State the Limits Rule and explain what it means

Mathematics

1 answer:

Evgen [1.6K]3 years ago

4 0

Answer:

The limit of a sum is equal to the sum of the limits.

Step-by-step explanation:

The limits of a constant times a function is equal to the constant times the limit of the function.

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The Butlers bought a $332,000 house. They made a down payment of 42,000 and took out a mortgage for the rest. Over the course of

Zarrin [17]

Answer:

Step-by-step explanation:

(a)Mortgage = 332000 - 42000 = 290000

15 * 12 = 180 months

Total monthly payments = 180 * 2447.19 =440494.2

Total = 440494.2 + 42000 = 482494.2

(b) Interest = 482494.2 -290000

= 192494.2

4 0

3 years ago

Read 2 more answers

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .