, as shown. 2 stacked cubed. One cube has side lengths of 24 inches, and the second cube has side length

s of 12 inches. What is the total volume of the cubes? 1st cube volume: V = Bh V = (12)(12)(12) 2nd cube volume V = Bh V = (24)(24)(24) The total volume of the cubes is cubic inches.
Mathematics
1 answer:
MaRussiya [10]4 years ago
7 0

Answer:

15 552 in³

Step-by-step explanation:

Since cubes have the same side lengths all around, to find the volume, you need to have one side length and cube it.

Cube 1 : 24³ = 24 x 24 x 24 = 13 824 in³

Cube 2 : 12³ = 12 x 12 x 12 = 1 728 in³

Now, to find the total, just add the volumes.

13 824 + 1 728 = 15 552 in³

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Given the function f(x) = 5^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average r
Masteriza [31]
Part A)

f(x) = 5^x
f(0) = 5^0
f(0) = 1
----------
f(x) = 5^x
f(1) = 5^1
f(1) = 5
----------
f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
----------
f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125

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

Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4

Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100

================================================

Part B)

From part A) above, we found,

Rate of change for section A = 4
Rate of change for section B = 100

Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)

Answer for part B: 25

================================================

Extra:  Explain why one rate of change is greater than the other.

The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed. 

6 0
3 years ago
The volume of this cone is 602.88 cubic inches. What is the radius of this cone?
choli [55]

Answer:

8

Step-by-step explanation:

Volume of a cone formula: V = \pi r^{2} \frac{h}{3}

where,

h is the height             <u>9 in  (assuming)</u>

r is the radius              <u>want</u>

v is the volume           <u> 602.88 cubic inches</u>

\pi is                              <u>a = 3.14 </u>

Plug in everything:

602.88 = 3.14r^{2} (\frac{9}{3} )\\602.88 = 3.14r^{2} (3)\\1808.64 = 28.26r^{2}\\\frac{1808.64}{28.26} = \frac{28.26r^{2}}{28.26} \\r^{2} = 64\\r = \sqrt{64} \\r = 8\\or\\r =-8

8 0
3 years ago
A regulat pentagon has side lenghts of 5.8cm and apothem of 4cm. calculate its perimeter and area​
Kryger [21]

PENTA = 5.

a regular polygon has all equal sides, so if one side is 5.8, all are, so the perimeter for this pentagon with 5 sides is 5.8 + 5.8 + 5.8 + 5.8 + 5.8 = 29.

\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} p=perimeter\\ a=apothem\\ \cline{1-1} p=29\\ a=4 \end{cases}\implies A=\cfrac{1}{2}(4)(29)\implies A=58

6 0
3 years ago
Please help me I don’t understand
Scilla [17]
I think 8. Plug in -4 for x. 1/2-4^2
Using pemdas -4^2 is 16 and 1/2•16 is 8. If there were parenthesis around 1/2x then 1/2•-4 would be -2 and -2^2 is 4 but since there aren’t parentheses then 8
3 0
3 years ago
What is the approximate side length of the square
Lady bird [3.3K]

Answer:

Option C. 4.2 units

Step-by-step explanation:

Diagonals of a square intersect each other at 90°.

Therefore, From the right angle triangle formed at the center will be,

(Length of square)² = 3² + 3² [By Pythagoras theorem}

Length of the square = \sqrt{9+9}=\sqrt{18}

                                   = 4.24 units

                                   ≈ 4.2 units

Option C is the answer.

5 0
3 years ago
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