Answer:
See below
Step-by-step explanation:
x=a-2by^2 Subtract 'a' from both sides
x -a = - 2 by^2 divide both sides by - 2b
(a-x)/2b = y^2 sqrt both sides
y = +- sqrt ( (a-x)/2b))
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
#SPJ1
Answer:
(a) Circle Q is 9.4 units to the center of circle P
(b) Circle Q has a smaller radius
Step-by-step explanation:
Given
Solving (a): The distance between both
The equation of a circle is:
Where
P and Q can be rewritten as:
So, for P:
For Q:
The distance between them is:
Where:
---
---
So:
Solving (b): The radius;
In (a), we have:
--- circle P
--- circle Q
By comparison
<em>Hence, circle Q has a smaller radius</em>
According to your statement, it's expression would be:
9 + 2x
So, your correct answer is 9 + 2x
Hope it helped.
Answer:
We need to remember that the deviation is a measure od disperion and for this case is the deviation is larger then we have more spread out the distribution of interest. And largest deviation for this case is from the dataset C so then the answer would be:
D. Data set C
Step-by-step explanation:
For this case the standard deviation can be calculated with the following formula:
And for this case we have the deviations for each dataset are given by:
We need to remember that the deviation is a measure od disperion and for this case is the deviation is larger then we have more spread out the distribution of interest. And largest deviation for this case is from the dataset C so then the answer would be:
D. Data set C