What is a factor of 12
1 answer:
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Answer:
The first derivative of is
.
Step-by-step explanation:
Let . we can determine its first derivative by Rule for the Square Root Function, Rule for Power Function, Rule of Chain and Rule for the Addition of Functions, Rule for the Subtraction of Functions, Rule for the Division of Functions:
The first derivative of is
.
Using logarithmic laws: log(a) + log(b) = log(ab)
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
log₄ (x + 9) + log₄ (x + 21) = log₄ [(x + 9)(x + 21)] = 3
Since we want the equation in terms of x, the next intuitive step is take 4 to the power of both sides, because the left hand side will simplify easily.
Solving the quadratic we get:
BUT, for the logarithmic equation to be defined, x > -9, so x≠ -25
Thus, the only solution is x = -5.
Answer:
1. AC = 5 cm
2. CD = 10.7 cm
Step-by-step explanation:
Looking at the left triangle, we see that AC is the side "opposite" of the angle given and AB is the "hypotenuse".
Which trigonometric ratio relates "opposite" to "hypotenuse"?
<em>Yes, that's SINE.</em>
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So we can write:
We know from 30-60-90 triangle, Sin(30) = 0.5, so we have:
Thus,
AC = 5 cm
Now, looking at right side triangle, we know AC, side "opposite" and we want to find CD, side "adjacent". Which trig ratio relates these 2 sides?
<em>Yes, that's tan!</em>
Thus we can write:
Now using calculator, we get our answer to be:
CD =
So
CD = 10.7 cm