2 years ago

Identify the intervals on which the function x^2 -2x -48 is positive

Mathematics

1 answer:

lions [1.4K]2 years ago

7 0

Step-by-step explanation:

x² - 2x - 48

= (x - 8)(x + 6)

Coefficient of x² is positive, => Happy shape curved upwards

Hence x < -6 or x > 8.

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Zielflug [23.3K]

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2 years ago

Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

1 year ago

A cylinder has a height of 14 centimeters and a radius of 17 centimeters. What is its volume? Use ≈ 3.14 and round your answer

9966 [12]

<h2><u>Answer</u></h2>

Volume = $\sf{\pi r^2 h}$