The piecewise function tells us specific rules he should execute based on the input x we put in. For example for answer A is true since we use the top function f(x) = -x + 1 since the input is -1 which is less than 0 (x < 0). We check to make sure the equation comes out true:
f(-1) = -(-1) + 1
f(-1) = 2 ✓
B. <span>The independent variable is the amount of sugar dissolved, and the dependent variable is the temperature of the water. Hope this helps. </span>
Answer:
CHEEEEEEEEESE
Step-by-step explanation:
Answer:
Part A:
Blueprint 10 inches ⇒ Actual 35 feet
Blueprint 20 inches ⇒ Actual 70 feet
Part B:
The cost of the cover is $857.5
Step-by-step explanation:
Part A:
∵ The drawing scale is 2 inches for 7 feet
∵ The length = 20 inches and the width = 10 inches
∴ The actual length = (20 × 7) ÷ 2 = 70 feet
∴ The actual width = (10 × 7) ÷ 2 = 35 feet
Part B:
∵ The cost per square foot = $0.35
∵ The area of the pool = 70 × 35 = 2450 feet ²
∴ The cost of the cover = 2450 × 0.35 = $857.5
]Eigenvectors are found by the equation
implying that
. We then can write:
![A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]](https://tex.z-dn.net/?f=%20A-%5Clambda%20I%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204-%5Clambda%20%26%202%20%5C%5C%205%20%26%201-%5Clambda%20%5Cend%7Barray%7D%5Cright%20%5D%20)
And:
Gives us the characteristic polynomial:
So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line
We can see then that 3 is the answer.
