Answer:
V =41.41³
A = 94.41²
----
V =225.16³
SA =283.25²
----
V = 64³
SA =113.32²
----
V =433.33³
SA = 378.57²
Step-by-step explanation:
Picture 2 = a = 1/2 base = 3.5 x 3.5 = 12.25 b= 5 x 5 = 25
c²= a² + b² = 3.5² + 5²
c ²= √12.25 + √25
c ²= √ 37.5 = 6.12372435696
c ² = 6.1237 missing side
Picture 1 + 2 formula SA = bh + (s1 + s2 + s3)H
V = V= 1/2 b x h h x SA
Picture 3 + 4 formula SA= a²+ 2a a² / 4 + h² V= a² h/3
<u>Answer:</u>
The vertical axis should begin with 0 inches.
<u>Step-by-step explanation:</u>
The vertical axis must start with 0 inches to ensure accuracy for the measures of every plant since 28% of the plants in the garden are under 6 inches.
If the vertical axis begins with 6 inches or above, we can miss a lot of the gardener's data, especially the plants which are under 6 inches.
Therefore, to ensure that the graph does not mislead any measures of the plant, the vertical axis must begin with 0 inches.
Answer:
a) ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
b) therefore Basis of W is
={ ![{\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
}
Step-by-step explanation:
Given the data in the question;
W = { A| Air Skew symmetric matrix}
= {A | A = -A^T }
A ; O⁻ = -O⁻^T O⁻ : Zero mstrix
O⁻ ∈ W
now let A, B ∈ W
A = -A^T B = -B^T
(A+B)^T = A^T + B^T
= -A - B
- ( A + B )
⇒ A + B = -( A + B)^T
∴ A + B ∈ W.
∝ ∈ | R
(∝.A)^T = ∝A^T
= ∝( -A)
= -( ∝A)
(∝A) = -( ∝A)^T
∴ ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
A ∈ W
A = -AT
A = ![\left[\begin{array}{ccc}o&a&b\\-a&o&c\\-b&-c&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Do%26a%26b%5C%5C-a%26o%26c%5C%5C-b%26-c%260%5Cend%7Barray%7D%5Cright%5D)
= ![a\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=a%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![+b\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![+c\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bc%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
therefore Basis of W is
={ }
