$let \: f(x) = ax {}^{2} + bx + c \\ thus \: f(x) \: represents \: a \: parabola \: whose \: axis \: is \: parallel \: to \: the \: y \: axis \: and \: vertex \: is \: \frac{ - b}{2a} ,\frac{ - d}{4a} \\$

At the respective max and min values

8 0

3 years ago

Prove the following identity true. Show work.

yulyashka [42]

Answer:

The Pythagorean identity states that

$\sin^2 t + \cos^2 t = 1$

Using that we can rewrite the left denominator as:

$1 - \sin^2 t$

Which can be factored as

$(1 - \sin t)(1+ \sin t)$

The numerator we can expand as:

$(1 - \sin t)(1 - \sin t)$

On the right hand side, let's multply numerator and denominator with (1 - sin t):

The total formula then becomes:

$\dfrac{(1-\sin t)(1-\sin t)}{(1 - \sin t)(1 + \sin t)} = \dfrac{(1-\sin t)(1 - \sin t)}{(1+\sin t)(1 - \sin t)}$

There you go... left and right are equal.

3 0

3 years ago

Read 2 more answers

Write a problem that involves finding the unknown measure of a side of a rectangle include the solution?

tankabanditka [31]

Problem:
The area of the patio of a relative's house is 20 square meters.
The width of the patio is 2 meters.
What is the length of the patio?
Solution:
The area is:
A = (w) * (l)
Where,
w: width
l: long
Clearing l we have:
l = A / w
Substituting values:
l = 20/2
l = 10 meters

7 0

3 years ago