Answer:
side of base, a = 10.1 inches, height, h = 40.1 inches
Step-by-step explanation:
Volume of rectangular solid, V = 4096 cubic inches
Let the side of base is a and the height is h.
![V = a^2h\\\\4096 = a^2 h ..... (1)](https://tex.z-dn.net/?f=V%20%3D%20a%5E2h%5C%5C%5C%5C4096%20%3D%20a%5E2%20h%20.....%20%281%29)
surface area of the solid
![S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches](https://tex.z-dn.net/?f=S%20%3D%202a%5E2%20%2B%204%20ah%20%5C%5C%5C%5CS%20%3D%202a%5E2%20%2B%204%20%5Ctimes%20a%20%5Ctimes%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%20%20%20%20from%20%281%29%5C%5C%5CS%20%3D%202a%5E2%20%2B%20%5Cfrac%7B4096%7D%7Ba%7D%5C%5C%5C%5C%5Cfrac%7BdS%7D%7Bda%7D%3D%204%20a%20-%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%5C%5C%5C%5C4%20a%20-%20%5Cfrac%7B4096%7D%7Ba%5E2%7D%20%3D%200%20%5C%5C%5C%5Ca%5E3%20%3D%201024%5C%5C%5C%5Ca%20%3D10.1%20inches)
So, h = 40.2 inches
Answer:
Pattern B
<h3>
Explain: </h3>
A quadratic relationship is characterized by constant second differences.
<em><u>Pattern A
</u></em>
Sequence: 0, 2, 4, 6
First Differences: 2, 2, 2 . . . . constant indicates a 1st-degree (linear, arithmetic) sequence
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<em><u>Pattern B</u></em>
Sequence: 1, 2, 5, 10
First Differences: 1, 3, 5
Second Differences: 2, 2 . . . . constant indicates a 2nd-degree (quadratic) sequence
__________________________________________________________
<em><u>Pattern C</u></em>
Sequence: 1, 3, 9, 27
First Differences: 2, 6, 18
Second Differences: 4, 12 . . . . each set of differences has a common ratio, indicating an exponential (geometric) sequence
__________________________________________________________
Pattern B shows a geometric relationship between step number and dot count.
Answer:
∠A = ∠D (**but very important Δ ABC has to be congruent to Δ DEF)
Step-by-step explanation:
It will help if you draw the triangles out and label the same sides. Then according to the side-angle-side (SAS) rule, ∠A should be equal to ∠D
The length of the garden is 4.3 m while the width is 4.3 m
Let x represent the length of the garden. Therefore:
The area of the garden = x × x = x²
The width of the walkaway is 1.8 m, hence the length of the garden and walkaway = x + 1.8. The width of the garden and walkaway = x + 1.8.
Hence the area of the garden and walkaway = (x + 1.8) × (x + 1.8) = x² + 3.6x + 3.24
The area of walkaway = (x² + 3.6x + 3.24) - x² = 3.6x + 3.24
Since the area of the walkway is equal to the area of the garden, hence:
3.6x + 3.24 = x²
x² -3.6x - 3.24 = 0
x= 4.34 m or -0.74 m
Since the length cannot be negative, hence x = 4.3 m
Therefore the garden is 4.3 m by 4.3 m
Find out more at: brainly.com/question/2077866
Answer:
1) 4 packs of balloons
2) He played 2 rounds
3) She would watch 56 minutes per day
4) She would have 54 apps left
5) 8 x (9+8) = 136
6) 2 1/4 x 3 1/4 = 117/16 OR 7 5/16
Step-by-step explanation:
Good Luck and I hope that you pass!!! :D